-------------
      name:  <unnamed>
       log:  C:\Users\schamk\No Backup and Personal\Dropbox\StataLasso\Current\cs_ivlasso.smcl
  log type:  smcl
 opened on:  12 Sep 2018, 21:41:29
r; t=0.01 21:41:29

. about

Stata/SE 14.2 for Windows (64-bit x86-64)
Revision 29 Jan 2018
Copyright 1985-2015 StataCorp LLC

Total physical memory:     4072380 KB
Available physical memory: 1149192 KB

Single-user Stata perpetual license:
       Serial number:  401406247588
         Licensed to:  Mark Schaffer
                       Heriot-Watt University
r; t=0.00 21:41:29

. which pdslasso
.\pdslasso.ado
*! pdslasso 1.0.03 04sept2018
*! authors aa/cbh/ms
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. which ivlasso
.\ivlasso.ado
*! ivlasso 1.0.08 27aug2018
*! authors aa/cbh/ms
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. which rlasso
.\rlasso.ado
*! rlasso 1.0.07 29aug2018
*! authors aa/cbh/ms
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. which lassoutils
.\lassoutils.ado
*! lassoutils 1.0.14 5sep2018
*! authors aa/cbh/ms
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.
.
. // ***************** LEVITT DATASET ************************* //
.
. // Based on BCH JEP replication do file.
. // Differences:
. //   changed locals to globals (easier to check contents)
. //   fixed typo in constructing initial differences
. //   all generated vars are doubles
. //   instead of dropping if trend==0, added "if trend>0" to original commands
. //   use tweaked lassoShootingCBH instead of original lassoShooting
. //   because of different varnames (FVs vs created by hand), coef vectors
. //     are sorted before comparing
.
. insheet using Data\levitt_ex.dat, clear
(17 vars, 1,734 obs)
r; t=0.11 21:41:29

.
. * Drop DC, Alaska, and Hawaii
. *drop if statenum == 9 | statenum == 2 | statenum == 12
. * Drop DC
. drop if statenum == 9
(34 observations deleted)
r; t=0.00 21:41:29

.
. * Drop years not used
. drop if year < 85 | year > 97
(1,050 observations deleted)
r; t=0.00 21:41:29

.
. * Normalized trend variable
. qui gen double trend = (year - 85)/12
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.
. // added
. qui gen double trendsq=trend^2
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.
. tsset statenum year
       panel variable:  statenum (strongly balanced)
        time variable:   year, 85 to 97
                delta:  1 unit
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.
. xi i.year
i.year            _Iyear_85-97        (naturally coded; _Iyear_85 omitted)
r; t=0.48 21:41:29

.
. * Generate variables for LASSO
. replace xxincome = xxincome/100
(650 real changes made)
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. replace xxpover = xxpover/100
(650 real changes made)
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. replace xxafdc15 = xxafdc15/10000
(650 real changes made)
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. replace xxbeer = xxbeer/100
(650 real changes made)
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.
. global tdums    _Iyear_87 _Iyear_88 _Iyear_89 _Iyear_90 _Iyear_91 _Iyear_92 _Iyear_93 _Iyear_94 _Iyear_95 _Iyear_96 _Iyear_97
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. global xx               xxprison xxpolice xxunemp xxincome xxpover xxafdc15 xxgunlaw xxbeer
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.
. // Time dummies
. sum $tdums

    Variable |        Obs        Mean    Std. Dev.       Min        Max
-------------+---------------------------------------------------------
   _Iyear_87 |        650    .0769231    .2666746          0          1
   _Iyear_88 |        650    .0769231    .2666746          0          1
   _Iyear_89 |        650    .0769231    .2666746          0          1
   _Iyear_90 |        650    .0769231    .2666746          0          1
   _Iyear_91 |        650    .0769231    .2666746          0          1
-------------+---------------------------------------------------------
   _Iyear_92 |        650    .0769231    .2666746          0          1
   _Iyear_93 |        650    .0769231    .2666746          0          1
   _Iyear_94 |        650    .0769231    .2666746          0          1
   _Iyear_95 |        650    .0769231    .2666746          0          1
   _Iyear_96 |        650    .0769231    .2666746          0          1
-------------+---------------------------------------------------------
   _Iyear_97 |        650    .0769231    .2666746          0          1
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. sum i.year

    Variable |        Obs        Mean    Std. Dev.       Min        Max
-------------+---------------------------------------------------------
        year |
         86  |        650    .0769231    .2666746          0          1
         87  |        650    .0769231    .2666746          0          1
         88  |        650    .0769231    .2666746          0          1
         89  |        650    .0769231    .2666746          0          1
-------------+---------------------------------------------------------
         90  |        650    .0769231    .2666746          0          1
         91  |        650    .0769231    .2666746          0          1
         92  |        650    .0769231    .2666746          0          1
         93  |        650    .0769231    .2666746          0          1
         94  |        650    .0769231    .2666746          0          1
-------------+---------------------------------------------------------
         95  |        650    .0769231    .2666746          0          1
         96  |        650    .0769231    .2666746          0          1
         97  |        650    .0769231    .2666746          0          1
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.
. * Differences
. global Dxx
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. foreach x of global xx {
  2.         qui gen double D`x' = D.`x'
  3.         local tempname = "D`x'"
  4.         global Dxx : list global(Dxx) | tempname
  5. }
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.
. sum $Dxx

    Variable |        Obs        Mean    Std. Dev.       Min        Max
-------------+---------------------------------------------------------
   Dxxprison |        600    .0649119    .0676885  -.1984695   .5325034
   Dxxpolice |        600    .0131697     .061486   -.274835   .4509063
    Dxxunemp |        600   -.0019904    .0084619    -.02975     .03017
   Dxxincome |        600    .0001556    .0002243  -.0009784    .000984
    Dxxpover |        600    -.001095    .0195652      -.069       .061
-------------+---------------------------------------------------------
   Dxxafdc15 |        600   -.0220477    .0528339  -.3080261    .345165
   Dxxgunlaw |        600    .0366667    .1880989          0          1
     Dxxbeer |        600   -.0011667    .0118118      -.208       .089
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. sum D.($xx)

    Variable |        Obs        Mean    Std. Dev.       Min        Max
-------------+---------------------------------------------------------
    xxprison |
         D1. |        600    .0649119    .0676885  -.1984695   .5325034
             |
    xxpolice |
         D1. |        600    .0131697     .061486   -.274835   .4509063
             |
     xxunemp |
         D1. |        600   -.0019904    .0084619    -.02975     .03017
             |
    xxincome |
         D1. |        600    .0001556    .0002243  -.0009784    .000984
             |
     xxpover |
         D1. |        600    -.001095    .0195652      -.069       .061
-------------+---------------------------------------------------------
             |
    xxafdc15 |
         D1. |        600   -.0220477    .0528339  -.3080261    .345165
             |
    xxgunlaw |
         D1. |        600    .0366667    .1880989          0          1
             |
      xxbeer |
         D1. |        600   -.0011667    .0118118      -.208       .089
r; t=0.00 21:41:29

.
. * Squared Differences
. global Dxx2
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. foreach x of global Dxx {
  2.         qui gen double `x'2 = `x'^2
  3.         local tempname = "`x'2"
  4.         global Dxx2 : list global(Dxx2) | tempname
  5. }
r; t=0.00 21:41:29

.
. * Difference Interactions
. global DxxInt
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. local nxx : word count $Dxx
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. forvalues ii = 1/`nxx' {
  2.         local start = `ii'+1
  3.         forvalues jj = `start'/`nxx' {
  4.                 local temp1 : word `ii' of $Dxx
  5.                 local temp2 : word `jj' of $Dxx
  6.                 qui gen double `temp1'X`temp2' = `temp1'*`temp2'
  7.                 local tempname = "`temp1'X`temp2'"
  8.                 global DxxInt : list global(DxxInt) | tempname
  9.         }
 10. }
r; t=0.00 21:41:29

.
. * Lags
. global Lxx
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. foreach x of global xx {
  2.         qui gen double L`x' = L.`x'
  3.         local tempname = "L`x'"
  4.         global Lxx : list global(Lxx) | tempname
  5. }
r; t=0.00 21:41:29

.
. * Squared Lags
. global Lxx2
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. foreach x of global Lxx {
  2.         qui gen double `x'2 = `x'^2
  3.         local tempname = "`x'2"
  4.         global Lxx2 : list global(Lxx2) | tempname
  5. }
r; t=0.00 21:41:29

.
. * Means
. global Mxx
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. foreach x of global xx {
  2.         qui by statenum: egen double M`x' = mean(`x')
  3.         local tempname = "M`x'"
  4.         global Mxx : list global(Mxx) | tempname
  5. }
r; t=0.13 21:41:29

.
. * Squared Means
. global Mxx2
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. foreach x of global Mxx {
  2.         qui gen double `x'2 = `x'^2
  3.         local tempname = "`x'2"
  4.         global Mxx2 : list global(Mxx2) | tempname
  5. }
r; t=0.00 21:41:29

.
. * Initial Levels
. local xx0
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. foreach x of global xx {
  2.         qui by statenum: gen double `x'0 = `x'[1]
  3.         local tempname = "`x'0"
  4.         global xx0 : list global(xx0) | tempname
  5. }
r; t=0.00 21:41:29

.
. * Squared Initial Levels
. global xx02
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. foreach x of global xx0 {
  2.         qui gen double `x'2 = `x'^2
  3.         local tempname = "`x'2"
  4.         global xx02 : list global(xx02) | tempname
  5. }
r; t=0.00 21:41:29

.
. * Initial Differences
. global Dxx0
r; t=0.00 21:41:29

. foreach x of global Dxx {
  2.         qui by statenum: gen double `x'0 = `x'[2]
  3.         local tempname = "`x'0"
  4. // typo in original code?
. //      local xx0 : list local xx0 | tempname
.         global Dxx0 : list global(Dxx0) | tempname
  5. }
r; t=0.01 21:41:30

.
. * Squared Initial Differences
. global Dxx02
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. foreach x of global Dxx0 {
  2.         qui gen double `x'2 = `x'^2
  3.         local tempname = "`x'2"
  4.         global Dxx02 : list global(Dxx02) | tempname
  5. }
r; t=0.03 21:41:30

.
. * Interactions with trends
. global biglist : list global(Dxx) | global(Dxx2)
r; t=0.00 21:41:30

. global biglist : list global(biglist) | global(DxxInt)
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. global biglist : list global(biglist) | global(Lxx)
r; t=0.00 21:41:30

. global biglist : list global(biglist) | global(Lxx2)
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. global biglist : list global(biglist) | global(Mxx)
r; t=0.00 21:41:30

. global biglist : list global(biglist) | global(Mxx2)
r; t=0.00 21:41:30

. global biglist : list global(biglist) | global(xx0)
r; t=0.00 21:41:30

. global biglist : list global(biglist) | global(xx02)
r; t=0.00 21:41:30

. global biglist : list global(biglist) | global(Dxx0)
r; t=0.00 21:41:30

. global biglist : list global(biglist) | global(Dxx02)
r; t=0.00 21:41:30

.
. global IntT
r; t=0.00 21:41:30

. local nxx : word count $biglist
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. foreach x of global biglist {
  2.         qui gen double `x'Xt = `x'*trend
  3.         qui gen double `x'Xt2 = `x'*(trend^2)
  4.         local tempname = "`x'Xt `x'Xt2"
  5.         global IntT : list global(IntT) | tempname
  6. }
r; t=0.03 21:41:30

.
. global shared : list global(biglist) | global(IntT)
r; t=0.01 21:41:30

.
. * Violence specific controls
. qui gen double Dviol = D.efaviol
r; t=0.00 21:41:30

. qui by statenum: gen double viol0 = efaviol[1]
r; t=0.00 21:41:30

. qui by statenum: gen double Dviol0 = Dviol[2]
r; t=0.00 21:41:30

. qui gen double viol02 = viol0^2
r; t=0.00 21:41:30

. qui gen double Dviol02 = Dviol0^2
r; t=0.00 21:41:30

. qui gen double viol0Xt = viol0*trend
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. qui gen double viol0Xt2 = viol0*(trend^2)
r; t=0.00 21:41:30

. qui gen double viol02Xt = viol02*trend
r; t=0.00 21:41:30

. qui gen double viol02Xt2 = viol02*(trend^2)
r; t=0.00 21:41:30

. qui gen double Dviol0Xt = Dviol0*trend
r; t=0.00 21:41:30

. qui gen double Dviol0Xt2 = Dviol0*(trend^2)
r; t=0.00 21:41:30

. qui gen double Dviol02Xt = Dviol02*trend
r; t=0.00 21:41:30

. qui gen double Dviol02Xt2 = Dviol02*(trend^2)
r; t=0.00 21:41:30

.
. global contviol         viol0 viol0Xt viol0Xt2 viol02 viol02Xt viol02Xt2 Dviol0 Dviol0Xt Dviol0Xt2 Dviol02 Dviol02Xt Dviol02Xt2
r; t=0.00 21:41:30

.
. global AllViol : list global(contviol) | global(shared)
r; t=0.00 21:41:30

.
. * Property specifc controls
. qui gen double Dprop = D.efaprop
r; t=0.00 21:41:30

. qui by statenum: gen double prop0 = efaprop[1]
r; t=0.00 21:41:30

. qui by statenum: gen double Dprop0 = Dprop[2]
r; t=0.00 21:41:30

. qui gen double prop02 = prop0^2
r; t=0.00 21:41:30

. qui gen double Dprop02 = Dprop0^2
r; t=0.00 21:41:30

. qui gen double prop0Xt = prop0*trend
r; t=0.00 21:41:30

. qui gen double prop0Xt2 = prop0*(trend^2)
r; t=0.00 21:41:30

. qui gen double prop02Xt = prop02*trend
r; t=0.00 21:41:30

. qui gen double prop02Xt2 = prop02*(trend^2)
r; t=0.00 21:41:30

. qui gen double Dprop0Xt = Dprop0*trend
r; t=0.00 21:41:30

. qui gen double Dprop0Xt2 = Dprop0*(trend^2)
r; t=0.00 21:41:30

. qui gen double Dprop02Xt = Dprop02*trend
r; t=0.00 21:41:30

. qui gen double Dprop02Xt2 = Dprop02*(trend^2)
r; t=0.00 21:41:30

.
. global contprop         prop0 prop0Xt prop0Xt2 prop02 prop02Xt prop02Xt2 Dprop0 Dprop0Xt Dprop0Xt2 Dprop02 Dprop02Xt Dprop02Xt2
r; t=0.00 21:41:30

.
. global AllProp : list global(contprop) | global(shared)
r; t=0.00 21:41:30

.
. * Murder specific controls
. qui gen double Dmurd = D.efamurd
r; t=0.00 21:41:30

. qui by statenum: gen double murd0 = efamurd[1]
r; t=0.00 21:41:30

. qui by statenum: gen double Dmurd0 = Dmurd[2]
r; t=0.00 21:41:30

. qui gen double murd02 = murd0^2
r; t=0.00 21:41:30

. qui gen double Dmurd02 = Dmurd0^2
r; t=0.00 21:41:30

. qui gen double murd0Xt = murd0*trend
r; t=0.00 21:41:30

. qui gen double murd0Xt2 = murd0*(trend^2)
r; t=0.00 21:41:30

. qui gen double murd02Xt = murd02*trend
r; t=0.00 21:41:30

. qui gen double murd02Xt2 = murd02*(trend^2)
r; t=0.00 21:41:30

. qui gen double Dmurd0Xt = Dmurd0*trend
r; t=0.00 21:41:30

. qui gen double Dmurd0Xt2 = Dmurd0*(trend^2)
r; t=0.00 21:41:30

. qui gen double Dmurd02Xt = Dmurd02*trend
r; t=0.00 21:41:30

. qui gen double Dmurd02Xt2 = Dmurd02*(trend^2)
r; t=0.00 21:41:30

.
. global contmurd         murd0 murd0Xt murd0Xt2 murd02 murd02Xt murd02Xt2 Dmurd0 Dmurd0Xt Dmurd0Xt2 Dmurd02 Dmurd02Xt Dmurd02Xt2
r; t=0.00 21:41:30

.
. global AllMurd : list global(contmurd) | global(shared)
r; t=0.00 21:41:30

.
. * Differenced outcomes
. qui gen double Dyviol = D.lpc_viol
r; t=0.00 21:41:30

. qui gen double Dyprop = D.lpc_prop
r; t=0.00 21:41:30

. qui gen double Dymurd = D.lpc_murd
r; t=0.00 21:41:30

.
. // replaced with "if trend>0" below
. // drop if trend == 0
.
. *********************** Violence ************************************
.
. * Variable selection
.
. * Violence Outcome
. rlasso D.lpc_viol                                                                                                       ///
>                                                                                                                                         /// no trend
>                 c.viol0##c.viol0                                                                                        ///
>                 c.Dviol0##c.Dviol0                                                                                      ///
>                 c.(D.($xx))##c.(D.($xx))                                                                        /// note macro
>                 c.(L.xxprison)##c.(L.xxprison)                                                          ///
>                 c.(L.xxpolice)##c.(L.xxpolice)                                                          ///
>                 c.(L.xxunemp)##c.(L.xxunemp)                                                            ///
>                 c.(L.xxincome)##c.(L.xxincome)                                                          ///
>                 c.(L.xxpover)##c.(L.xxpover)                                                            ///
>                 c.(L.xxafdc15)##c.(L.xxafdc15)                                                          ///
>                 c.(L.xxgunlaw)##c.(L.xxgunlaw)                                                          ///
>                 c.(L.xxbeer)##c.(L.xxbeer)                                                                      ///
>                 c.Mxxprison##c.Mxxprison                                                                        ///
>                 c.Mxxpolice##c.Mxxpolice                                                                        ///
>                 c.Mxxunemp##c.Mxxunemp                                                                          ///
>                 c.Mxxincome##c.Mxxincome                                                                        ///
>                 c.Mxxpover##c.Mxxpover                                                                          ///
>                 c.Mxxafdc15##c.Mxxafdc15                                                                        ///
>                 c.Mxxgunlaw##c.Mxxgunlaw                                                                        ///
>                 c.Mxxbeer##c.Mxxbeer                                                                            ///
>                 c.xxprison0##c.xxprison0                                                                        ///
>                 c.xxpolice0##c.xxpolice0                                                                        ///
>                 c.xxunemp0##c.xxunemp0                                                                          ///
>                 c.xxincome0##c.xxincome0                                                                        ///
>                 c.xxpover0##c.xxpover0                                                                          ///
>                 c.xxafdc150##c.xxafdc150                                                                        ///
>                 c.xxgunlaw0##c.xxgunlaw0                                                                        ///
>                 c.xxbeer0##c.xxbeer0                                                                            ///
>                 c.Dxxprison0##c.Dxxprison0                                                                      ///
>                 c.Dxxpolice0##c.Dxxpolice0                                                                      ///
>                 c.Dxxunemp0##c.Dxxunemp0                                                                        ///
>                 c.Dxxincome0##c.Dxxincome0                                                                      ///
>                 c.Dxxpover0##c.Dxxpover0                                                                        ///
>                 c.Dxxafdc150##c.Dxxafdc150                                                                      ///
>                 c.Dxxgunlaw0##c.Dxxgunlaw0                                                                      ///
>                 c.Dxxbeer0##c.Dxxbeer0                                                                          ///
>                                                                                                                                         ///
>                 (c.viol0##c.viol0)#(c.trend##c.trend)                                           /// now interacted with trend
>                 (c.Dviol0##c.Dviol0)#(c.trend##c.trend)                                         ///
>                 (c.(D.($xx))##c.(D.($xx)))#(c.trend##c.trend)                           /// note macro
>                 (c.(L.xxprison)##c.(L.xxprison))#(c.trend##c.trend)                     ///
>                 (c.(L.xxpolice)##c.(L.xxpolice))#(c.trend##c.trend)                     ///
>                 (c.(L.xxunemp)##c.(L.xxunemp))#(c.trend##c.trend)                       ///
>                 (c.(L.xxincome)##c.(L.xxincome))#(c.trend##c.trend)                     ///
>                 (c.(L.xxpover)##c.(L.xxpover))#(c.trend##c.trend)                       ///
>                 (c.(L.xxafdc15)##c.(L.xxafdc15))#(c.trend##c.trend)                     ///
>                 (c.(L.xxgunlaw)##c.(L.xxgunlaw))#(c.trend##c.trend)                     ///
>                 (c.(L.xxbeer)##c.(L.xxbeer))#(c.trend##c.trend)                         ///
>                 (c.Mxxprison##c.Mxxprison)#(c.trend##c.trend)                           ///
>                 (c.Mxxpolice##c.Mxxpolice)#(c.trend##c.trend)                           ///
>                 (c.Mxxunemp##c.Mxxunemp )#(c.trend##c.trend)                            ///
>                 (c.Mxxincome##c.Mxxincome)#(c.trend##c.trend)                           ///
>                 (c.Mxxpover##c.Mxxpover )#(c.trend##c.trend)                            ///
>                 (c.Mxxafdc15##c.Mxxafdc15)#(c.trend##c.trend)                           ///
>                 (c.Mxxgunlaw##c.Mxxgunlaw)#(c.trend##c.trend)                           ///
>                 (c.Mxxbeer##c.Mxxbeer)#(c.trend##c.trend)                                       ///
>                 (c.xxprison0##c.xxprison0)#(c.trend##c.trend)                           ///
>                 (c.xxpolice0##c.xxpolice0)#(c.trend##c.trend)                           ///
>                 (c.xxunemp0##c.xxunemp0)#(c.trend##c.trend)                                     ///
>                 (c.xxincome0##c.xxincome0)#(c.trend##c.trend)                           ///
>                 (c.xxpover0##c.xxpover0)#(c.trend##c.trend)                                     ///
>                 (c.xxafdc150##c.xxafdc150)#(c.trend##c.trend)                           ///
>                 (c.xxgunlaw0##c.xxgunlaw0)#(c.trend##c.trend)                           ///
>                 (c.xxbeer0##c.xxbeer0)#(c.trend##c.trend)                                       ///
>                 (c.Dxxprison0##c.Dxxprison0)#(c.trend##c.trend)                         ///
>                 (c.Dxxpolice0##c.Dxxpolice0)#(c.trend##c.trend)                         ///
>                 (c.Dxxunemp0##c.Dxxunemp0)#(c.trend##c.trend)                           ///
>                 (c.Dxxincome0##c.Dxxincome0)#(c.trend##c.trend)                         ///
>                 (c.Dxxpover0##c.Dxxpover0)#(c.trend##c.trend)                           ///
>                 (c.Dxxafdc150##c.Dxxafdc150)#(c.trend##c.trend)                         ///
>                 (c.Dxxgunlaw0##c.Dxxgunlaw0)#(c.trend##c.trend)                         ///
>                 (c.Dxxbeer0##c.Dxxbeer0 )#(c.trend##c.trend)                            ///
>                 i.year, partial(i.year) robust lalt corrnum(0) maxupsiter(100)

------------------+--------------------------------
         Selected |           Lasso   Post-est OLS
------------------+--------------------------------
------------------+--------------------------------
   Partialled-out*|
------------------+--------------------------------
             year |
              86  |       (omitted)      (omitted)
              87  |      -0.0826862     -0.0826862
              88  |      -0.0194795     -0.0194795
              89  |      -0.0224281     -0.0224281
              90  |       0.0300247      0.0300247
              91  |      -0.0196531     -0.0196531
              92  |      -0.0419442     -0.0419442
              93  |      -0.0515528     -0.0515528
              94  |      -0.0767805     -0.0767805
              95  |      -0.0734506     -0.0734506
              96  |      -0.1209961     -0.1209961
              97  |      -0.0768959     -0.0768959
                  |
            _cons |       0.0578956      0.0578956
------------------+--------------------------------
r; t=2.48 21:41:32

. di "p=" e(p)
p=336
r; t=0.00 21:41:32

. global yvSelrlasso `e(selected)'
r; t=0.00 21:41:32

. di "$yvSelrlasso"

r; t=0.00 21:41:32

. mat b_rlasso=e(b)
r; t=0.00 21:41:32

. if `e(s)' {
.         mat b_rlasso=b_rlasso[1,1..`e(s)']
r; t=0.00 21:41:32
. }
r; t=0.00 21:41:32

. else {
.         mat b_rlasso=.
r; t=0.00 21:41:32
. }
r; t=0.00 21:41:32

.
. /*
> * Violence Outcome
> lassoShootingCBH Dyviol $AllViol if trend>0, controls($tdums) lasiter(100) verbose(0) fdisplay(1)
> // no vars selected
> di "p=" r(p)
> global yvSel `r(selected)'
> di "$yvSel"
> mat b_cbh=r(betaL)
> mat b_cbh=b_cbh'
> */
. global yvSel
r; t=0.00 21:41:32

. mat b_cbh=.
r; t=0.00 21:41:32

.
. // sort cols and compare
. mata: st_matrix("b_rlasso",sort(st_matrix("b_rlasso")',1)')
r; t=0.01 21:41:32

. mata: st_matrix("b_cbh",sort(st_matrix("b_cbh")',1)')
r; t=0.00 21:41:32

. assert mreldif(b_rlasso,b_cbh)<1e-4
r; t=0.00 21:41:32

.
. * Violence Abortion
. rlasso D.efaviol                                                                                                        ///
>                                                                                                                                         /// no trend
>                 c.viol0##c.viol0                                                                                        ///
>                 c.Dviol0##c.Dviol0                                                                                      ///
>                 c.(D.($xx))##c.(D.($xx))                                                                        /// note macro
>                 c.(L.xxprison)##c.(L.xxprison)                                                          ///
>                 c.(L.xxpolice)##c.(L.xxpolice)                                                          ///
>                 c.(L.xxunemp)##c.(L.xxunemp)                                                            ///
>                 c.(L.xxincome)##c.(L.xxincome)                                                          ///
>                 c.(L.xxpover)##c.(L.xxpover)                                                            ///
>                 c.(L.xxafdc15)##c.(L.xxafdc15)                                                          ///
>                 c.(L.xxgunlaw)##c.(L.xxgunlaw)                                                          ///
>                 c.(L.xxbeer)##c.(L.xxbeer)                                                                      ///
>                 c.Mxxprison##c.Mxxprison                                                                        ///
>                 c.Mxxpolice##c.Mxxpolice                                                                        ///
>                 c.Mxxunemp##c.Mxxunemp                                                                          ///
>                 c.Mxxincome##c.Mxxincome                                                                        ///
>                 c.Mxxpover##c.Mxxpover                                                                          ///
>                 c.Mxxafdc15##c.Mxxafdc15                                                                        ///
>                 c.Mxxgunlaw##c.Mxxgunlaw                                                                        ///
>                 c.Mxxbeer##c.Mxxbeer                                                                            ///
>                 c.xxprison0##c.xxprison0                                                                        ///
>                 c.xxpolice0##c.xxpolice0                                                                        ///
>                 c.xxunemp0##c.xxunemp0                                                                          ///
>                 c.xxincome0##c.xxincome0                                                                        ///
>                 c.xxpover0##c.xxpover0                                                                          ///
>                 c.xxafdc150##c.xxafdc150                                                                        ///
>                 c.xxgunlaw0##c.xxgunlaw0                                                                        ///
>                 c.xxbeer0##c.xxbeer0                                                                            ///
>                 c.Dxxprison0##c.Dxxprison0                                                                      ///
>                 c.Dxxpolice0##c.Dxxpolice0                                                                      ///
>                 c.Dxxunemp0##c.Dxxunemp0                                                                        ///
>                 c.Dxxincome0##c.Dxxincome0                                                                      ///
>                 c.Dxxpover0##c.Dxxpover0                                                                        ///
>                 c.Dxxafdc150##c.Dxxafdc150                                                                      ///
>                 c.Dxxgunlaw0##c.Dxxgunlaw0                                                                      ///
>                 c.Dxxbeer0##c.Dxxbeer0                                                                          ///
>                                                                                                                                         ///
>                 (c.viol0##c.viol0)#(c.trend##c.trend)                                           /// now interacted with trend
>                 (c.Dviol0##c.Dviol0)#(c.trend##c.trend)                                         ///
>                 (c.(D.($xx))##c.(D.($xx)))#(c.trend##c.trend)                           /// note macro
>                 (c.(L.xxprison)##c.(L.xxprison))#(c.trend##c.trend)                     ///
>                 (c.(L.xxpolice)##c.(L.xxpolice))#(c.trend##c.trend)                     ///
>                 (c.(L.xxunemp)##c.(L.xxunemp))#(c.trend##c.trend)                       ///
>                 (c.(L.xxincome)##c.(L.xxincome))#(c.trend##c.trend)                     ///
>                 (c.(L.xxpover)##c.(L.xxpover))#(c.trend##c.trend)                       ///
>                 (c.(L.xxafdc15)##c.(L.xxafdc15))#(c.trend##c.trend)                     ///
>                 (c.(L.xxgunlaw)##c.(L.xxgunlaw))#(c.trend##c.trend)                     ///
>                 (c.(L.xxbeer)##c.(L.xxbeer))#(c.trend##c.trend)                         ///
>                 (c.Mxxprison##c.Mxxprison)#(c.trend##c.trend)                           ///
>                 (c.Mxxpolice##c.Mxxpolice)#(c.trend##c.trend)                           ///
>                 (c.Mxxunemp##c.Mxxunemp )#(c.trend##c.trend)                            ///
>                 (c.Mxxincome##c.Mxxincome)#(c.trend##c.trend)                           ///
>                 (c.Mxxpover##c.Mxxpover )#(c.trend##c.trend)                            ///
>                 (c.Mxxafdc15##c.Mxxafdc15)#(c.trend##c.trend)                           ///
>                 (c.Mxxgunlaw##c.Mxxgunlaw)#(c.trend##c.trend)                           ///
>                 (c.Mxxbeer##c.Mxxbeer)#(c.trend##c.trend)                                       ///
>                 (c.xxprison0##c.xxprison0)#(c.trend##c.trend)                           ///
>                 (c.xxpolice0##c.xxpolice0)#(c.trend##c.trend)                           ///
>                 (c.xxunemp0##c.xxunemp0)#(c.trend##c.trend)                                     ///
>                 (c.xxincome0##c.xxincome0)#(c.trend##c.trend)                           ///
>                 (c.xxpover0##c.xxpover0)#(c.trend##c.trend)                                     ///
>                 (c.xxafdc150##c.xxafdc150)#(c.trend##c.trend)                           ///
>                 (c.xxgunlaw0##c.xxgunlaw0)#(c.trend##c.trend)                           ///
>                 (c.xxbeer0##c.xxbeer0)#(c.trend##c.trend)                                       ///
>                 (c.Dxxprison0##c.Dxxprison0)#(c.trend##c.trend)                         ///
>                 (c.Dxxpolice0##c.Dxxpolice0)#(c.trend##c.trend)                         ///
>                 (c.Dxxunemp0##c.Dxxunemp0)#(c.trend##c.trend)                           ///
>                 (c.Dxxincome0##c.Dxxincome0)#(c.trend##c.trend)                         ///
>                 (c.Dxxpover0##c.Dxxpover0)#(c.trend##c.trend)                           ///
>                 (c.Dxxafdc150##c.Dxxafdc150)#(c.trend##c.trend)                         ///
>                 (c.Dxxgunlaw0##c.Dxxgunlaw0)#(c.trend##c.trend)                         ///
>                 (c.Dxxbeer0##c.Dxxbeer0 )#(c.trend##c.trend)                            ///
>                 i.year, partial(i.year) robust lalt corrnum(0) maxupsiter(100)

------------------+--------------------------------
         Selected |           Lasso   Post-est OLS
------------------+--------------------------------
            viol0 |       0.6584211      0.9131896
                  |
         xxprison |
              L1. |       0.0034611      0.0077216
                  |
         xxpolice |
              L1. |       0.0181368     -0.0221341
                  |
        Mxxincome |       3.5867320      2.5260909
       Dxxincome0 |       5.6965005    -13.9662267
                  |
      cL.xxpolice#|
          c.trend |       0.0043489      0.1113696
                  |
      c.Mxxincome#|
          c.trend |      23.9248253     23.1342596
                  |
     c.Dxxincome0#|
          c.trend |      30.4204612    103.2901389
                  |
       c.Dxxbeer0#|
          c.trend |       0.5716035      1.9696697
------------------+--------------------------------
   Partialled-out*|
------------------+--------------------------------
                  |
             year |
              86  |       (omitted)      (omitted)
              87  |      -0.1810657     -0.1847363
              88  |      -0.3702974     -0.3775118
              89  |      -0.5460017     -0.5571106
              90  |      -0.7243831     -0.7397676
              91  |      -0.9015995     -0.9216336
              92  |      -1.0878356     -1.1124079
              93  |      -1.2746326     -1.3040715
              94  |      -1.4655161     -1.4994041
              95  |      -1.6591865     -1.6983314
              96  |      -1.8588846     -1.9035423
              97  |      -2.0611131     -2.1120807
                  |
            _cons |      -0.5793466     -0.4436241
------------------+--------------------------------
r; t=2.03 21:41:34

. di "p=" e(p)
p=336
r; t=0.00 21:41:34

. global xvSelrlasso `e(selected)'
r; t=0.00 21:41:34

. di "$xvSelrlasso"
viol0 L.xxprison L.xxpolice Mxxincome Dxxincome0 cL.xxpolice#c.trend c.Mxxincome#c.trend c.Dxxincome0#c.trend c.Dxxbeer0#c.trend
r; t=0.00 21:41:34

. mat b_rlasso=e(b)
r; t=0.00 21:41:34

. if `e(s)' {
.         mat b_rlasso=b_rlasso[1,1..`e(s)']
r; t=0.00 21:41:34
. }
r; t=0.00 21:41:34

. else {
.         mat b_rlasso=.
r; t=0.00 21:41:34
. }
r; t=0.00 21:41:34

.
. /*
> * Violence Abortion
> lassoShootingCBH Dviol $AllViol if trend>0, controls($tdums) lasiter(100) verbose(0) fdisplay(1)
> di "p=" r(p)
> global xvSel `r(selected)'
> di "$xvSel"
> mat b_cbh=r(betaL)
> mat b_cbh=b_cbh'
> */
. global xvSel viol0 Lxxprison Lxxpolice Mxxincome Dxxincome0 LxxpoliceXt MxxincomeXt Dxxincome0Xt Dxxbeer0Xt
r; t=0.00 21:41:34

. mat b_cbh = .65842111 , .00346113 , .01813694 , 3.5867181 , 5.6965391 , .00434867 , 23.924844 , 30.420403 , .5716038
r; t=0.00 21:41:34

.
. // sort cols and compare
. mata: st_matrix("b_rlasso",sort(st_matrix("b_rlasso")',1)')
r; t=0.00 21:41:34

. mata: st_matrix("b_cbh",sort(st_matrix("b_cbh")',1)')
r; t=0.00 21:41:34

. assert mreldif(b_rlasso,b_cbh)<1e-4
r; t=0.00 21:41:34

.
.
. * Violence equation with selected controls
. pdslasso D.lpc_viol D.efaviol                                                                           ///
>                 (                                                                                                                       /// no trend
>                 c.viol0##c.viol0                                                                                        ///
>                 c.Dviol0##c.Dviol0                                                                                      ///
>                 c.(D.($xx))##c.(D.($xx))                                                                        /// note macro
>                 c.(L.xxprison)##c.(L.xxprison)                                                          ///
>                 c.(L.xxpolice)##c.(L.xxpolice)                                                          ///
>                 c.(L.xxunemp)##c.(L.xxunemp)                                                            ///
>                 c.(L.xxincome)##c.(L.xxincome)                                                          ///
>                 c.(L.xxpover)##c.(L.xxpover)                                                            ///
>                 c.(L.xxafdc15)##c.(L.xxafdc15)                                                          ///
>                 c.(L.xxgunlaw)##c.(L.xxgunlaw)                                                          ///
>                 c.(L.xxbeer)##c.(L.xxbeer)                                                                      ///
>                 c.Mxxprison##c.Mxxprison                                                                        ///
>                 c.Mxxpolice##c.Mxxpolice                                                                        ///
>                 c.Mxxunemp##c.Mxxunemp                                                                          ///
>                 c.Mxxincome##c.Mxxincome                                                                        ///
>                 c.Mxxpover##c.Mxxpover                                                                          ///
>                 c.Mxxafdc15##c.Mxxafdc15                                                                        ///
>                 c.Mxxgunlaw##c.Mxxgunlaw                                                                        ///
>                 c.Mxxbeer##c.Mxxbeer                                                                            ///
>                 c.xxprison0##c.xxprison0                                                                        ///
>                 c.xxpolice0##c.xxpolice0                                                                        ///
>                 c.xxunemp0##c.xxunemp0                                                                          ///
>                 c.xxincome0##c.xxincome0                                                                        ///
>                 c.xxpover0##c.xxpover0                                                                          ///
>                 c.xxafdc150##c.xxafdc150                                                                        ///
>                 c.xxgunlaw0##c.xxgunlaw0                                                                        ///
>                 c.xxbeer0##c.xxbeer0                                                                            ///
>                 c.Dxxprison0##c.Dxxprison0                                                                      ///
>                 c.Dxxpolice0##c.Dxxpolice0                                                                      ///
>                 c.Dxxunemp0##c.Dxxunemp0                                                                        ///
>                 c.Dxxincome0##c.Dxxincome0                                                                      ///
>                 c.Dxxpover0##c.Dxxpover0                                                                        ///
>                 c.Dxxafdc150##c.Dxxafdc150                                                                      ///
>                 c.Dxxgunlaw0##c.Dxxgunlaw0                                                                      ///
>                 c.Dxxbeer0##c.Dxxbeer0                                                                          ///
>                                                                                                                                         ///
>                 (c.viol0##c.viol0)#(c.trend##c.trend)                                           /// now interacted with trend
>                 (c.Dviol0##c.Dviol0)#(c.trend##c.trend)                                         ///
>                 (c.(D.($xx))##c.(D.($xx)))#(c.trend##c.trend)                           /// note macro
>                 (c.(L.xxprison)##c.(L.xxprison))#(c.trend##c.trend)                     ///
>                 (c.(L.xxpolice)##c.(L.xxpolice))#(c.trend##c.trend)                     ///
>                 (c.(L.xxunemp)##c.(L.xxunemp))#(c.trend##c.trend)                       ///
>                 (c.(L.xxincome)##c.(L.xxincome))#(c.trend##c.trend)                     ///
>                 (c.(L.xxpover)##c.(L.xxpover))#(c.trend##c.trend)                       ///
>                 (c.(L.xxafdc15)##c.(L.xxafdc15))#(c.trend##c.trend)                     ///
>                 (c.(L.xxgunlaw)##c.(L.xxgunlaw))#(c.trend##c.trend)                     ///
>                 (c.(L.xxbeer)##c.(L.xxbeer))#(c.trend##c.trend)                         ///
>                 (c.Mxxprison##c.Mxxprison)#(c.trend##c.trend)                           ///
>                 (c.Mxxpolice##c.Mxxpolice)#(c.trend##c.trend)                           ///
>                 (c.Mxxunemp##c.Mxxunemp )#(c.trend##c.trend)                            ///
>                 (c.Mxxincome##c.Mxxincome)#(c.trend##c.trend)                           ///
>                 (c.Mxxpover##c.Mxxpover )#(c.trend##c.trend)                            ///
>                 (c.Mxxafdc15##c.Mxxafdc15)#(c.trend##c.trend)                           ///
>                 (c.Mxxgunlaw##c.Mxxgunlaw)#(c.trend##c.trend)                           ///
>                 (c.Mxxbeer##c.Mxxbeer)#(c.trend##c.trend)                                       ///
>                 (c.xxprison0##c.xxprison0)#(c.trend##c.trend)                           ///
>                 (c.xxpolice0##c.xxpolice0)#(c.trend##c.trend)                           ///
>                 (c.xxunemp0##c.xxunemp0)#(c.trend##c.trend)                                     ///
>                 (c.xxincome0##c.xxincome0)#(c.trend##c.trend)                           ///
>                 (c.xxpover0##c.xxpover0)#(c.trend##c.trend)                                     ///
>                 (c.xxafdc150##c.xxafdc150)#(c.trend##c.trend)                           ///
>                 (c.xxgunlaw0##c.xxgunlaw0)#(c.trend##c.trend)                           ///
>                 (c.xxbeer0##c.xxbeer0)#(c.trend##c.trend)                                       ///
>                 (c.Dxxprison0##c.Dxxprison0)#(c.trend##c.trend)                         ///
>                 (c.Dxxpolice0##c.Dxxpolice0)#(c.trend##c.trend)                         ///
>                 (c.Dxxunemp0##c.Dxxunemp0)#(c.trend##c.trend)                           ///
>                 (c.Dxxincome0##c.Dxxincome0)#(c.trend##c.trend)                         ///
>                 (c.Dxxpover0##c.Dxxpover0)#(c.trend##c.trend)                           ///
>                 (c.Dxxafdc150##c.Dxxafdc150)#(c.trend##c.trend)                         ///
>                 (c.Dxxgunlaw0##c.Dxxgunlaw0)#(c.trend##c.trend)                         ///
>                 (c.Dxxbeer0##c.Dxxbeer0 )#(c.trend##c.trend)                            ///
>                 i.year                                                                                                          ///
>                 )                                                                                                                       ///
>                 , partial(i.year) robust lopt(lalt corrnum(0) maxupsiter(100))
Partialling out unpenalized controls...
1.  (PDS/CHS) Selecting HD controls for dep var D.lpc_viol...
Selected:
2.  (PDS/CHS) Selecting HD controls for exog regressor D.efaviol...
Selected:  viol0 L.xxprison L.xxpolice Mxxincome Dxxincome0 cL.xxpolice#c.trend
          c.Mxxincome#c.trend c.Dxxincome0#c.trend c.Dxxbeer0#c.trend


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      heteroskedastic
Number of observations:                600
Exogenous (1):                         D.efaviol
High-dim controls (336):               viol0 c.viol0#c.viol0 Dviol0
                                       c.Dviol0#c.Dviol0 D.xxprison D.xxpolice
                                       D.xxunemp D.xxincome D.xxpover
                                       D.xxafdc15 D.xxgunlaw D.xxbeer
                                       cD.xxprison#cD.xxprison
                                       cD.xxprison#cD.xxpolice
                                       cD.xxprison#cD.xxunemp
                                       cD.xxprison#cD.xxincome
                                       cD.xxprison#cD.xxpover
                                       cD.xxprison#cD.xxafdc15
                                       cD.xxprison#cD.xxgunlaw
                                       cD.xxprison#cD.xxbeer
                                       cD.xxpolice#cD.xxpolice
                                       cD.xxpolice#cD.xxunemp
                                       cD.xxpolice#cD.xxincome
                                       cD.xxpolice#cD.xxpover
                                       cD.xxpolice#cD.xxafdc15
                                       cD.xxpolice#cD.xxgunlaw
                                       cD.xxpolice#cD.xxbeer
                                       cD.xxunemp#cD.xxunemp
                                       cD.xxunemp#cD.xxincome
                                       cD.xxunemp#cD.xxpover
                                       cD.xxunemp#cD.xxafdc15
                                       cD.xxunemp#cD.xxgunlaw
                                       cD.xxunemp#cD.xxbeer
                                       cD.xxincome#cD.xxincome
                                       cD.xxincome#cD.xxpover
                                       cD.xxincome#cD.xxafdc15
                                       cD.xxincome#cD.xxgunlaw
                                       cD.xxincome#cD.xxbeer
                                       cD.xxpover#cD.xxpover
                                       cD.xxpover#cD.xxafdc15
                                       cD.xxpover#cD.xxgunlaw
                                       cD.xxpover#cD.xxbeer
                                       cD.xxafdc15#cD.xxafdc15
                                       cD.xxafdc15#cD.xxgunlaw
                                       cD.xxafdc15#cD.xxbeer
                                       cD.xxgunlaw#cD.xxgunlaw
                                       cD.xxgunlaw#cD.xxbeer
                                       cD.xxbeer#cD.xxbeer L.xxprison
                                       cL.xxprison#cL.xxprison L.xxpolice
                                       cL.xxpolice#cL.xxpolice L.xxunemp
                                       cL.xxunemp#cL.xxunemp L.xxincome
                                       cL.xxincome#cL.xxincome L.xxpover
                                       cL.xxpover#cL.xxpover L.xxafdc15
                                       cL.xxafdc15#cL.xxafdc15 L.xxgunlaw
                                       cL.xxgunlaw#cL.xxgunlaw L.xxbeer
                                       cL.xxbeer#cL.xxbeer Mxxprison
                                       c.Mxxprison#c.Mxxprison Mxxpolice
                                       c.Mxxpolice#c.Mxxpolice Mxxunemp
                                       c.Mxxunemp#c.Mxxunemp Mxxincome
                                       c.Mxxincome#c.Mxxincome Mxxpover
                                       c.Mxxpover#c.Mxxpover Mxxafdc15
                                       c.Mxxafdc15#c.Mxxafdc15 Mxxgunlaw
                                       c.Mxxgunlaw#c.Mxxgunlaw Mxxbeer
                                       c.Mxxbeer#c.Mxxbeer xxprison0
                                       c.xxprison0#c.xxprison0 xxpolice0
                                       c.xxpolice0#c.xxpolice0 xxunemp0
                                       c.xxunemp0#c.xxunemp0 xxincome0
                                       c.xxincome0#c.xxincome0 xxpover0
                                       c.xxpover0#c.xxpover0 xxafdc150
                                       c.xxafdc150#c.xxafdc150 xxgunlaw0
                                       c.xxgunlaw0#c.xxgunlaw0 xxbeer0
                                       c.xxbeer0#c.xxbeer0 Dxxprison0
                                       c.Dxxprison0#c.Dxxprison0 Dxxpolice0
                                       c.Dxxpolice0#c.Dxxpolice0 Dxxunemp0
                                       c.Dxxunemp0#c.Dxxunemp0 Dxxincome0
                                       c.Dxxincome0#c.Dxxincome0 Dxxpover0
                                       c.Dxxpover0#c.Dxxpover0 Dxxafdc150
                                       c.Dxxafdc150#c.Dxxafdc150 Dxxgunlaw0
                                       c.Dxxgunlaw0#c.Dxxgunlaw0 Dxxbeer0
                                       c.Dxxbeer0#c.Dxxbeer0 c.viol0#c.trend
                                       c.viol0#c.trend#c.trend
                                       c.viol0#c.viol0#c.trend
                                       c.viol0#c.viol0#c.trend#c.trend
                                       c.Dviol0#c.trend
                                       c.Dviol0#c.trend#c.trend
                                       c.Dviol0#c.Dviol0#c.trend
                                       c.Dviol0#c.Dviol0#c.trend#c.trend
                                       cD.xxprison#c.trend
                                       cD.xxprison#c.trend#c.trend
                                       cD.xxpolice#c.trend
                                       cD.xxpolice#c.trend#c.trend
                                       cD.xxunemp#c.trend
                                       cD.xxunemp#c.trend#c.trend
                                       cD.xxincome#c.trend
                                       cD.xxincome#c.trend#c.trend
                                       cD.xxpover#c.trend
                                       cD.xxpover#c.trend#c.trend
                                       cD.xxafdc15#c.trend
                                       cD.xxafdc15#c.trend#c.trend
                                       cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#c.trend#c.trend
                                       cD.xxbeer#c.trend
                                       cD.xxbeer#c.trend#c.trend
                                       cD.xxprison#cD.xxprison#c.trend
                                       cD.xxprison#cD.xxprison#c.trend#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend#c.trend
                                       cD.xxprison#cD.xxincome#c.trend
                                       cD.xxprison#cD.xxincome#c.trend#c.trend
                                       cD.xxprison#cD.xxpover#c.trend
                                       cD.xxprison#cD.xxpover#c.trend#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend#c.trend
                                       cD.xxincome#cD.xxincome#c.trend
                                       cD.xxincome#cD.xxincome#c.trend#c.trend
                                       cD.xxincome#cD.xxpover#c.trend
                                       cD.xxincome#cD.xxpover#c.trend#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend#c.trend
                                       cD.xxpover#cD.xxpover#c.trend
                                       cD.xxpover#cD.xxpover#c.trend#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend#c.trend
                                       cL.xxprison#c.trend
                                       cL.xxprison#c.trend#c.trend
                                       cL.xxprison#cL.xxprison#c.trend
                                       cL.xxprison#cL.xxprison#c.trend#c.trend
                                       cL.xxpolice#c.trend
                                       cL.xxpolice#c.trend#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend#c.trend
                                       cL.xxunemp#c.trend
                                       cL.xxunemp#c.trend#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend#c.trend
                                       cL.xxincome#c.trend
                                       cL.xxincome#c.trend#c.trend
                                       cL.xxincome#cL.xxincome#c.trend
                                       cL.xxincome#cL.xxincome#c.trend#c.trend
                                       cL.xxpover#c.trend
                                       cL.xxpover#c.trend#c.trend
                                       cL.xxpover#cL.xxpover#c.trend
                                       cL.xxpover#cL.xxpover#c.trend#c.trend
                                       cL.xxafdc15#c.trend
                                       cL.xxafdc15#c.trend#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend#c.trend
                                       cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#c.trend#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend#c.trend
                                       cL.xxbeer#c.trend
                                       cL.xxbeer#c.trend#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend#c.trend
                                       c.Mxxprison#c.trend
                                       c.Mxxprison#c.trend#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend#c.trend
                                       c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.trend#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend#c.trend
                                       c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.trend#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend#c.trend
                                       c.Mxxincome#c.trend
                                       c.Mxxincome#c.trend#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend#c.trend
                                       c.Mxxpover#c.trend
                                       c.Mxxpover#c.trend#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend#c.trend
                                       c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.trend#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend#c.trend
                                       c.xxprison0#c.trend
                                       c.xxprison0#c.trend#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.xxprison0#c.xxprison0#c.trend#c.trend
                                       c.xxpolice0#c.trend
                                       c.xxpolice0#c.trend#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend#c.trend
                                       c.xxunemp0#c.trend
                                       c.xxunemp0#c.trend#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend#c.trend
                                       c.xxincome0#c.trend
                                       c.xxincome0#c.trend#c.trend
                                       c.xxincome0#c.xxincome0#c.trend
                                       c.xxincome0#c.xxincome0#c.trend#c.trend
                                       c.xxpover0#c.trend
                                       c.xxpover0#c.trend#c.trend
                                       c.xxpover0#c.xxpover0#c.trend
                                       c.xxpover0#c.xxpover0#c.trend#c.trend
                                       c.xxafdc150#c.trend
                                       c.xxafdc150#c.trend#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend#c.trend
                                       c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.trend#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend#c.trend
                                       c.xxbeer0#c.trend
                                       c.xxbeer0#c.trend#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend#c.trend
                                       c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.trend#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend#c.trend
                                       c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.trend#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend#c.trend
                                       c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.trend#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend#c.trend
                                       c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.trend#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend#c.trend
Selected controls (9):                 viol0 L.xxprison L.xxpolice Mxxincome
                                       Dxxincome0 cL.xxpolice#c.trend
                                       c.Mxxincome#c.trend c.Dxxincome0#c.trend
                                       c.Dxxbeer0#c.trend
Partialled-out controls (12):          86b.year 87.year 88.year 89.year
                                       90.year 91.year 92.year 93.year 94.year
                                       95.year 96.year 97.year

Structural equation:

OLS using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_viol |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaviol |
         D1. |   -.2459116    .0963237     -2.55    0.011     -.4347026    -.0571206
-------------+----------------------------------------------------------------

OLS using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_viol |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaviol |
         D1. |   -.1711088    .1117782     -1.53    0.126       -.39019     .0479725
-------------+----------------------------------------------------------------

OLS with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_viol |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaviol |
         D1. |   -.1711088    .1052318     -1.63    0.104     -.3773594     .0351419
             |
       viol0 |    .0802068    .1123317      0.71    0.475     -.1399592     .3003728
             |
    xxprison |
         L1. |    .0098219    .0080763      1.22    0.224     -.0060074     .0256511
             |
    xxpolice |
         L1. |   -.0207962    .0442332     -0.47    0.638     -.1074916     .0658993
             |
   Mxxincome |    5.818101    6.663788      0.87    0.383     -7.242684     18.87889
  Dxxincome0 |   -22.96235    38.53946     -0.60    0.551      -98.4983      52.5736
             |
 cL.xxpolice#|
     c.trend |   -.0475145    .0592313     -0.80    0.422     -.1636057     .0685767
             |
 c.Mxxincome#|
     c.trend |   -6.052322    9.153732     -0.66    0.508     -23.99331     11.88866
             |
          c. |
  Dxxincome0#|
     c.trend |    21.16915    55.50893      0.38    0.703     -87.62636     129.9647
             |
  c.Dxxbeer0#|
     c.trend |     1.27701    .8047562      1.59    0.113     -.3002827     2.854303
             |
        year |
         87  |   -.0267732    .0785487     -0.34    0.733     -.1807258     .1271795
         88  |    .0916358    .1481915      0.62    0.536     -.1988143     .3820859
         89  |    .1464181     .222012      0.66    0.510     -.2887175     .5815537
         90  |    .2561346    .2944133      0.87    0.384     -.3209047      .833174
         91  |    .2631304    .3670148      0.72    0.473     -.4562053     .9824662
         92  |    .2963432     .440092      0.67    0.501     -.5662212     1.158908
         93  |    .3426997    .5123033      0.67    0.504     -.6613963     1.346796
         94  |    .3720091    .5849451      0.64    0.525     -.7744622      1.51848
         95  |    .4305491    .6577177      0.65    0.513     -.8585539     1.719652
         96  |    .4360978     .729915      0.60    0.550     -.9945094     1.866705
         97  |    .5344969    .8037134      0.67    0.506     -1.040752     2.109746
             |
       _cons |   -.4479954    .5745768     -0.78    0.436     -1.574145     .6781544
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    D.efaviol
------------------------------------------------------------------------------
r; t=3.50 21:41:38

. mat b_pdslasso=e(b)
r; t=0.00 21:41:38

.
. * Get union of selected instruments
. global vDS : list global(yvSel) | global(xvSel)
r; t=0.00 21:41:38

.
. * Violence equation with selected controls
. // Original - clustered SEs (but not cluster lasso)
. // reg Dyviol Dviol $vDS $tdums if trend>0, cluster(statenum)
. // robust, no cluster
. reg Dyviol Dviol $vDS $tdums if trend>0, robust

Linear regression                               Number of obs     =        600
                                                F(21, 578)        =      13.01
                                                Prob > F          =     0.0000
                                                R-squared         =     0.2712
                                                Root MSE          =      .0713

-------------+----------------------------------------------------------------
             |               Robust
       Dyviol |      Coef.    Std. Err.       t    P>|t|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
       Dviol |   -.1711088    .1072158     -1.60    0.111     -.3816889     .0394713
       viol0 |    .0802068    .1144495      0.70    0.484     -.1445808     .3049944
   Lxxprison |    .0098219    .0082286      1.19    0.233     -.0063397     .0259834
   Lxxpolice |   -.0207962    .0450671     -0.46    0.645     -.1093115     .0677191
   Mxxincome |    5.818101    6.789423      0.86    0.392     -7.516848     19.15305
  Dxxincome0 |   -22.96235    39.26606     -0.58    0.559     -100.0839      54.1592
 LxxpoliceXt |   -.0475145     .060348     -0.79    0.431     -.1660426     .0710136
 MxxincomeXt |   -6.052322    9.326311     -0.65    0.517     -24.36991     12.26527
Dxxincome0Xt |    21.16915    56.55546      0.37    0.708     -89.91012     132.2484
  Dxxbeer0Xt |     1.27701    .8199286      1.56    0.120     -.3333922     2.887413
   _Iyear_87 |   -.0267732    .0800296     -0.33    0.738     -.1839575     .1304112
   _Iyear_88 |    .0916358    .1509855      0.61    0.544     -.2049112     .3881828
   _Iyear_89 |    .1464181    .2261977      0.65    0.518     -.2978516     .5906878
   _Iyear_90 |    .2561346     .299964      0.85    0.394     -.3330176     .8452869
   _Iyear_91 |    .2631305    .3739343      0.70    0.482     -.4713051      .997566
   _Iyear_92 |    .2963433    .4483892      0.66    0.509     -.5843276     1.177014
   _Iyear_93 |    .3426997     .521962      0.66    0.512     -.6824736     1.367873
   _Iyear_94 |    .3720092    .5959733      0.62    0.533     -.7985282     1.542547
   _Iyear_95 |    .4305491    .6701179      0.64    0.521     -.8856139     1.746712
   _Iyear_96 |    .4360978    .7436764      0.59    0.558      -1.02454     1.896735
   _Iyear_97 |     .534497    .8188662      0.65    0.514     -1.073819     2.142813
       _cons |   -.4479954    .5854096     -0.77    0.444     -1.597785     .7017938
-------------+----------------------------------------------------------------
r; t=0.02 21:41:38

. mat b_regress=e(b)
r; t=0.00 21:41:38

.
. // sort cols and compare
. // may be diff lengths and include 0s (for dropped base vars)
. // so compare abs values > 0
. mata: st_matrix("b_pdslasso",abs(sort(-abs(st_matrix("b_pdslasso"))',1))')
r; t=0.00 21:41:38

. mata: st_matrix("b_regress",abs(sort(-abs(st_matrix("b_regress"))',1))')
r; t=0.00 21:41:38

. local k1 = colsof(b_pdslasso)
r; t=0.00 21:41:38

. local k2 = colsof(b_regress)
r; t=0.00 21:41:38

. mat b_pdslasso = b_pdslasso[1,1..min(`k1',`k2')]
r; t=0.00 21:41:38

. mat b_regress = b_regress[1,1..min(`k1',`k2')]
r; t=0.00 21:41:38

. assert mreldif(b_pdslasso,b_regress)<1e-6
r; t=0.00 21:41:38

.
. ******************************** Property ******************************
.
. * Property Outcome
. // need low tol settings in order to match
. rlasso D.lpc_prop                                                                                                       ///
>                                                                                                                                         /// no trend
>                 c.prop0##c.prop0                                                                                        ///
>                 c.Dprop0##c.Dprop0                                                                                      ///
>                 c.(D.($xx))##c.(D.($xx))                                                                        /// note macro
>                 c.(L.xxprison)##c.(L.xxprison)                                                          ///
>                 c.(L.xxpolice)##c.(L.xxpolice)                                                          ///
>                 c.(L.xxunemp)##c.(L.xxunemp)                                                            ///
>                 c.(L.xxincome)##c.(L.xxincome)                                                          ///
>                 c.(L.xxpover)##c.(L.xxpover)                                                            ///
>                 c.(L.xxafdc15)##c.(L.xxafdc15)                                                          ///
>                 c.(L.xxgunlaw)##c.(L.xxgunlaw)                                                          ///
>                 c.(L.xxbeer)##c.(L.xxbeer)                                                                      ///
>                 c.Mxxprison##c.Mxxprison                                                                        ///
>                 c.Mxxpolice##c.Mxxpolice                                                                        ///
>                 c.Mxxunemp##c.Mxxunemp                                                                          ///
>                 c.Mxxincome##c.Mxxincome                                                                        ///
>                 c.Mxxpover##c.Mxxpover                                                                          ///
>                 c.Mxxafdc15##c.Mxxafdc15                                                                        ///
>                 c.Mxxgunlaw##c.Mxxgunlaw                                                                        ///
>                 c.Mxxbeer##c.Mxxbeer                                                                            ///
>                 c.xxprison0##c.xxprison0                                                                        ///
>                 c.xxpolice0##c.xxpolice0                                                                        ///
>                 c.xxunemp0##c.xxunemp0                                                                          ///
>                 c.xxincome0##c.xxincome0                                                                        ///
>                 c.xxpover0##c.xxpover0                                                                          ///
>                 c.xxafdc150##c.xxafdc150                                                                        ///
>                 c.xxgunlaw0##c.xxgunlaw0                                                                        ///
>                 c.xxbeer0##c.xxbeer0                                                                            ///
>                 c.Dxxprison0##c.Dxxprison0                                                                      ///
>                 c.Dxxpolice0##c.Dxxpolice0                                                                      ///
>                 c.Dxxunemp0##c.Dxxunemp0                                                                        ///
>                 c.Dxxincome0##c.Dxxincome0                                                                      ///
>                 c.Dxxpover0##c.Dxxpover0                                                                        ///
>                 c.Dxxafdc150##c.Dxxafdc150                                                                      ///
>                 c.Dxxgunlaw0##c.Dxxgunlaw0                                                                      ///
>                 c.Dxxbeer0##c.Dxxbeer0                                                                          ///
>                                                                                                                                         ///
>                 (c.prop0##c.prop0)#(c.trend##c.trend)                                           /// now interacted with trend
>                 (c.Dprop0##c.Dprop0)#(c.trend##c.trend)                                         ///
>                 (c.(D.($xx))##c.(D.($xx)))#(c.trend##c.trend)                           /// note macro
>                 (c.(L.xxprison)##c.(L.xxprison))#(c.trend##c.trend)                     ///
>                 (c.(L.xxpolice)##c.(L.xxpolice))#(c.trend##c.trend)                     ///
>                 (c.(L.xxunemp)##c.(L.xxunemp))#(c.trend##c.trend)                       ///
>                 (c.(L.xxincome)##c.(L.xxincome))#(c.trend##c.trend)                     ///
>                 (c.(L.xxpover)##c.(L.xxpover))#(c.trend##c.trend)                       ///
>                 (c.(L.xxafdc15)##c.(L.xxafdc15))#(c.trend##c.trend)                     ///
>                 (c.(L.xxgunlaw)##c.(L.xxgunlaw))#(c.trend##c.trend)                     ///
>                 (c.(L.xxbeer)##c.(L.xxbeer))#(c.trend##c.trend)                         ///
>                 (c.Mxxprison##c.Mxxprison)#(c.trend##c.trend)                           ///
>                 (c.Mxxpolice##c.Mxxpolice)#(c.trend##c.trend)                           ///
>                 (c.Mxxunemp##c.Mxxunemp )#(c.trend##c.trend)                            ///
>                 (c.Mxxincome##c.Mxxincome)#(c.trend##c.trend)                           ///
>                 (c.Mxxpover##c.Mxxpover )#(c.trend##c.trend)                            ///
>                 (c.Mxxafdc15##c.Mxxafdc15)#(c.trend##c.trend)                           ///
>                 (c.Mxxgunlaw##c.Mxxgunlaw)#(c.trend##c.trend)                           ///
>                 (c.Mxxbeer##c.Mxxbeer)#(c.trend##c.trend)                                       ///
>                 (c.xxprison0##c.xxprison0)#(c.trend##c.trend)                           ///
>                 (c.xxpolice0##c.xxpolice0)#(c.trend##c.trend)                           ///
>                 (c.xxunemp0##c.xxunemp0)#(c.trend##c.trend)                                     ///
>                 (c.xxincome0##c.xxincome0)#(c.trend##c.trend)                           ///
>                 (c.xxpover0##c.xxpover0)#(c.trend##c.trend)                                     ///
>                 (c.xxafdc150##c.xxafdc150)#(c.trend##c.trend)                           ///
>                 (c.xxgunlaw0##c.xxgunlaw0)#(c.trend##c.trend)                           ///
>                 (c.xxbeer0##c.xxbeer0)#(c.trend##c.trend)                                       ///
>                 (c.Dxxprison0##c.Dxxprison0)#(c.trend##c.trend)                         ///
>                 (c.Dxxpolice0##c.Dxxpolice0)#(c.trend##c.trend)                         ///
>                 (c.Dxxunemp0##c.Dxxunemp0)#(c.trend##c.trend)                           ///
>                 (c.Dxxincome0##c.Dxxincome0)#(c.trend##c.trend)                         ///
>                 (c.Dxxpover0##c.Dxxpover0)#(c.trend##c.trend)                           ///
>                 (c.Dxxafdc150##c.Dxxafdc150)#(c.trend##c.trend)                         ///
>                 (c.Dxxgunlaw0##c.Dxxgunlaw0)#(c.trend##c.trend)                         ///
>                 (c.Dxxbeer0##c.Dxxbeer0 )#(c.trend##c.trend)                            ///
>                 i.year, partial(i.year) robust lalt corrnum(0) maxupsiter(100) tolopt(1e-10) tolzero(1e-10) tolups(1e-10)

------------------+--------------------------------
         Selected |           Lasso   Post-est OLS
------------------+--------------------------------
      c.Mxxincome#|
      c.Mxxincome#|
  c.trend#c.trend |     -11.1799670    -43.4306990
                  |
      c.xxincome0#|
      c.xxincome0#|
  c.trend#c.trend |      -0.9184118    -26.3748761
------------------+--------------------------------
   Partialled-out*|
------------------+--------------------------------
                  |
             year |
              86  |       (omitted)      (omitted)
              87  |      -0.0182359     -0.0063398
              88  |      -0.0335413     -0.0018184
              89  |      -0.0164519      0.0430285
              90  |      -0.0068453      0.0883234
              91  |       0.0048084      0.1435960
              92  |      -0.0377348      0.1526025
              93  |      -0.0146442      0.2351736
              94  |       0.0280936      0.3453226
              95  |       0.0552992      0.4478701
              96  |       0.0288768      0.5047202
              97  |       0.0592118      0.6262585
                  |
            _cons |       0.0391858      0.0431512
------------------+--------------------------------
r; t=7.71 21:41:45

. di "p=" e(p)
p=336
r; t=0.00 21:41:45

. global ypSelrlasso `e(selected)'
r; t=0.00 21:41:45

. di "$ypSelrlasso"
c.Mxxincome#c.Mxxincome#c.trend#c.trend c.xxincome0#c.xxincome0#c.trend#c.trend
r; t=0.00 21:41:45

. mat b_rlasso=e(b)
r; t=0.00 21:41:45

. if `e(s)' {
.         mat b_rlasso=b_rlasso[1,1..`e(s)']
r; t=0.00 21:41:45
. }
r; t=0.00 21:41:45

. else {
.         mat b_rlasso=.
r; t=0.00 21:41:45
. }
r; t=0.00 21:41:45

.
. * Property Outcome
. /*
> lassoShootingCBH Dyprop $AllProp if trend>0, controls($tdums) lasiter(100) verbose(0) fdisplay(1) ltol(1e-10) tolups(1e-10) tolzero(1e-10)
> di "p=" r(p)
> global ypSel `r(selected)'
> di "$ypSel"
> mat b_cbh=r(betaL)
> mat b_cbh=b_cbh'
> */
. global ypSel Mxxincome2Xt2 xxincome02Xt2
r; t=0.00 21:41:45

. mat b_cbh = -11.179967 , -.91841177
r; t=0.00 21:41:45

.
. // sort cols and compare
. mata: st_matrix("b_rlasso",sort(st_matrix("b_rlasso")',1)')
r; t=0.00 21:41:45

. mata: st_matrix("b_cbh",sort(st_matrix("b_cbh")',1)')
r; t=0.00 21:41:45

. assert mreldif(b_rlasso,b_cbh)<1e-4
r; t=0.00 21:41:45

.
. * Property Abortion
. rlasso D.efaprop                                                                                                        ///
>                                                                                                                                         /// no trend
>                 c.prop0##c.prop0                                                                                        ///
>                 c.Dprop0##c.Dprop0                                                                                      ///
>                 c.(D.($xx))##c.(D.($xx))                                                                        /// note macro
>                 c.(L.xxprison)##c.(L.xxprison)                                                          ///
>                 c.(L.xxpolice)##c.(L.xxpolice)                                                          ///
>                 c.(L.xxunemp)##c.(L.xxunemp)                                                            ///
>                 c.(L.xxincome)##c.(L.xxincome)                                                          ///
>                 c.(L.xxpover)##c.(L.xxpover)                                                            ///
>                 c.(L.xxafdc15)##c.(L.xxafdc15)                                                          ///
>                 c.(L.xxgunlaw)##c.(L.xxgunlaw)                                                          ///
>                 c.(L.xxbeer)##c.(L.xxbeer)                                                                      ///
>                 c.Mxxprison##c.Mxxprison                                                                        ///
>                 c.Mxxpolice##c.Mxxpolice                                                                        ///
>                 c.Mxxunemp##c.Mxxunemp                                                                          ///
>                 c.Mxxincome##c.Mxxincome                                                                        ///
>                 c.Mxxpover##c.Mxxpover                                                                          ///
>                 c.Mxxafdc15##c.Mxxafdc15                                                                        ///
>                 c.Mxxgunlaw##c.Mxxgunlaw                                                                        ///
>                 c.Mxxbeer##c.Mxxbeer                                                                            ///
>                 c.xxprison0##c.xxprison0                                                                        ///
>                 c.xxpolice0##c.xxpolice0                                                                        ///
>                 c.xxunemp0##c.xxunemp0                                                                          ///
>                 c.xxincome0##c.xxincome0                                                                        ///
>                 c.xxpover0##c.xxpover0                                                                          ///
>                 c.xxafdc150##c.xxafdc150                                                                        ///
>                 c.xxgunlaw0##c.xxgunlaw0                                                                        ///
>                 c.xxbeer0##c.xxbeer0                                                                            ///
>                 c.Dxxprison0##c.Dxxprison0                                                                      ///
>                 c.Dxxpolice0##c.Dxxpolice0                                                                      ///
>                 c.Dxxunemp0##c.Dxxunemp0                                                                        ///
>                 c.Dxxincome0##c.Dxxincome0                                                                      ///
>                 c.Dxxpover0##c.Dxxpover0                                                                        ///
>                 c.Dxxafdc150##c.Dxxafdc150                                                                      ///
>                 c.Dxxgunlaw0##c.Dxxgunlaw0                                                                      ///
>                 c.Dxxbeer0##c.Dxxbeer0                                                                          ///
>                                                                                                                                         ///
>                 (c.prop0##c.prop0)#(c.trend##c.trend)                                           /// now interacted with trend
>                 (c.Dprop0##c.Dprop0)#(c.trend##c.trend)                                         ///
>                 (c.(D.($xx))##c.(D.($xx)))#(c.trend##c.trend)                           /// note macro
>                 (c.(L.xxprison)##c.(L.xxprison))#(c.trend##c.trend)                     ///
>                 (c.(L.xxpolice)##c.(L.xxpolice))#(c.trend##c.trend)                     ///
>                 (c.(L.xxunemp)##c.(L.xxunemp))#(c.trend##c.trend)                       ///
>                 (c.(L.xxincome)##c.(L.xxincome))#(c.trend##c.trend)                     ///
>                 (c.(L.xxpover)##c.(L.xxpover))#(c.trend##c.trend)                       ///
>                 (c.(L.xxafdc15)##c.(L.xxafdc15))#(c.trend##c.trend)                     ///
>                 (c.(L.xxgunlaw)##c.(L.xxgunlaw))#(c.trend##c.trend)                     ///
>                 (c.(L.xxbeer)##c.(L.xxbeer))#(c.trend##c.trend)                         ///
>                 (c.Mxxprison##c.Mxxprison)#(c.trend##c.trend)                           ///
>                 (c.Mxxpolice##c.Mxxpolice)#(c.trend##c.trend)                           ///
>                 (c.Mxxunemp##c.Mxxunemp )#(c.trend##c.trend)                            ///
>                 (c.Mxxincome##c.Mxxincome)#(c.trend##c.trend)                           ///
>                 (c.Mxxpover##c.Mxxpover )#(c.trend##c.trend)                            ///
>                 (c.Mxxafdc15##c.Mxxafdc15)#(c.trend##c.trend)                           ///
>                 (c.Mxxgunlaw##c.Mxxgunlaw)#(c.trend##c.trend)                           ///
>                 (c.Mxxbeer##c.Mxxbeer)#(c.trend##c.trend)                                       ///
>                 (c.xxprison0##c.xxprison0)#(c.trend##c.trend)                           ///
>                 (c.xxpolice0##c.xxpolice0)#(c.trend##c.trend)                           ///
>                 (c.xxunemp0##c.xxunemp0)#(c.trend##c.trend)                                     ///
>                 (c.xxincome0##c.xxincome0)#(c.trend##c.trend)                           ///
>                 (c.xxpover0##c.xxpover0)#(c.trend##c.trend)                                     ///
>                 (c.xxafdc150##c.xxafdc150)#(c.trend##c.trend)                           ///
>                 (c.xxgunlaw0##c.xxgunlaw0)#(c.trend##c.trend)                           ///
>                 (c.xxbeer0##c.xxbeer0)#(c.trend##c.trend)                                       ///
>                 (c.Dxxprison0##c.Dxxprison0)#(c.trend##c.trend)                         ///
>                 (c.Dxxpolice0##c.Dxxpolice0)#(c.trend##c.trend)                         ///
>                 (c.Dxxunemp0##c.Dxxunemp0)#(c.trend##c.trend)                           ///
>                 (c.Dxxincome0##c.Dxxincome0)#(c.trend##c.trend)                         ///
>                 (c.Dxxpover0##c.Dxxpover0)#(c.trend##c.trend)                           ///
>                 (c.Dxxafdc150##c.Dxxafdc150)#(c.trend##c.trend)                         ///
>                 (c.Dxxgunlaw0##c.Dxxgunlaw0)#(c.trend##c.trend)                         ///
>                 (c.Dxxbeer0##c.Dxxbeer0 )#(c.trend##c.trend)                            ///
>                 i.year, partial(i.year) robust lalt corrnum(0) maxupsiter(100)

------------------+--------------------------------
         Selected |           Lasso   Post-est OLS
------------------+--------------------------------
            prop0 |       0.0922567      0.2700187
                  |
         xxprison |
              L1. |       0.0080278      0.0213549
                  |
         xxpolice |
              L1. |       0.0208115      0.0574836
                  |
         xxincome |
              L1. |       7.9549904      4.1595062
                  |
        Mxxincome |      16.9979738     16.4546375
       Dxxincome0 |      24.9380995     35.1477100
                  |
     c.Dxxincome0#|
          c.trend |      28.1408004     86.7684481
------------------+--------------------------------
   Partialled-out*|
------------------+--------------------------------
                  |
             year |
              86  |       (omitted)      (omitted)
              87  |       0.0393715      0.0378249
              88  |       0.0599750      0.0556922
              89  |       0.0965196      0.0899067
              90  |       0.1169339      0.1081761
              91  |       0.1350784      0.1233133
              92  |       0.1379838      0.1234689
              93  |       0.1313096      0.1148510
              94  |       0.1206878      0.1024151
              95  |       0.1046600      0.0848436
              96  |       0.0852372      0.0633753
              97  |       0.0663609      0.0422181
                  |
            _cons |      -2.4754711     -2.1054021
------------------+--------------------------------
r; t=4.44 21:41:50

. di "p=" e(p)
p=336
r; t=0.00 21:41:50

. global ypSelrlasso `e(selected)'
r; t=0.00 21:41:50

. di "$xpSelrlasso"

r; t=0.00 21:41:50

. mat b_rlasso=e(b)
r; t=0.00 21:41:50

. if `e(s)' {
.         mat b_rlasso=b_rlasso[1,1..`e(s)']
r; t=0.00 21:41:50
. }
r; t=0.00 21:41:50

. else {
.         mat b_rlasso=.
r; t=0.00 21:41:50
. }
r; t=0.00 21:41:50

.
. * Property Abortion
. /*
> lassoShootingCBH Dprop $AllProp if trend>0, controls($tdums) lasiter(100) verbose(0) fdisplay(1)
> global xpSel `r(selected)'
> di "$xpSel"
> mat b_cbh=r(betaL)
> mat b_cbh=b_cbh'
> */
. global xpSel prop0 Lxxprison Lxxpolice Lxxincome Mxxincome Dxxincome0 Dxxincome0Xt
r; t=0.00 21:41:50

. mat b_cbh = .09225667 , .00802776 , .02081152 , 7.955133 , 16.997832 , 24.938141 , 28.140729
r; t=0.00 21:41:50

.
. // sort cols and compare
. mata: st_matrix("b_rlasso",sort(st_matrix("b_rlasso")',1)')
r; t=0.00 21:41:50

. mata: st_matrix("b_cbh",sort(st_matrix("b_cbh")',1)')
r; t=0.00 21:41:50

. assert mreldif(b_rlasso,b_cbh)<1e-4
r; t=0.00 21:41:50

.
. * Property equation with selected controls
. pdslasso D.lpc_prop D.efaprop                                                                           ///
>                 (                                                                                                                       /// no trend
>                 c.prop0##c.prop0                                                                                        ///
>                 c.Dprop0##c.Dprop0                                                                                      ///
>                 c.(D.($xx))##c.(D.($xx))                                                                        /// note macro
>                 c.(L.xxprison)##c.(L.xxprison)                                                          ///
>                 c.(L.xxpolice)##c.(L.xxpolice)                                                          ///
>                 c.(L.xxunemp)##c.(L.xxunemp)                                                            ///
>                 c.(L.xxincome)##c.(L.xxincome)                                                          ///
>                 c.(L.xxpover)##c.(L.xxpover)                                                            ///
>                 c.(L.xxafdc15)##c.(L.xxafdc15)                                                          ///
>                 c.(L.xxgunlaw)##c.(L.xxgunlaw)                                                          ///
>                 c.(L.xxbeer)##c.(L.xxbeer)                                                                      ///
>                 c.Mxxprison##c.Mxxprison                                                                        ///
>                 c.Mxxpolice##c.Mxxpolice                                                                        ///
>                 c.Mxxunemp##c.Mxxunemp                                                                          ///
>                 c.Mxxincome##c.Mxxincome                                                                        ///
>                 c.Mxxpover##c.Mxxpover                                                                          ///
>                 c.Mxxafdc15##c.Mxxafdc15                                                                        ///
>                 c.Mxxgunlaw##c.Mxxgunlaw                                                                        ///
>                 c.Mxxbeer##c.Mxxbeer                                                                            ///
>                 c.xxprison0##c.xxprison0                                                                        ///
>                 c.xxpolice0##c.xxpolice0                                                                        ///
>                 c.xxunemp0##c.xxunemp0                                                                          ///
>                 c.xxincome0##c.xxincome0                                                                        ///
>                 c.xxpover0##c.xxpover0                                                                          ///
>                 c.xxafdc150##c.xxafdc150                                                                        ///
>                 c.xxgunlaw0##c.xxgunlaw0                                                                        ///
>                 c.xxbeer0##c.xxbeer0                                                                            ///
>                 c.Dxxprison0##c.Dxxprison0                                                                      ///
>                 c.Dxxpolice0##c.Dxxpolice0                                                                      ///
>                 c.Dxxunemp0##c.Dxxunemp0                                                                        ///
>                 c.Dxxincome0##c.Dxxincome0                                                                      ///
>                 c.Dxxpover0##c.Dxxpover0                                                                        ///
>                 c.Dxxafdc150##c.Dxxafdc150                                                                      ///
>                 c.Dxxgunlaw0##c.Dxxgunlaw0                                                                      ///
>                 c.Dxxbeer0##c.Dxxbeer0                                                                          ///
>                                                                                                                                         ///
>                 (c.prop0##c.prop0)#(c.trend##c.trend)                                           /// now interacted with trend
>                 (c.Dprop0##c.Dprop0)#(c.trend##c.trend)                                         ///
>                 (c.(D.($xx))##c.(D.($xx)))#(c.trend##c.trend)                           /// note macro
>                 (c.(L.xxprison)##c.(L.xxprison))#(c.trend##c.trend)                     ///
>                 (c.(L.xxpolice)##c.(L.xxpolice))#(c.trend##c.trend)                     ///
>                 (c.(L.xxunemp)##c.(L.xxunemp))#(c.trend##c.trend)                       ///
>                 (c.(L.xxincome)##c.(L.xxincome))#(c.trend##c.trend)                     ///
>                 (c.(L.xxpover)##c.(L.xxpover))#(c.trend##c.trend)                       ///
>                 (c.(L.xxafdc15)##c.(L.xxafdc15))#(c.trend##c.trend)                     ///
>                 (c.(L.xxgunlaw)##c.(L.xxgunlaw))#(c.trend##c.trend)                     ///
>                 (c.(L.xxbeer)##c.(L.xxbeer))#(c.trend##c.trend)                         ///
>                 (c.Mxxprison##c.Mxxprison)#(c.trend##c.trend)                           ///
>                 (c.Mxxpolice##c.Mxxpolice)#(c.trend##c.trend)                           ///
>                 (c.Mxxunemp##c.Mxxunemp )#(c.trend##c.trend)                            ///
>                 (c.Mxxincome##c.Mxxincome)#(c.trend##c.trend)                           ///
>                 (c.Mxxpover##c.Mxxpover )#(c.trend##c.trend)                            ///
>                 (c.Mxxafdc15##c.Mxxafdc15)#(c.trend##c.trend)                           ///
>                 (c.Mxxgunlaw##c.Mxxgunlaw)#(c.trend##c.trend)                           ///
>                 (c.Mxxbeer##c.Mxxbeer)#(c.trend##c.trend)                                       ///
>                 (c.xxprison0##c.xxprison0)#(c.trend##c.trend)                           ///
>                 (c.xxpolice0##c.xxpolice0)#(c.trend##c.trend)                           ///
>                 (c.xxunemp0##c.xxunemp0)#(c.trend##c.trend)                                     ///
>                 (c.xxincome0##c.xxincome0)#(c.trend##c.trend)                           ///
>                 (c.xxpover0##c.xxpover0)#(c.trend##c.trend)                                     ///
>                 (c.xxafdc150##c.xxafdc150)#(c.trend##c.trend)                           ///
>                 (c.xxgunlaw0##c.xxgunlaw0)#(c.trend##c.trend)                           ///
>                 (c.xxbeer0##c.xxbeer0)#(c.trend##c.trend)                                       ///
>                 (c.Dxxprison0##c.Dxxprison0)#(c.trend##c.trend)                         ///
>                 (c.Dxxpolice0##c.Dxxpolice0)#(c.trend##c.trend)                         ///
>                 (c.Dxxunemp0##c.Dxxunemp0)#(c.trend##c.trend)                           ///
>                 (c.Dxxincome0##c.Dxxincome0)#(c.trend##c.trend)                         ///
>                 (c.Dxxpover0##c.Dxxpover0)#(c.trend##c.trend)                           ///
>                 (c.Dxxafdc150##c.Dxxafdc150)#(c.trend##c.trend)                         ///
>                 (c.Dxxgunlaw0##c.Dxxgunlaw0)#(c.trend##c.trend)                         ///
>                 (c.Dxxbeer0##c.Dxxbeer0 )#(c.trend##c.trend)                            ///
>                 i.year                                                                                                          ///
>                 )                                                                                                                       ///
>                 , partial(i.year) robust lopt(lalt corrnum(0) maxupsiter(100))
Partialling out unpenalized controls...
1.  (PDS/CHS) Selecting HD controls for dep var D.lpc_prop...
Selected:  c.Mxxincome#c.Mxxincome#c.trend#c.trend
          c.xxincome0#c.xxincome0#c.trend#c.trend
2.  (PDS/CHS) Selecting HD controls for exog regressor D.efaprop...
Selected:  prop0 L.xxprison L.xxpolice L.xxincome Mxxincome Dxxincome0
          c.Dxxincome0#c.trend


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      heteroskedastic
Number of observations:                600
Exogenous (1):                         D.efaprop
High-dim controls (336):               prop0 c.prop0#c.prop0 Dprop0
                                       c.Dprop0#c.Dprop0 D.xxprison D.xxpolice
                                       D.xxunemp D.xxincome D.xxpover
                                       D.xxafdc15 D.xxgunlaw D.xxbeer
                                       cD.xxprison#cD.xxprison
                                       cD.xxprison#cD.xxpolice
                                       cD.xxprison#cD.xxunemp
                                       cD.xxprison#cD.xxincome
                                       cD.xxprison#cD.xxpover
                                       cD.xxprison#cD.xxafdc15
                                       cD.xxprison#cD.xxgunlaw
                                       cD.xxprison#cD.xxbeer
                                       cD.xxpolice#cD.xxpolice
                                       cD.xxpolice#cD.xxunemp
                                       cD.xxpolice#cD.xxincome
                                       cD.xxpolice#cD.xxpover
                                       cD.xxpolice#cD.xxafdc15
                                       cD.xxpolice#cD.xxgunlaw
                                       cD.xxpolice#cD.xxbeer
                                       cD.xxunemp#cD.xxunemp
                                       cD.xxunemp#cD.xxincome
                                       cD.xxunemp#cD.xxpover
                                       cD.xxunemp#cD.xxafdc15
                                       cD.xxunemp#cD.xxgunlaw
                                       cD.xxunemp#cD.xxbeer
                                       cD.xxincome#cD.xxincome
                                       cD.xxincome#cD.xxpover
                                       cD.xxincome#cD.xxafdc15
                                       cD.xxincome#cD.xxgunlaw
                                       cD.xxincome#cD.xxbeer
                                       cD.xxpover#cD.xxpover
                                       cD.xxpover#cD.xxafdc15
                                       cD.xxpover#cD.xxgunlaw
                                       cD.xxpover#cD.xxbeer
                                       cD.xxafdc15#cD.xxafdc15
                                       cD.xxafdc15#cD.xxgunlaw
                                       cD.xxafdc15#cD.xxbeer
                                       cD.xxgunlaw#cD.xxgunlaw
                                       cD.xxgunlaw#cD.xxbeer
                                       cD.xxbeer#cD.xxbeer L.xxprison
                                       cL.xxprison#cL.xxprison L.xxpolice
                                       cL.xxpolice#cL.xxpolice L.xxunemp
                                       cL.xxunemp#cL.xxunemp L.xxincome
                                       cL.xxincome#cL.xxincome L.xxpover
                                       cL.xxpover#cL.xxpover L.xxafdc15
                                       cL.xxafdc15#cL.xxafdc15 L.xxgunlaw
                                       cL.xxgunlaw#cL.xxgunlaw L.xxbeer
                                       cL.xxbeer#cL.xxbeer Mxxprison
                                       c.Mxxprison#c.Mxxprison Mxxpolice
                                       c.Mxxpolice#c.Mxxpolice Mxxunemp
                                       c.Mxxunemp#c.Mxxunemp Mxxincome
                                       c.Mxxincome#c.Mxxincome Mxxpover
                                       c.Mxxpover#c.Mxxpover Mxxafdc15
                                       c.Mxxafdc15#c.Mxxafdc15 Mxxgunlaw
                                       c.Mxxgunlaw#c.Mxxgunlaw Mxxbeer
                                       c.Mxxbeer#c.Mxxbeer xxprison0
                                       c.xxprison0#c.xxprison0 xxpolice0
                                       c.xxpolice0#c.xxpolice0 xxunemp0
                                       c.xxunemp0#c.xxunemp0 xxincome0
                                       c.xxincome0#c.xxincome0 xxpover0
                                       c.xxpover0#c.xxpover0 xxafdc150
                                       c.xxafdc150#c.xxafdc150 xxgunlaw0
                                       c.xxgunlaw0#c.xxgunlaw0 xxbeer0
                                       c.xxbeer0#c.xxbeer0 Dxxprison0
                                       c.Dxxprison0#c.Dxxprison0 Dxxpolice0
                                       c.Dxxpolice0#c.Dxxpolice0 Dxxunemp0
                                       c.Dxxunemp0#c.Dxxunemp0 Dxxincome0
                                       c.Dxxincome0#c.Dxxincome0 Dxxpover0
                                       c.Dxxpover0#c.Dxxpover0 Dxxafdc150
                                       c.Dxxafdc150#c.Dxxafdc150 Dxxgunlaw0
                                       c.Dxxgunlaw0#c.Dxxgunlaw0 Dxxbeer0
                                       c.Dxxbeer0#c.Dxxbeer0 c.prop0#c.trend
                                       c.prop0#c.trend#c.trend
                                       c.prop0#c.prop0#c.trend
                                       c.prop0#c.prop0#c.trend#c.trend
                                       c.Dprop0#c.trend
                                       c.Dprop0#c.trend#c.trend
                                       c.Dprop0#c.Dprop0#c.trend
                                       c.Dprop0#c.Dprop0#c.trend#c.trend
                                       cD.xxprison#c.trend
                                       cD.xxprison#c.trend#c.trend
                                       cD.xxpolice#c.trend
                                       cD.xxpolice#c.trend#c.trend
                                       cD.xxunemp#c.trend
                                       cD.xxunemp#c.trend#c.trend
                                       cD.xxincome#c.trend
                                       cD.xxincome#c.trend#c.trend
                                       cD.xxpover#c.trend
                                       cD.xxpover#c.trend#c.trend
                                       cD.xxafdc15#c.trend
                                       cD.xxafdc15#c.trend#c.trend
                                       cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#c.trend#c.trend
                                       cD.xxbeer#c.trend
                                       cD.xxbeer#c.trend#c.trend
                                       cD.xxprison#cD.xxprison#c.trend
                                       cD.xxprison#cD.xxprison#c.trend#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend#c.trend
                                       cD.xxprison#cD.xxincome#c.trend
                                       cD.xxprison#cD.xxincome#c.trend#c.trend
                                       cD.xxprison#cD.xxpover#c.trend
                                       cD.xxprison#cD.xxpover#c.trend#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend#c.trend
                                       cD.xxincome#cD.xxincome#c.trend
                                       cD.xxincome#cD.xxincome#c.trend#c.trend
                                       cD.xxincome#cD.xxpover#c.trend
                                       cD.xxincome#cD.xxpover#c.trend#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend#c.trend
                                       cD.xxpover#cD.xxpover#c.trend
                                       cD.xxpover#cD.xxpover#c.trend#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend#c.trend
                                       cL.xxprison#c.trend
                                       cL.xxprison#c.trend#c.trend
                                       cL.xxprison#cL.xxprison#c.trend
                                       cL.xxprison#cL.xxprison#c.trend#c.trend
                                       cL.xxpolice#c.trend
                                       cL.xxpolice#c.trend#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend#c.trend
                                       cL.xxunemp#c.trend
                                       cL.xxunemp#c.trend#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend#c.trend
                                       cL.xxincome#c.trend
                                       cL.xxincome#c.trend#c.trend
                                       cL.xxincome#cL.xxincome#c.trend
                                       cL.xxincome#cL.xxincome#c.trend#c.trend
                                       cL.xxpover#c.trend
                                       cL.xxpover#c.trend#c.trend
                                       cL.xxpover#cL.xxpover#c.trend
                                       cL.xxpover#cL.xxpover#c.trend#c.trend
                                       cL.xxafdc15#c.trend
                                       cL.xxafdc15#c.trend#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend#c.trend
                                       cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#c.trend#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend#c.trend
                                       cL.xxbeer#c.trend
                                       cL.xxbeer#c.trend#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend#c.trend
                                       c.Mxxprison#c.trend
                                       c.Mxxprison#c.trend#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend#c.trend
                                       c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.trend#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend#c.trend
                                       c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.trend#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend#c.trend
                                       c.Mxxincome#c.trend
                                       c.Mxxincome#c.trend#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend#c.trend
                                       c.Mxxpover#c.trend
                                       c.Mxxpover#c.trend#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend#c.trend
                                       c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.trend#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend#c.trend
                                       c.xxprison0#c.trend
                                       c.xxprison0#c.trend#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.xxprison0#c.xxprison0#c.trend#c.trend
                                       c.xxpolice0#c.trend
                                       c.xxpolice0#c.trend#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend#c.trend
                                       c.xxunemp0#c.trend
                                       c.xxunemp0#c.trend#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend#c.trend
                                       c.xxincome0#c.trend
                                       c.xxincome0#c.trend#c.trend
                                       c.xxincome0#c.xxincome0#c.trend
                                       c.xxincome0#c.xxincome0#c.trend#c.trend
                                       c.xxpover0#c.trend
                                       c.xxpover0#c.trend#c.trend
                                       c.xxpover0#c.xxpover0#c.trend
                                       c.xxpover0#c.xxpover0#c.trend#c.trend
                                       c.xxafdc150#c.trend
                                       c.xxafdc150#c.trend#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend#c.trend
                                       c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.trend#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend#c.trend
                                       c.xxbeer0#c.trend
                                       c.xxbeer0#c.trend#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend#c.trend
                                       c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.trend#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend#c.trend
                                       c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.trend#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend#c.trend
                                       c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.trend#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend#c.trend
                                       c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.trend#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend#c.trend
Selected controls (9):                 prop0 L.xxprison L.xxpolice L.xxincome
                                       Mxxincome Dxxincome0
                                       c.Mxxincome#c.Mxxincome#c.trend#c.trend
                                       c.xxincome0#c.xxincome0#c.trend#c.trend
                                       c.Dxxincome0#c.trend
Partialled-out controls (12):          86b.year 87.year 88.year 89.year
                                       90.year 91.year 92.year 93.year 94.year
                                       95.year 96.year 97.year

Structural equation:

OLS using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.0896324    .0341676     -2.62    0.009     -.1565997    -.0226652
-------------+----------------------------------------------------------------

OLS using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |    -.068489    .0415875     -1.65    0.100     -.1499989      .013021
-------------+----------------------------------------------------------------

OLS with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.0611018    .0402843     -1.52    0.129     -.1400575     .0178539
             |
       prop0 |   -.0124398    .0199672     -0.62    0.533     -.0515748     .0266952
             |
    xxprison |
         L1. |    .0121946    .0046003      2.65    0.008      .0031781      .021211
             |
    xxpolice |
         L1. |   -.0140262    .0132884     -1.06    0.291     -.0400709     .0120185
             |
    xxincome |
         L1. |     36.2695      8.8808      4.08    0.000      18.86345     53.67555
             |
   Mxxincome |   -37.98595    9.546917     -3.98    0.000     -56.69757    -19.27434
  Dxxincome0 |    48.66548    24.40175      1.99    0.046      .8389293     96.49203
             |
 c.Mxxincome#|
 c.Mxxincome#|
     c.trend#|
     c.trend |   -22.11397    90.72935     -0.24    0.807     -199.9402     155.7123
             |
 c.xxincome0#|
 c.xxincome0#|
     c.trend#|
     c.trend |    .7050396    85.29188      0.01    0.993      -166.464      167.874
             |
          c. |
  Dxxincome0#|
     c.trend |   -61.55626    45.59009     -1.35    0.177     -150.9112     27.79868
             |
        year |
         87  |   -.0240758    .0099248     -2.43    0.015     -.0435281    -.0046236
         88  |   -.0368411    .0149945     -2.46    0.014     -.0662297    -.0074525
         89  |    -.017784    .0233799     -0.76    0.447     -.0636077     .0280397
         90  |   -.0074651    .0362534     -0.21    0.837     -.0785205     .0635903
         91  |    .0113905    .0506941      0.22    0.822     -.0879681      .110749
         92  |   -.0190333    .0675879     -0.28    0.778     -.1515031     .1134366
         93  |    .0072723    .0889787      0.08    0.935     -.1671227     .1816674
         94  |    .0594937     .112384      0.53    0.597     -.1607749     .2797622
         95  |    .0893581    .1397526      0.64    0.523     -.1845519      .363268
         96  |    .0621677    .1705276      0.36    0.715     -.2720602     .3963956
         97  |    .0995271    .2015611      0.49    0.621     -.2955255     .4945797
             |
       _cons |    .2438855     .256085      0.95    0.341     -.2580319     .7458028
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    D.efaprop
------------------------------------------------------------------------------
r; t=9.43 21:41:59

. mat b_pdslasso=e(b)
r; t=0.00 21:41:59

.
. * Get union of selected instruments
. global pDS : list global(ypSel) | global(xpSel)
r; t=0.00 21:41:59

.
. * Property equation with selected controls
. // Original - clustered SEs (but not cluster lasso)
. // reg Dyprop Dprop $pDS $tdums if trend>0, cluster(statenum)
. // robust, no cluster
. reg Dyprop Dprop $pDS $tdums if trend>0, robust

Linear regression                               Number of obs     =        600
                                                F(21, 578)        =      11.09
                                                Prob > F          =     0.0000
                                                R-squared         =     0.2635
                                                Root MSE          =     .04613

-------------+----------------------------------------------------------------
             |               Robust
       Dyprop |      Coef.    Std. Err.       t    P>|t|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
       Dprop |   -.0611018    .0410438     -1.49    0.137     -.1417149     .0195113
Mxxincome2~2 |   -22.11397    92.43989     -0.24    0.811      -203.673     159.4451
xxincome02~2 |    .7050382    86.89991      0.01    0.994     -169.9731     171.3831
       prop0 |   -.0124398    .0203436     -0.61    0.541     -.0523963     .0275167
   Lxxprison |    .0121946     .004687      2.60    0.010      .0029889     .0214003
   Lxxpolice |   -.0140262    .0135389     -1.04    0.301     -.0406177     .0125652
   Lxxincome |     36.2695    9.048234      4.01    0.000      18.49807     54.04092
   Mxxincome |   -37.98595    9.726909     -3.91    0.000     -57.09035    -18.88156
  Dxxincome0 |    48.66548    24.86181      1.96    0.051     -.1650141     97.49597
Dxxincome0Xt |   -61.55626    46.44962     -1.33    0.186     -152.7869     29.67435
   _Iyear_87 |   -.0240758    .0101119     -2.38    0.018     -.0439364    -.0042153
   _Iyear_88 |   -.0368411    .0152772     -2.41    0.016     -.0668466    -.0068356
   _Iyear_89 |    -.017784    .0238206     -0.75    0.456     -.0645696     .0290016
   _Iyear_90 |   -.0074651    .0369369     -0.20    0.840     -.0800121     .0650819
   _Iyear_91 |    .0113905    .0516498      0.22    0.826     -.0900538     .1128347
   _Iyear_92 |   -.0190333    .0688621     -0.28    0.782     -.1542838     .1162173
   _Iyear_93 |    .0072723    .0906562      0.08    0.936     -.1707835     .1853282
   _Iyear_94 |    .0594937    .1145028      0.52    0.604     -.1653986     .2843859
   _Iyear_95 |    .0893581    .1423874      0.63    0.531     -.1903016     .3690178
   _Iyear_96 |    .0621677    .1737426      0.36    0.721     -.2790761     .4034115
   _Iyear_97 |    .0995271    .2053613      0.48    0.628     -.3038182     .5028724
       _cons |    .2438855    .2609131      0.93    0.350     -.2685678     .7563387
-------------+----------------------------------------------------------------
r; t=0.03 21:41:59

. mat b_regress=e(b)
r; t=0.00 21:41:59

.
. // sort cols and compare
. // may be diff lengths and include 0s (for dropped base vars)
. // so compare abs values > 0
. mata: st_matrix("b_pdslasso",abs(sort(-abs(st_matrix("b_pdslasso"))',1))')
r; t=0.00 21:41:59

. mata: st_matrix("b_regress",abs(sort(-abs(st_matrix("b_regress"))',1))')
r; t=0.00 21:41:59

. local k1 = colsof(b_pdslasso)
r; t=0.00 21:41:59

. local k2 = colsof(b_regress)
r; t=0.00 21:41:59

. mat b_pdslasso = b_pdslasso[1,1..min(`k1',`k2')]
r; t=0.00 21:41:59

. mat b_regress = b_regress[1,1..min(`k1',`k2')]
r; t=0.00 21:41:59

. assert mreldif(b_pdslasso,b_regress)<1e-6
r; t=0.00 21:41:59

.
. ********************************* Murder ***********************************
.
. * Violence Outcome
. rlasso D.lpc_murd                                                                                                       ///
>                                                                                                                                         /// no trend
>                 c.murd0##c.murd0                                                                                        ///
>                 c.Dmurd0##c.Dmurd0                                                                                      ///
>                 c.(D.($xx))##c.(D.($xx))                                                                        /// note macro
>                 c.(L.xxprison)##c.(L.xxprison)                                                          ///
>                 c.(L.xxpolice)##c.(L.xxpolice)                                                          ///
>                 c.(L.xxunemp)##c.(L.xxunemp)                                                            ///
>                 c.(L.xxincome)##c.(L.xxincome)                                                          ///
>                 c.(L.xxpover)##c.(L.xxpover)                                                            ///
>                 c.(L.xxafdc15)##c.(L.xxafdc15)                                                          ///
>                 c.(L.xxgunlaw)##c.(L.xxgunlaw)                                                          ///
>                 c.(L.xxbeer)##c.(L.xxbeer)                                                                      ///
>                 c.Mxxprison##c.Mxxprison                                                                        ///
>                 c.Mxxpolice##c.Mxxpolice                                                                        ///
>                 c.Mxxunemp##c.Mxxunemp                                                                          ///
>                 c.Mxxincome##c.Mxxincome                                                                        ///
>                 c.Mxxpover##c.Mxxpover                                                                          ///
>                 c.Mxxafdc15##c.Mxxafdc15                                                                        ///
>                 c.Mxxgunlaw##c.Mxxgunlaw                                                                        ///
>                 c.Mxxbeer##c.Mxxbeer                                                                            ///
>                 c.xxprison0##c.xxprison0                                                                        ///
>                 c.xxpolice0##c.xxpolice0                                                                        ///
>                 c.xxunemp0##c.xxunemp0                                                                          ///
>                 c.xxincome0##c.xxincome0                                                                        ///
>                 c.xxpover0##c.xxpover0                                                                          ///
>                 c.xxafdc150##c.xxafdc150                                                                        ///
>                 c.xxgunlaw0##c.xxgunlaw0                                                                        ///
>                 c.xxbeer0##c.xxbeer0                                                                            ///
>                 c.Dxxprison0##c.Dxxprison0                                                                      ///
>                 c.Dxxpolice0##c.Dxxpolice0                                                                      ///
>                 c.Dxxunemp0##c.Dxxunemp0                                                                        ///
>                 c.Dxxincome0##c.Dxxincome0                                                                      ///
>                 c.Dxxpover0##c.Dxxpover0                                                                        ///
>                 c.Dxxafdc150##c.Dxxafdc150                                                                      ///
>                 c.Dxxgunlaw0##c.Dxxgunlaw0                                                                      ///
>                 c.Dxxbeer0##c.Dxxbeer0                                                                          ///
>                                                                                                                                         ///
>                 (c.murd0##c.murd0)#(c.trend##c.trend)                                           /// now interacted with trend
>                 (c.Dmurd0##c.Dmurd0)#(c.trend##c.trend)                                         ///
>                 (c.(D.($xx))##c.(D.($xx)))#(c.trend##c.trend)                           /// note macro
>                 (c.(L.xxprison)##c.(L.xxprison))#(c.trend##c.trend)                     ///
>                 (c.(L.xxpolice)##c.(L.xxpolice))#(c.trend##c.trend)                     ///
>                 (c.(L.xxunemp)##c.(L.xxunemp))#(c.trend##c.trend)                       ///
>                 (c.(L.xxincome)##c.(L.xxincome))#(c.trend##c.trend)                     ///
>                 (c.(L.xxpover)##c.(L.xxpover))#(c.trend##c.trend)                       ///
>                 (c.(L.xxafdc15)##c.(L.xxafdc15))#(c.trend##c.trend)                     ///
>                 (c.(L.xxgunlaw)##c.(L.xxgunlaw))#(c.trend##c.trend)                     ///
>                 (c.(L.xxbeer)##c.(L.xxbeer))#(c.trend##c.trend)                         ///
>                 (c.Mxxprison##c.Mxxprison)#(c.trend##c.trend)                           ///
>                 (c.Mxxpolice##c.Mxxpolice)#(c.trend##c.trend)                           ///
>                 (c.Mxxunemp##c.Mxxunemp )#(c.trend##c.trend)                            ///
>                 (c.Mxxincome##c.Mxxincome)#(c.trend##c.trend)                           ///
>                 (c.Mxxpover##c.Mxxpover )#(c.trend##c.trend)                            ///
>                 (c.Mxxafdc15##c.Mxxafdc15)#(c.trend##c.trend)                           ///
>                 (c.Mxxgunlaw##c.Mxxgunlaw)#(c.trend##c.trend)                           ///
>                 (c.Mxxbeer##c.Mxxbeer)#(c.trend##c.trend)                                       ///
>                 (c.xxprison0##c.xxprison0)#(c.trend##c.trend)                           ///
>                 (c.xxpolice0##c.xxpolice0)#(c.trend##c.trend)                           ///
>                 (c.xxunemp0##c.xxunemp0)#(c.trend##c.trend)                                     ///
>                 (c.xxincome0##c.xxincome0)#(c.trend##c.trend)                           ///
>                 (c.xxpover0##c.xxpover0)#(c.trend##c.trend)                                     ///
>                 (c.xxafdc150##c.xxafdc150)#(c.trend##c.trend)                           ///
>                 (c.xxgunlaw0##c.xxgunlaw0)#(c.trend##c.trend)                           ///
>                 (c.xxbeer0##c.xxbeer0)#(c.trend##c.trend)                                       ///
>                 (c.Dxxprison0##c.Dxxprison0)#(c.trend##c.trend)                         ///
>                 (c.Dxxpolice0##c.Dxxpolice0)#(c.trend##c.trend)                         ///
>                 (c.Dxxunemp0##c.Dxxunemp0)#(c.trend##c.trend)                           ///
>                 (c.Dxxincome0##c.Dxxincome0)#(c.trend##c.trend)                         ///
>                 (c.Dxxpover0##c.Dxxpover0)#(c.trend##c.trend)                           ///
>                 (c.Dxxafdc150##c.Dxxafdc150)#(c.trend##c.trend)                         ///
>                 (c.Dxxgunlaw0##c.Dxxgunlaw0)#(c.trend##c.trend)                         ///
>                 (c.Dxxbeer0##c.Dxxbeer0 )#(c.trend##c.trend)                            ///
>                 i.year, partial(i.year) robust lalt corrnum(0) maxupsiter(100)

------------------+--------------------------------
         Selected |           Lasso   Post-est OLS
------------------+--------------------------------
------------------+--------------------------------
   Partialled-out*|
------------------+--------------------------------
             year |
              86  |       (omitted)      (omitted)
              87  |      -0.0935796     -0.0935796
              88  |      -0.0682364     -0.0682364
              89  |      -0.0673222     -0.0673222
              90  |      -0.0202385     -0.0202385
              91  |      -0.0418626     -0.0418626
              92  |      -0.0996307     -0.0996307
              93  |       0.0162177      0.0162177
              94  |      -0.1802718     -0.1802718
              95  |      -0.0510089     -0.0510089
              96  |      -0.1279937     -0.1279937
              97  |      -0.1504809     -0.1504809
                  |
            _cons |       0.0637239      0.0637239
------------------+--------------------------------
r; t=1.15 21:42:00

. di "p=" e(p)
p=336
r; t=0.00 21:42:00

. global ymSelrlasso `e(selected)'
r; t=0.00 21:42:00

. di "$ymSelrlasso"

r; t=0.00 21:42:00

. mat b_rlasso=e(b)
r; t=0.00 21:42:00

. if `e(s)' {
.         mat b_rlasso=b_rlasso[1,1..`e(s)']
r; t=0.00 21:42:00
. }
r; t=0.00 21:42:00

. else {
.         mat b_rlasso=.
r; t=0.00 21:42:00
. }
r; t=0.00 21:42:00

.
. * Murder Outcome
. /*
> // no variables selected
> lassoShootingCBH Dymurd $AllMurd if trend>0, controls($tdums) lasiter(100) verbose(0) fdisplay(1)
> global ymSel `r(selected)'
> di "`$mSel"
> mat b_cbh=r(betaL)
> mat b_cbh=b_cbh'
> */
. global ymSel
r; t=0.00 21:42:00

. mat b_cbh=.
r; t=0.00 21:42:00

.
. // sort cols and compare
. mata: st_matrix("b_rlasso",sort(st_matrix("b_rlasso")',1)')
r; t=0.00 21:42:00

. mata: st_matrix("b_cbh",sort(st_matrix("b_cbh")',1)')
r; t=0.00 21:42:00

. assert mreldif(b_rlasso,b_cbh)<1e-4
r; t=0.00 21:42:00

.
. * Murder Abortion
. rlasso D.efamurd                                                                                                        ///
>                                                                                                                                         /// no trend
>                 c.murd0##c.murd0                                                                                        ///
>                 c.Dmurd0##c.Dmurd0                                                                                      ///
>                 c.(D.($xx))##c.(D.($xx))                                                                        /// note macro
>                 c.(L.xxprison)##c.(L.xxprison)                                                          ///
>                 c.(L.xxpolice)##c.(L.xxpolice)                                                          ///
>                 c.(L.xxunemp)##c.(L.xxunemp)                                                            ///
>                 c.(L.xxincome)##c.(L.xxincome)                                                          ///
>                 c.(L.xxpover)##c.(L.xxpover)                                                            ///
>                 c.(L.xxafdc15)##c.(L.xxafdc15)                                                          ///
>                 c.(L.xxgunlaw)##c.(L.xxgunlaw)                                                          ///
>                 c.(L.xxbeer)##c.(L.xxbeer)                                                                      ///
>                 c.Mxxprison##c.Mxxprison                                                                        ///
>                 c.Mxxpolice##c.Mxxpolice                                                                        ///
>                 c.Mxxunemp##c.Mxxunemp                                                                          ///
>                 c.Mxxincome##c.Mxxincome                                                                        ///
>                 c.Mxxpover##c.Mxxpover                                                                          ///
>                 c.Mxxafdc15##c.Mxxafdc15                                                                        ///
>                 c.Mxxgunlaw##c.Mxxgunlaw                                                                        ///
>                 c.Mxxbeer##c.Mxxbeer                                                                            ///
>                 c.xxprison0##c.xxprison0                                                                        ///
>                 c.xxpolice0##c.xxpolice0                                                                        ///
>                 c.xxunemp0##c.xxunemp0                                                                          ///
>                 c.xxincome0##c.xxincome0                                                                        ///
>                 c.xxpover0##c.xxpover0                                                                          ///
>                 c.xxafdc150##c.xxafdc150                                                                        ///
>                 c.xxgunlaw0##c.xxgunlaw0                                                                        ///
>                 c.xxbeer0##c.xxbeer0                                                                            ///
>                 c.Dxxprison0##c.Dxxprison0                                                                      ///
>                 c.Dxxpolice0##c.Dxxpolice0                                                                      ///
>                 c.Dxxunemp0##c.Dxxunemp0                                                                        ///
>                 c.Dxxincome0##c.Dxxincome0                                                                      ///
>                 c.Dxxpover0##c.Dxxpover0                                                                        ///
>                 c.Dxxafdc150##c.Dxxafdc150                                                                      ///
>                 c.Dxxgunlaw0##c.Dxxgunlaw0                                                                      ///
>                 c.Dxxbeer0##c.Dxxbeer0                                                                          ///
>                                                                                                                                         ///
>                 (c.murd0##c.murd0)#(c.trend##c.trend)                                           /// now interacted with trend
>                 (c.Dmurd0##c.Dmurd0)#(c.trend##c.trend)                                         ///
>                 (c.(D.($xx))##c.(D.($xx)))#(c.trend##c.trend)                           /// note macro
>                 (c.(L.xxprison)##c.(L.xxprison))#(c.trend##c.trend)                     ///
>                 (c.(L.xxpolice)##c.(L.xxpolice))#(c.trend##c.trend)                     ///
>                 (c.(L.xxunemp)##c.(L.xxunemp))#(c.trend##c.trend)                       ///
>                 (c.(L.xxincome)##c.(L.xxincome))#(c.trend##c.trend)                     ///
>                 (c.(L.xxpover)##c.(L.xxpover))#(c.trend##c.trend)                       ///
>                 (c.(L.xxafdc15)##c.(L.xxafdc15))#(c.trend##c.trend)                     ///
>                 (c.(L.xxgunlaw)##c.(L.xxgunlaw))#(c.trend##c.trend)                     ///
>                 (c.(L.xxbeer)##c.(L.xxbeer))#(c.trend##c.trend)                         ///
>                 (c.Mxxprison##c.Mxxprison)#(c.trend##c.trend)                           ///
>                 (c.Mxxpolice##c.Mxxpolice)#(c.trend##c.trend)                           ///
>                 (c.Mxxunemp##c.Mxxunemp )#(c.trend##c.trend)                            ///
>                 (c.Mxxincome##c.Mxxincome)#(c.trend##c.trend)                           ///
>                 (c.Mxxpover##c.Mxxpover )#(c.trend##c.trend)                            ///
>                 (c.Mxxafdc15##c.Mxxafdc15)#(c.trend##c.trend)                           ///
>                 (c.Mxxgunlaw##c.Mxxgunlaw)#(c.trend##c.trend)                           ///
>                 (c.Mxxbeer##c.Mxxbeer)#(c.trend##c.trend)                                       ///
>                 (c.xxprison0##c.xxprison0)#(c.trend##c.trend)                           ///
>                 (c.xxpolice0##c.xxpolice0)#(c.trend##c.trend)                           ///
>                 (c.xxunemp0##c.xxunemp0)#(c.trend##c.trend)                                     ///
>                 (c.xxincome0##c.xxincome0)#(c.trend##c.trend)                           ///
>                 (c.xxpover0##c.xxpover0)#(c.trend##c.trend)                                     ///
>                 (c.xxafdc150##c.xxafdc150)#(c.trend##c.trend)                           ///
>                 (c.xxgunlaw0##c.xxgunlaw0)#(c.trend##c.trend)                           ///
>                 (c.xxbeer0##c.xxbeer0)#(c.trend##c.trend)                                       ///
>                 (c.Dxxprison0##c.Dxxprison0)#(c.trend##c.trend)                         ///
>                 (c.Dxxpolice0##c.Dxxpolice0)#(c.trend##c.trend)                         ///
>                 (c.Dxxunemp0##c.Dxxunemp0)#(c.trend##c.trend)                           ///
>                 (c.Dxxincome0##c.Dxxincome0)#(c.trend##c.trend)                         ///
>                 (c.Dxxpover0##c.Dxxpover0)#(c.trend##c.trend)                           ///
>                 (c.Dxxafdc150##c.Dxxafdc150)#(c.trend##c.trend)                         ///
>                 (c.Dxxgunlaw0##c.Dxxgunlaw0)#(c.trend##c.trend)                         ///
>                 (c.Dxxbeer0##c.Dxxbeer0 )#(c.trend##c.trend)                            ///
>                 i.year, partial(i.year) robust lalt corrnum(0) maxupsiter(100)

------------------+--------------------------------
         Selected |           Lasso   Post-est OLS
------------------+--------------------------------
            murd0 |       2.3966459      3.3139922
                  |
         xxprison |
              L1. |       0.0009642     -0.0017484
                  |
  c.murd0#c.trend |       0.5523064      1.2435406
                  |
      cL.xxprison#|
          c.trend |       0.0020874      0.0213212
                  |
      cL.xxpolice#|
          c.trend |       0.0242993      0.0684859
                  |
      c.Mxxincome#|
          c.trend |      28.9775849     26.2798837
                  |
     c.Dxxincome0#|
          c.trend |      26.1837730     85.4858548
------------------+--------------------------------
   Partialled-out*|
------------------+--------------------------------
                  |
             year |
              86  |       (omitted)      (omitted)
              87  |      -0.2368293     -0.2201090
              88  |      -0.4752904     -0.4422622
              89  |      -0.7039194     -0.6549002
              90  |      -0.9267216     -0.8620111
              91  |      -1.1475410     -1.0675409
              92  |      -1.3675715     -1.2722268
              93  |      -1.5904245     -1.4801522
              94  |      -1.8209207     -1.6953657
              95  |      -2.0478173     -1.9076971
              96  |      -2.2889897     -2.1355199
              97  |      -2.5284800     -2.3616697
                  |
            _cons |      -0.2492286     -0.2345259
------------------+--------------------------------
r; t=11.65 21:42:12

. di "p=" e(p)
p=336
r; t=0.00 21:42:12

. global xmSelrlasso `e(selected)'
r; t=0.00 21:42:12

. di "$xmSelrlasso"
murd0 L.xxprison c.murd0#c.trend cL.xxprison#c.trend cL.xxpolice#c.trend c.Mxxincome#c.trend c.Dxxincome0#c.trend
r; t=0.00 21:42:12

. mat b_rlasso=e(b)
r; t=0.00 21:42:12

. if `e(s)' {
.         mat b_rlasso=b_rlasso[1,1..`e(s)']
r; t=0.00 21:42:12
. }
r; t=0.00 21:42:12

. else {
.         mat b_rlasso=.
r; t=0.00 21:42:12
. }
r; t=0.00 21:42:12

.
. * Murder Abortion
. /*
> lassoShootingCBH Dmurd $AllMurd if trend>0, controls($tdums) lasiter(100) verbose(0) fdisplay(1)
> global xmSel `r(selected)'
> di "$xmSel"
> mat b_cbh=r(betaL)
> mat b_cbh=b_cbh'
> */
. global xmSel murd0 murd0Xt Lxxprison LxxprisonXt LxxpoliceXt MxxincomeXt Dxxincome0Xt
r; t=0.00 21:42:12

. mat b_cbh = 2.3966347 , .55232244 , .00096424 , .0020873 , .02429935 , 28.977584 , 26.183775
r; t=0.00 21:42:12

.
. // sort cols and compare
. mata: st_matrix("b_rlasso",sort(st_matrix("b_rlasso")',1)')
r; t=0.00 21:42:12

. mata: st_matrix("b_cbh",sort(st_matrix("b_cbh")',1)')
r; t=0.00 21:42:12

. assert mreldif(b_rlasso,b_cbh)<1e-4
r; t=0.00 21:42:12

.
. * Murder equation with selected controls
. pdslasso D.lpc_murd D.efamurd                                                                           ///
>                 (                                                                                                                       /// no trend
>                 c.murd0##c.murd0                                                                                        ///
>                 c.Dmurd0##c.Dmurd0                                                                                      ///
>                 c.(D.($xx))##c.(D.($xx))                                                                        /// note macro
>                 c.(L.xxprison)##c.(L.xxprison)                                                          ///
>                 c.(L.xxpolice)##c.(L.xxpolice)                                                          ///
>                 c.(L.xxunemp)##c.(L.xxunemp)                                                            ///
>                 c.(L.xxincome)##c.(L.xxincome)                                                          ///
>                 c.(L.xxpover)##c.(L.xxpover)                                                            ///
>                 c.(L.xxafdc15)##c.(L.xxafdc15)                                                          ///
>                 c.(L.xxgunlaw)##c.(L.xxgunlaw)                                                          ///
>                 c.(L.xxbeer)##c.(L.xxbeer)                                                                      ///
>                 c.Mxxprison##c.Mxxprison                                                                        ///
>                 c.Mxxpolice##c.Mxxpolice                                                                        ///
>                 c.Mxxunemp##c.Mxxunemp                                                                          ///
>                 c.Mxxincome##c.Mxxincome                                                                        ///
>                 c.Mxxpover##c.Mxxpover                                                                          ///
>                 c.Mxxafdc15##c.Mxxafdc15                                                                        ///
>                 c.Mxxgunlaw##c.Mxxgunlaw                                                                        ///
>                 c.Mxxbeer##c.Mxxbeer                                                                            ///
>                 c.xxprison0##c.xxprison0                                                                        ///
>                 c.xxpolice0##c.xxpolice0                                                                        ///
>                 c.xxunemp0##c.xxunemp0                                                                          ///
>                 c.xxincome0##c.xxincome0                                                                        ///
>                 c.xxpover0##c.xxpover0                                                                          ///
>                 c.xxafdc150##c.xxafdc150                                                                        ///
>                 c.xxgunlaw0##c.xxgunlaw0                                                                        ///
>                 c.xxbeer0##c.xxbeer0                                                                            ///
>                 c.Dxxprison0##c.Dxxprison0                                                                      ///
>                 c.Dxxpolice0##c.Dxxpolice0                                                                      ///
>                 c.Dxxunemp0##c.Dxxunemp0                                                                        ///
>                 c.Dxxincome0##c.Dxxincome0                                                                      ///
>                 c.Dxxpover0##c.Dxxpover0                                                                        ///
>                 c.Dxxafdc150##c.Dxxafdc150                                                                      ///
>                 c.Dxxgunlaw0##c.Dxxgunlaw0                                                                      ///
>                 c.Dxxbeer0##c.Dxxbeer0                                                                          ///
>                                                                                                                                         ///
>                 (c.murd0##c.murd0)#(c.trend##c.trend)                                           /// now interacted with trend
>                 (c.Dmurd0##c.Dmurd0)#(c.trend##c.trend)                                         ///
>                 (c.(D.($xx))##c.(D.($xx)))#(c.trend##c.trend)                           /// note macro
>                 (c.(L.xxprison)##c.(L.xxprison))#(c.trend##c.trend)                     ///
>                 (c.(L.xxpolice)##c.(L.xxpolice))#(c.trend##c.trend)                     ///
>                 (c.(L.xxunemp)##c.(L.xxunemp))#(c.trend##c.trend)                       ///
>                 (c.(L.xxincome)##c.(L.xxincome))#(c.trend##c.trend)                     ///
>                 (c.(L.xxpover)##c.(L.xxpover))#(c.trend##c.trend)                       ///
>                 (c.(L.xxafdc15)##c.(L.xxafdc15))#(c.trend##c.trend)                     ///
>                 (c.(L.xxgunlaw)##c.(L.xxgunlaw))#(c.trend##c.trend)                     ///
>                 (c.(L.xxbeer)##c.(L.xxbeer))#(c.trend##c.trend)                         ///
>                 (c.Mxxprison##c.Mxxprison)#(c.trend##c.trend)                           ///
>                 (c.Mxxpolice##c.Mxxpolice)#(c.trend##c.trend)                           ///
>                 (c.Mxxunemp##c.Mxxunemp )#(c.trend##c.trend)                            ///
>                 (c.Mxxincome##c.Mxxincome)#(c.trend##c.trend)                           ///
>                 (c.Mxxpover##c.Mxxpover )#(c.trend##c.trend)                            ///
>                 (c.Mxxafdc15##c.Mxxafdc15)#(c.trend##c.trend)                           ///
>                 (c.Mxxgunlaw##c.Mxxgunlaw)#(c.trend##c.trend)                           ///
>                 (c.Mxxbeer##c.Mxxbeer)#(c.trend##c.trend)                                       ///
>                 (c.xxprison0##c.xxprison0)#(c.trend##c.trend)                           ///
>                 (c.xxpolice0##c.xxpolice0)#(c.trend##c.trend)                           ///
>                 (c.xxunemp0##c.xxunemp0)#(c.trend##c.trend)                                     ///
>                 (c.xxincome0##c.xxincome0)#(c.trend##c.trend)                           ///
>                 (c.xxpover0##c.xxpover0)#(c.trend##c.trend)                                     ///
>                 (c.xxafdc150##c.xxafdc150)#(c.trend##c.trend)                           ///
>                 (c.xxgunlaw0##c.xxgunlaw0)#(c.trend##c.trend)                           ///
>                 (c.xxbeer0##c.xxbeer0)#(c.trend##c.trend)                                       ///
>                 (c.Dxxprison0##c.Dxxprison0)#(c.trend##c.trend)                         ///
>                 (c.Dxxpolice0##c.Dxxpolice0)#(c.trend##c.trend)                         ///
>                 (c.Dxxunemp0##c.Dxxunemp0)#(c.trend##c.trend)                           ///
>                 (c.Dxxincome0##c.Dxxincome0)#(c.trend##c.trend)                         ///
>                 (c.Dxxpover0##c.Dxxpover0)#(c.trend##c.trend)                           ///
>                 (c.Dxxafdc150##c.Dxxafdc150)#(c.trend##c.trend)                         ///
>                 (c.Dxxgunlaw0##c.Dxxgunlaw0)#(c.trend##c.trend)                         ///
>                 (c.Dxxbeer0##c.Dxxbeer0 )#(c.trend##c.trend)                            ///
>                 i.year                                                                                                          ///
>                 )                                                                                                                       ///
>                 , partial(i.year) robust lopt(lalt corrnum(0) maxupsiter(100))
Partialling out unpenalized controls...
1.  (PDS/CHS) Selecting HD controls for dep var D.lpc_murd...
Selected:
2.  (PDS/CHS) Selecting HD controls for exog regressor D.efamurd...
Selected:  murd0 L.xxprison c.murd0#c.trend cL.xxprison#c.trend
          cL.xxpolice#c.trend c.Mxxincome#c.trend c.Dxxincome0#c.trend


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      heteroskedastic
Number of observations:                600
Exogenous (1):                         D.efamurd
High-dim controls (336):               murd0 c.murd0#c.murd0 Dmurd0
                                       c.Dmurd0#c.Dmurd0 D.xxprison D.xxpolice
                                       D.xxunemp D.xxincome D.xxpover
                                       D.xxafdc15 D.xxgunlaw D.xxbeer
                                       cD.xxprison#cD.xxprison
                                       cD.xxprison#cD.xxpolice
                                       cD.xxprison#cD.xxunemp
                                       cD.xxprison#cD.xxincome
                                       cD.xxprison#cD.xxpover
                                       cD.xxprison#cD.xxafdc15
                                       cD.xxprison#cD.xxgunlaw
                                       cD.xxprison#cD.xxbeer
                                       cD.xxpolice#cD.xxpolice
                                       cD.xxpolice#cD.xxunemp
                                       cD.xxpolice#cD.xxincome
                                       cD.xxpolice#cD.xxpover
                                       cD.xxpolice#cD.xxafdc15
                                       cD.xxpolice#cD.xxgunlaw
                                       cD.xxpolice#cD.xxbeer
                                       cD.xxunemp#cD.xxunemp
                                       cD.xxunemp#cD.xxincome
                                       cD.xxunemp#cD.xxpover
                                       cD.xxunemp#cD.xxafdc15
                                       cD.xxunemp#cD.xxgunlaw
                                       cD.xxunemp#cD.xxbeer
                                       cD.xxincome#cD.xxincome
                                       cD.xxincome#cD.xxpover
                                       cD.xxincome#cD.xxafdc15
                                       cD.xxincome#cD.xxgunlaw
                                       cD.xxincome#cD.xxbeer
                                       cD.xxpover#cD.xxpover
                                       cD.xxpover#cD.xxafdc15
                                       cD.xxpover#cD.xxgunlaw
                                       cD.xxpover#cD.xxbeer
                                       cD.xxafdc15#cD.xxafdc15
                                       cD.xxafdc15#cD.xxgunlaw
                                       cD.xxafdc15#cD.xxbeer
                                       cD.xxgunlaw#cD.xxgunlaw
                                       cD.xxgunlaw#cD.xxbeer
                                       cD.xxbeer#cD.xxbeer L.xxprison
                                       cL.xxprison#cL.xxprison L.xxpolice
                                       cL.xxpolice#cL.xxpolice L.xxunemp
                                       cL.xxunemp#cL.xxunemp L.xxincome
                                       cL.xxincome#cL.xxincome L.xxpover
                                       cL.xxpover#cL.xxpover L.xxafdc15
                                       cL.xxafdc15#cL.xxafdc15 L.xxgunlaw
                                       cL.xxgunlaw#cL.xxgunlaw L.xxbeer
                                       cL.xxbeer#cL.xxbeer Mxxprison
                                       c.Mxxprison#c.Mxxprison Mxxpolice
                                       c.Mxxpolice#c.Mxxpolice Mxxunemp
                                       c.Mxxunemp#c.Mxxunemp Mxxincome
                                       c.Mxxincome#c.Mxxincome Mxxpover
                                       c.Mxxpover#c.Mxxpover Mxxafdc15
                                       c.Mxxafdc15#c.Mxxafdc15 Mxxgunlaw
                                       c.Mxxgunlaw#c.Mxxgunlaw Mxxbeer
                                       c.Mxxbeer#c.Mxxbeer xxprison0
                                       c.xxprison0#c.xxprison0 xxpolice0
                                       c.xxpolice0#c.xxpolice0 xxunemp0
                                       c.xxunemp0#c.xxunemp0 xxincome0
                                       c.xxincome0#c.xxincome0 xxpover0
                                       c.xxpover0#c.xxpover0 xxafdc150
                                       c.xxafdc150#c.xxafdc150 xxgunlaw0
                                       c.xxgunlaw0#c.xxgunlaw0 xxbeer0
                                       c.xxbeer0#c.xxbeer0 Dxxprison0
                                       c.Dxxprison0#c.Dxxprison0 Dxxpolice0
                                       c.Dxxpolice0#c.Dxxpolice0 Dxxunemp0
                                       c.Dxxunemp0#c.Dxxunemp0 Dxxincome0
                                       c.Dxxincome0#c.Dxxincome0 Dxxpover0
                                       c.Dxxpover0#c.Dxxpover0 Dxxafdc150
                                       c.Dxxafdc150#c.Dxxafdc150 Dxxgunlaw0
                                       c.Dxxgunlaw0#c.Dxxgunlaw0 Dxxbeer0
                                       c.Dxxbeer0#c.Dxxbeer0 c.murd0#c.trend
                                       c.murd0#c.trend#c.trend
                                       c.murd0#c.murd0#c.trend
                                       c.murd0#c.murd0#c.trend#c.trend
                                       c.Dmurd0#c.trend
                                       c.Dmurd0#c.trend#c.trend
                                       c.Dmurd0#c.Dmurd0#c.trend
                                       c.Dmurd0#c.Dmurd0#c.trend#c.trend
                                       cD.xxprison#c.trend
                                       cD.xxprison#c.trend#c.trend
                                       cD.xxpolice#c.trend
                                       cD.xxpolice#c.trend#c.trend
                                       cD.xxunemp#c.trend
                                       cD.xxunemp#c.trend#c.trend
                                       cD.xxincome#c.trend
                                       cD.xxincome#c.trend#c.trend
                                       cD.xxpover#c.trend
                                       cD.xxpover#c.trend#c.trend
                                       cD.xxafdc15#c.trend
                                       cD.xxafdc15#c.trend#c.trend
                                       cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#c.trend#c.trend
                                       cD.xxbeer#c.trend
                                       cD.xxbeer#c.trend#c.trend
                                       cD.xxprison#cD.xxprison#c.trend
                                       cD.xxprison#cD.xxprison#c.trend#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend#c.trend
                                       cD.xxprison#cD.xxincome#c.trend
                                       cD.xxprison#cD.xxincome#c.trend#c.trend
                                       cD.xxprison#cD.xxpover#c.trend
                                       cD.xxprison#cD.xxpover#c.trend#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend#c.trend
                                       cD.xxincome#cD.xxincome#c.trend
                                       cD.xxincome#cD.xxincome#c.trend#c.trend
                                       cD.xxincome#cD.xxpover#c.trend
                                       cD.xxincome#cD.xxpover#c.trend#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend#c.trend
                                       cD.xxpover#cD.xxpover#c.trend
                                       cD.xxpover#cD.xxpover#c.trend#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend#c.trend
                                       cL.xxprison#c.trend
                                       cL.xxprison#c.trend#c.trend
                                       cL.xxprison#cL.xxprison#c.trend
                                       cL.xxprison#cL.xxprison#c.trend#c.trend
                                       cL.xxpolice#c.trend
                                       cL.xxpolice#c.trend#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend#c.trend
                                       cL.xxunemp#c.trend
                                       cL.xxunemp#c.trend#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend#c.trend
                                       cL.xxincome#c.trend
                                       cL.xxincome#c.trend#c.trend
                                       cL.xxincome#cL.xxincome#c.trend
                                       cL.xxincome#cL.xxincome#c.trend#c.trend
                                       cL.xxpover#c.trend
                                       cL.xxpover#c.trend#c.trend
                                       cL.xxpover#cL.xxpover#c.trend
                                       cL.xxpover#cL.xxpover#c.trend#c.trend
                                       cL.xxafdc15#c.trend
                                       cL.xxafdc15#c.trend#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend#c.trend
                                       cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#c.trend#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend#c.trend
                                       cL.xxbeer#c.trend
                                       cL.xxbeer#c.trend#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend#c.trend
                                       c.Mxxprison#c.trend
                                       c.Mxxprison#c.trend#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend#c.trend
                                       c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.trend#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend#c.trend
                                       c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.trend#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend#c.trend
                                       c.Mxxincome#c.trend
                                       c.Mxxincome#c.trend#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend#c.trend
                                       c.Mxxpover#c.trend
                                       c.Mxxpover#c.trend#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend#c.trend
                                       c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.trend#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend#c.trend
                                       c.xxprison0#c.trend
                                       c.xxprison0#c.trend#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.xxprison0#c.xxprison0#c.trend#c.trend
                                       c.xxpolice0#c.trend
                                       c.xxpolice0#c.trend#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend#c.trend
                                       c.xxunemp0#c.trend
                                       c.xxunemp0#c.trend#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend#c.trend
                                       c.xxincome0#c.trend
                                       c.xxincome0#c.trend#c.trend
                                       c.xxincome0#c.xxincome0#c.trend
                                       c.xxincome0#c.xxincome0#c.trend#c.trend
                                       c.xxpover0#c.trend
                                       c.xxpover0#c.trend#c.trend
                                       c.xxpover0#c.xxpover0#c.trend
                                       c.xxpover0#c.xxpover0#c.trend#c.trend
                                       c.xxafdc150#c.trend
                                       c.xxafdc150#c.trend#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend#c.trend
                                       c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.trend#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend#c.trend
                                       c.xxbeer0#c.trend
                                       c.xxbeer0#c.trend#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend#c.trend
                                       c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.trend#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend#c.trend
                                       c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.trend#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend#c.trend
                                       c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.trend#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend#c.trend
                                       c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.trend#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend#c.trend
Selected controls (7):                 murd0 L.xxprison c.murd0#c.trend
                                       cL.xxprison#c.trend cL.xxpolice#c.trend
                                       c.Mxxincome#c.trend c.Dxxincome0#c.trend
Partialled-out controls (12):          86b.year 87.year 88.year 89.year
                                       90.year 91.year 92.year 93.year 94.year
                                       95.year 96.year 97.year

Structural equation:

OLS using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_murd |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efamurd |
         D1. |   -.3044332    .3340465     -0.91    0.362     -.9591523     .3502859
-------------+----------------------------------------------------------------

OLS using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_murd |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efamurd |
         D1. |   -.1887576    .4254457     -0.44    0.657     -1.022616     .6451007
-------------+----------------------------------------------------------------

OLS with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_murd |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efamurd |
         D1. |   -.1887576     .422697     -0.45    0.655     -1.017228     .6397132
             |
       murd0 |    2.653453    1.828629      1.45    0.147     -.9305946     6.237501
             |
    xxprison |
         L1. |    .0027667    .0509253      0.05    0.957      -.097045     .1025785
             |
     c.murd0#|
     c.trend |   -3.879823    2.220761     -1.75    0.081     -8.232434     .4727883
             |
 cL.xxprison#|
     c.trend |    .0121999    .1389794      0.09    0.930     -.2601947     .2845944
             |
 cL.xxpolice#|
     c.trend |   -.0695053    .1040446     -0.67    0.504     -.2734291     .1344184
             |
 c.Mxxincome#|
     c.trend |    1.028486    17.54036      0.06    0.953     -33.34999     35.40697
             |
          c. |
  Dxxincome0#|
     c.trend |   -16.43936    103.9231     -0.16    0.874     -220.1249     187.2462
             |
        year |
         87  |   -.0947746    .1528971     -0.62    0.535     -.3944473     .2048981
         88  |   -.0706571    .2956472     -0.24    0.811     -.6501151     .5088008
         89  |   -.0689367     .444323     -0.16    0.877     -.9397938     .8019205
         90  |   -.0199241    .5832437     -0.03    0.973     -1.163061     1.123213
         91  |   -.0399221    .7273148     -0.05    0.956     -1.465433     1.385589
         92  |   -.0956864    .8711771     -0.11    0.913     -1.803162     1.611789
         93  |    .0220484     1.01971      0.02    0.983     -1.976546     2.020643
         94  |   -.1746812    1.187311     -0.15    0.883     -2.501769     2.152406
         95  |   -.0439519    1.326211     -0.03    0.974     -2.643278     2.555374
         96  |   -.1236045    1.477591     -0.08    0.933      -3.01963     2.772421
         97  |   -.1466517    1.629865     -0.09    0.928     -3.341128     3.047824
             |
       _cons |    .0516894    .1532147      0.34    0.736      -.248606     .3519847
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    D.efamurd
------------------------------------------------------------------------------
r; t=12.22 21:42:24

. mat b_pdslasso=e(b)
r; t=0.00 21:42:24

.
. * Get union of selected instruments
. global mDS : list global(ymSel) | global(xmSel)
r; t=0.00 21:42:24

.
. * Murder equation with selected controls
. // Original - clustered SEs (but not cluster lasso)
. // reg Dymurd Dmurd $mDS $tdums if trend>0, cluster(statenum)
. // robust, no cluster
. reg Dymurd Dmurd $mDS $tdums if trend>0, robust

Linear regression                               Number of obs     =        600
                                                F(19, 580)        =       2.89
                                                Prob > F          =     0.0000
                                                R-squared         =     0.0514
                                                Root MSE          =     .25999

-------------+----------------------------------------------------------------
             |               Robust
       Dymurd |      Coef.    Std. Err.       t    P>|t|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
       Dmurd |   -.1887576    .4299231     -0.44    0.661     -1.033153     .6556382
       murd0 |    2.653453     1.85989      1.43    0.154     -.9994876     6.306394
     murd0Xt |   -3.879823    2.258725     -1.72    0.086       -8.3161     .5564547
   Lxxprison |    .0027667    .0517959      0.05    0.957     -.0989635      .104497
 LxxprisonXt |    .0121999    .1413552      0.09    0.931     -.2654307     .2898304
 LxxpoliceXt |   -.0695053    .1058233     -0.66    0.512     -.2773489     .1383383
 MxxincomeXt |    1.028486    17.84022      0.06    0.954     -34.01082     36.06779
Dxxincome0Xt |   -16.43936    105.6997     -0.16    0.876     -224.0402     191.1615
   _Iyear_87 |   -.0947746    .1555109     -0.61    0.542     -.4002077     .2106584
   _Iyear_88 |   -.0706571    .3007014     -0.23    0.814     -.6612535     .5199392
   _Iyear_89 |   -.0689367    .4519189     -0.15    0.879     -.9565336     .8186602
   _Iyear_90 |   -.0199241    .5932144     -0.03    0.973     -1.185034     1.145186
   _Iyear_91 |   -.0399221    .7397484     -0.05    0.957     -1.492834      1.41299
   _Iyear_92 |   -.0956864    .8860701     -0.11    0.914     -1.835983     1.644611
   _Iyear_93 |    .0220484    1.037142      0.02    0.983     -2.014963      2.05906
   _Iyear_94 |   -.1746812    1.207609     -0.14    0.885       -2.5465     2.197138
   _Iyear_95 |   -.0439519    1.348883     -0.03    0.974     -2.693242     2.605338
   _Iyear_96 |   -.1236045    1.502851     -0.08    0.934     -3.075298     2.828089
   _Iyear_97 |   -.1466517    1.657728     -0.09    0.930     -3.402532     3.109229
       _cons |    .0516894     .155834      0.33    0.740     -.2543783     .3577571
-------------+----------------------------------------------------------------
r; t=0.03 21:42:24

. mat b_regress=e(b)
r; t=0.00 21:42:24

.
. // sort cols and compare
. // may be diff lengths and include 0s (for dropped base vars)
. // so compare abs values > 0
. mata: st_matrix("b_pdslasso",abs(sort(-abs(st_matrix("b_pdslasso"))',1))')
r; t=0.00 21:42:24

. mata: st_matrix("b_regress",abs(sort(-abs(st_matrix("b_regress"))',1))')
r; t=0.00 21:42:24

. local k1 = colsof(b_pdslasso)
r; t=0.00 21:42:24

. local k2 = colsof(b_regress)
r; t=0.00 21:42:24

. mat b_pdslasso = b_pdslasso[1,1..min(`k1',`k2')]
r; t=0.00 21:42:24

. mat b_regress = b_regress[1,1..min(`k1',`k2')]
r; t=0.00 21:42:24

. assert mreldif(b_pdslasso,b_regress)<1e-6
r; t=0.00 21:42:24

.
. // End replication.
.
. // Run misc options and combinations.
. foreach option1 in " " partial(i.year) pnotpen(i.year) aset(i.year)             {
  2. foreach option2 in " " robust cluster(statenum)                                                 {
  3. foreach option3 in " " fe nocons                                                                                {
  4.         di as text "Options: `option1' `option2' `option3'"
  5.         if "`option1'"=="partial(i.year)" & "`option3'"=="nocons" {
  6.                 // this is illegal so display but don't exit with error
.                 local capnoi cap noi
  7.         }
  8.         else {
  9.                 local capnoi
 10.         }
 11.         `capnoi' pdslasso D.lpc_prop D.efaprop                                                                  ///
>                         (                                                                                                                       /// no trend
>                         c.prop0##c.prop0                                                                                        ///
>                         c.Dprop0##c.Dprop0                                                                                      ///
>                         c.(D.($xx))##c.(D.($xx))                                                                        /// note macro
>                         c.(L.xxprison)##c.(L.xxprison)                                                          ///
>                         c.(L.xxpolice)##c.(L.xxpolice)                                                          ///
>                         c.(L.xxunemp)##c.(L.xxunemp)                                                            ///
>                         c.(L.xxincome)##c.(L.xxincome)                                                          ///
>                         c.(L.xxpover)##c.(L.xxpover)                                                            ///
>                         c.(L.xxafdc15)##c.(L.xxafdc15)                                                          ///
>                         c.(L.xxgunlaw)##c.(L.xxgunlaw)                                                          ///
>                         c.(L.xxbeer)##c.(L.xxbeer)                                                                      ///
>                         c.Mxxprison##c.Mxxprison                                                                        ///
>                         c.Mxxpolice##c.Mxxpolice                                                                        ///
>                         c.Mxxunemp##c.Mxxunemp                                                                          ///
>                         c.Mxxincome##c.Mxxincome                                                                        ///
>                         c.Mxxpover##c.Mxxpover                                                                          ///
>                         c.Mxxafdc15##c.Mxxafdc15                                                                        ///
>                         c.Mxxgunlaw##c.Mxxgunlaw                                                                        ///
>                         c.Mxxbeer##c.Mxxbeer                                                                            ///
>                         c.xxprison0##c.xxprison0                                                                        ///
>                         c.xxpolice0##c.xxpolice0                                                                        ///
>                         c.xxunemp0##c.xxunemp0                                                                          ///
>                         c.xxincome0##c.xxincome0                                                                        ///
>                         c.xxpover0##c.xxpover0                                                                          ///
>                         c.xxafdc150##c.xxafdc150                                                                        ///
>                         c.xxgunlaw0##c.xxgunlaw0                                                                        ///
>                         c.xxbeer0##c.xxbeer0                                                                            ///
>                         c.Dxxprison0##c.Dxxprison0                                                                      ///
>                         c.Dxxpolice0##c.Dxxpolice0                                                                      ///
>                         c.Dxxunemp0##c.Dxxunemp0                                                                        ///
>                         c.Dxxincome0##c.Dxxincome0                                                                      ///
>                         c.Dxxpover0##c.Dxxpover0                                                                        ///
>                         c.Dxxafdc150##c.Dxxafdc150                                                                      ///
>                         c.Dxxgunlaw0##c.Dxxgunlaw0                                                                      ///
>                         c.Dxxbeer0##c.Dxxbeer0                                                                          ///
>                                                                                                                                                 ///
>                         (c.prop0##c.prop0)#(c.trend##c.trend)                                           /// now interacted with trend
>                         (c.Dprop0##c.Dprop0)#(c.trend##c.trend)                                         ///
>                         (c.(D.($xx))##c.(D.($xx)))#(c.trend##c.trend)                           /// note macro
>                         (c.(L.xxprison)##c.(L.xxprison))#(c.trend##c.trend)                     ///
>                         (c.(L.xxpolice)##c.(L.xxpolice))#(c.trend##c.trend)                     ///
>                         (c.(L.xxunemp)##c.(L.xxunemp))#(c.trend##c.trend)                       ///
>                         (c.(L.xxincome)##c.(L.xxincome))#(c.trend##c.trend)                     ///
>                         (c.(L.xxpover)##c.(L.xxpover))#(c.trend##c.trend)                       ///
>                         (c.(L.xxafdc15)##c.(L.xxafdc15))#(c.trend##c.trend)                     ///
>                         (c.(L.xxgunlaw)##c.(L.xxgunlaw))#(c.trend##c.trend)                     ///
>                         (c.(L.xxbeer)##c.(L.xxbeer))#(c.trend##c.trend)                         ///
>                         (c.Mxxprison##c.Mxxprison)#(c.trend##c.trend)                           ///
>                         (c.Mxxpolice##c.Mxxpolice)#(c.trend##c.trend)                           ///
>                         (c.Mxxunemp##c.Mxxunemp )#(c.trend##c.trend)                            ///
>                         (c.Mxxincome##c.Mxxincome)#(c.trend##c.trend)                           ///
>                         (c.Mxxpover##c.Mxxpover )#(c.trend##c.trend)                            ///
>                         (c.Mxxafdc15##c.Mxxafdc15)#(c.trend##c.trend)                           ///
>                         (c.Mxxgunlaw##c.Mxxgunlaw)#(c.trend##c.trend)                           ///
>                         (c.Mxxbeer##c.Mxxbeer)#(c.trend##c.trend)                                       ///
>                         (c.xxprison0##c.xxprison0)#(c.trend##c.trend)                           ///
>                         (c.xxpolice0##c.xxpolice0)#(c.trend##c.trend)                           ///
>                         (c.xxunemp0##c.xxunemp0)#(c.trend##c.trend)                                     ///
>                         (c.xxincome0##c.xxincome0)#(c.trend##c.trend)                           ///
>                         (c.xxpover0##c.xxpover0)#(c.trend##c.trend)                                     ///
>                         (c.xxafdc150##c.xxafdc150)#(c.trend##c.trend)                           ///
>                         (c.xxgunlaw0##c.xxgunlaw0)#(c.trend##c.trend)                           ///
>                         (c.xxbeer0##c.xxbeer0)#(c.trend##c.trend)                                       ///
>                         (c.Dxxprison0##c.Dxxprison0)#(c.trend##c.trend)                         ///
>                         (c.Dxxpolice0##c.Dxxpolice0)#(c.trend##c.trend)                         ///
>                         (c.Dxxunemp0##c.Dxxunemp0)#(c.trend##c.trend)                           ///
>                         (c.Dxxincome0##c.Dxxincome0)#(c.trend##c.trend)                         ///
>                         (c.Dxxpover0##c.Dxxpover0)#(c.trend##c.trend)                           ///
>                         (c.Dxxafdc150##c.Dxxafdc150)#(c.trend##c.trend)                         ///
>                         (c.Dxxgunlaw0##c.Dxxgunlaw0)#(c.trend##c.trend)                         ///
>                         (c.Dxxbeer0##c.Dxxbeer0 )#(c.trend##c.trend)                            ///
>                         i.year                                                                                                          ///
>                         )                                                                                                                       ///
>                         , `option1' `option2' `option3'
 12.         }
 13.         }
 14.         }
Options:
1.  (PDS/CHS) Selecting HD controls for dep var D.lpc_prop...
Selected:  cL.xxunemp#c.trend c.xxafdc150#c.trend 92.year
2.  (PDS/CHS) Selecting HD controls for exog regressor D.efaprop...
Selected:  prop0 cD.xxprison#cD.xxunemp cD.xxincome#cD.xxincome L.xxpolice
          L.xxincome Mxxincome c.Dprop0#c.Dprop0#c.trend#c.trend
          cD.xxunemp#cD.xxunemp#c.trend cL.xxunemp#c.trend
          cL.xxbeer#cL.xxbeer#c.trend c.Mxxpolice#c.Mxxpolice#c.trend
          c.xxprison0#c.xxprison0#c.trend c.Dxxincome0#c.trend
          c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend c.Dxxbeer0#c.trend 89.year
          90.year 91.year 92.year 93.year 96.year 97.year


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      homoskedastic
Number of observations:                600
Exogenous (1):                         D.efaprop
High-dim controls (348):               prop0 c.prop0#c.prop0 Dprop0
                                       c.Dprop0#c.Dprop0 D.xxprison D.xxpolice
                                       D.xxunemp D.xxincome D.xxpover
                                       D.xxafdc15 D.xxgunlaw D.xxbeer
                                       cD.xxprison#cD.xxprison
                                       cD.xxprison#cD.xxpolice
                                       cD.xxprison#cD.xxunemp
                                       cD.xxprison#cD.xxincome
                                       cD.xxprison#cD.xxpover
                                       cD.xxprison#cD.xxafdc15
                                       cD.xxprison#cD.xxgunlaw
                                       cD.xxprison#cD.xxbeer
                                       cD.xxpolice#cD.xxpolice
                                       cD.xxpolice#cD.xxunemp
                                       cD.xxpolice#cD.xxincome
                                       cD.xxpolice#cD.xxpover
                                       cD.xxpolice#cD.xxafdc15
                                       cD.xxpolice#cD.xxgunlaw
                                       cD.xxpolice#cD.xxbeer
                                       cD.xxunemp#cD.xxunemp
                                       cD.xxunemp#cD.xxincome
                                       cD.xxunemp#cD.xxpover
                                       cD.xxunemp#cD.xxafdc15
                                       cD.xxunemp#cD.xxgunlaw
                                       cD.xxunemp#cD.xxbeer
                                       cD.xxincome#cD.xxincome
                                       cD.xxincome#cD.xxpover
                                       cD.xxincome#cD.xxafdc15
                                       cD.xxincome#cD.xxgunlaw
                                       cD.xxincome#cD.xxbeer
                                       cD.xxpover#cD.xxpover
                                       cD.xxpover#cD.xxafdc15
                                       cD.xxpover#cD.xxgunlaw
                                       cD.xxpover#cD.xxbeer
                                       cD.xxafdc15#cD.xxafdc15
                                       cD.xxafdc15#cD.xxgunlaw
                                       cD.xxafdc15#cD.xxbeer
                                       cD.xxgunlaw#cD.xxgunlaw
                                       cD.xxgunlaw#cD.xxbeer
                                       cD.xxbeer#cD.xxbeer L.xxprison
                                       cL.xxprison#cL.xxprison L.xxpolice
                                       cL.xxpolice#cL.xxpolice L.xxunemp
                                       cL.xxunemp#cL.xxunemp L.xxincome
                                       cL.xxincome#cL.xxincome L.xxpover
                                       cL.xxpover#cL.xxpover L.xxafdc15
                                       cL.xxafdc15#cL.xxafdc15 L.xxgunlaw
                                       cL.xxgunlaw#cL.xxgunlaw L.xxbeer
                                       cL.xxbeer#cL.xxbeer Mxxprison
                                       c.Mxxprison#c.Mxxprison Mxxpolice
                                       c.Mxxpolice#c.Mxxpolice Mxxunemp
                                       c.Mxxunemp#c.Mxxunemp Mxxincome
                                       c.Mxxincome#c.Mxxincome Mxxpover
                                       c.Mxxpover#c.Mxxpover Mxxafdc15
                                       c.Mxxafdc15#c.Mxxafdc15 Mxxgunlaw
                                       c.Mxxgunlaw#c.Mxxgunlaw Mxxbeer
                                       c.Mxxbeer#c.Mxxbeer xxprison0
                                       c.xxprison0#c.xxprison0 xxpolice0
                                       c.xxpolice0#c.xxpolice0 xxunemp0
                                       c.xxunemp0#c.xxunemp0 xxincome0
                                       c.xxincome0#c.xxincome0 xxpover0
                                       c.xxpover0#c.xxpover0 xxafdc150
                                       c.xxafdc150#c.xxafdc150 xxgunlaw0
                                       c.xxgunlaw0#c.xxgunlaw0 xxbeer0
                                       c.xxbeer0#c.xxbeer0 Dxxprison0
                                       c.Dxxprison0#c.Dxxprison0 Dxxpolice0
                                       c.Dxxpolice0#c.Dxxpolice0 Dxxunemp0
                                       c.Dxxunemp0#c.Dxxunemp0 Dxxincome0
                                       c.Dxxincome0#c.Dxxincome0 Dxxpover0
                                       c.Dxxpover0#c.Dxxpover0 Dxxafdc150
                                       c.Dxxafdc150#c.Dxxafdc150 Dxxgunlaw0
                                       c.Dxxgunlaw0#c.Dxxgunlaw0 Dxxbeer0
                                       c.Dxxbeer0#c.Dxxbeer0 c.prop0#c.trend
                                       c.prop0#c.trend#c.trend
                                       c.prop0#c.prop0#c.trend
                                       c.prop0#c.prop0#c.trend#c.trend
                                       c.Dprop0#c.trend
                                       c.Dprop0#c.trend#c.trend
                                       c.Dprop0#c.Dprop0#c.trend
                                       c.Dprop0#c.Dprop0#c.trend#c.trend
                                       cD.xxprison#c.trend
                                       cD.xxprison#c.trend#c.trend
                                       cD.xxpolice#c.trend
                                       cD.xxpolice#c.trend#c.trend
                                       cD.xxunemp#c.trend
                                       cD.xxunemp#c.trend#c.trend
                                       cD.xxincome#c.trend
                                       cD.xxincome#c.trend#c.trend
                                       cD.xxpover#c.trend
                                       cD.xxpover#c.trend#c.trend
                                       cD.xxafdc15#c.trend
                                       cD.xxafdc15#c.trend#c.trend
                                       cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#c.trend#c.trend
                                       cD.xxbeer#c.trend
                                       cD.xxbeer#c.trend#c.trend
                                       cD.xxprison#cD.xxprison#c.trend
                                       cD.xxprison#cD.xxprison#c.trend#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend#c.trend
                                       cD.xxprison#cD.xxincome#c.trend
                                       cD.xxprison#cD.xxincome#c.trend#c.trend
                                       cD.xxprison#cD.xxpover#c.trend
                                       cD.xxprison#cD.xxpover#c.trend#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend#c.trend
                                       cD.xxincome#cD.xxincome#c.trend
                                       cD.xxincome#cD.xxincome#c.trend#c.trend
                                       cD.xxincome#cD.xxpover#c.trend
                                       cD.xxincome#cD.xxpover#c.trend#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend#c.trend
                                       cD.xxpover#cD.xxpover#c.trend
                                       cD.xxpover#cD.xxpover#c.trend#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend#c.trend
                                       cL.xxprison#c.trend
                                       cL.xxprison#c.trend#c.trend
                                       cL.xxprison#cL.xxprison#c.trend
                                       cL.xxprison#cL.xxprison#c.trend#c.trend
                                       cL.xxpolice#c.trend
                                       cL.xxpolice#c.trend#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend#c.trend
                                       cL.xxunemp#c.trend
                                       cL.xxunemp#c.trend#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend#c.trend
                                       cL.xxincome#c.trend
                                       cL.xxincome#c.trend#c.trend
                                       cL.xxincome#cL.xxincome#c.trend
                                       cL.xxincome#cL.xxincome#c.trend#c.trend
                                       cL.xxpover#c.trend
                                       cL.xxpover#c.trend#c.trend
                                       cL.xxpover#cL.xxpover#c.trend
                                       cL.xxpover#cL.xxpover#c.trend#c.trend
                                       cL.xxafdc15#c.trend
                                       cL.xxafdc15#c.trend#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend#c.trend
                                       cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#c.trend#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend#c.trend
                                       cL.xxbeer#c.trend
                                       cL.xxbeer#c.trend#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend#c.trend
                                       c.Mxxprison#c.trend
                                       c.Mxxprison#c.trend#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend#c.trend
                                       c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.trend#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend#c.trend
                                       c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.trend#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend#c.trend
                                       c.Mxxincome#c.trend
                                       c.Mxxincome#c.trend#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend#c.trend
                                       c.Mxxpover#c.trend
                                       c.Mxxpover#c.trend#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend#c.trend
                                       c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.trend#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend#c.trend
                                       c.xxprison0#c.trend
                                       c.xxprison0#c.trend#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.xxprison0#c.xxprison0#c.trend#c.trend
                                       c.xxpolice0#c.trend
                                       c.xxpolice0#c.trend#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend#c.trend
                                       c.xxunemp0#c.trend
                                       c.xxunemp0#c.trend#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend#c.trend
                                       c.xxincome0#c.trend
                                       c.xxincome0#c.trend#c.trend
                                       c.xxincome0#c.xxincome0#c.trend
                                       c.xxincome0#c.xxincome0#c.trend#c.trend
                                       c.xxpover0#c.trend
                                       c.xxpover0#c.trend#c.trend
                                       c.xxpover0#c.xxpover0#c.trend
                                       c.xxpover0#c.xxpover0#c.trend#c.trend
                                       c.xxafdc150#c.trend
                                       c.xxafdc150#c.trend#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend#c.trend
                                       c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.trend#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend#c.trend
                                       c.xxbeer0#c.trend
                                       c.xxbeer0#c.trend#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend#c.trend
                                       c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.trend#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend#c.trend
                                       c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.trend#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend#c.trend
                                       c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.trend#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend#c.trend
                                       c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.trend#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend#c.trend
                                       86b.year 87.year 88.year 89.year 90.year
                                       91.year 92.year 93.year 94.year 95.year
                                       96.year 97.year
Selected controls (23):                prop0 cD.xxprison#cD.xxunemp
                                       cD.xxincome#cD.xxincome L.xxpolice
                                       L.xxincome Mxxincome
                                       c.Dprop0#c.Dprop0#c.trend#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend
                                       cL.xxunemp#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.xxafdc150#c.trend c.Dxxincome0#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxbeer0#c.trend 89.year 90.year
                                       91.year 92.year 93.year 96.year 97.year
Unpenalized controls (1):              _cons

Structural equation:

OLS using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.1341758    .0428122     -3.13    0.002     -.2180862    -.0502654
-------------+----------------------------------------------------------------

OLS using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.1862501    .0555889     -3.35    0.001     -.2952024    -.0772978
-------------+----------------------------------------------------------------

OLS with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.1956889    .0530381     -3.69    0.000     -.2996417     -.091736
             |
       prop0 |    .1275964    .0414573      3.08    0.002      .0463416     .2088512
             |
 cD.xxprison#|
  cD.xxunemp |      3.0934    2.974591      1.04    0.298     -2.736691     8.923491
             |
 cD.xxincome#|
 cD.xxincome |   -19429.04    18084.04     -1.07    0.283      -54873.1     16015.02
             |
    xxpolice |
         L1. |   -.0217364    .0213019     -1.02    0.308     -.0634874     .0200145
             |
    xxincome |
         L1. |    22.57804    7.086109      3.19    0.001      8.689523     36.46656
             |
   Mxxincome |   -23.75007    6.849277     -3.47    0.001      -37.1744    -10.32573
             |
    c.Dprop0#|
    c.Dprop0#|
     c.trend#|
     c.trend |   -1.189111    .3625685     -3.28    0.001     -1.899732    -.4784894
             |
  cD.xxunemp#|
  cD.xxunemp#|
     c.trend |      68.083    34.93481      1.95    0.051      -.387969      136.554
             |
  cL.xxunemp#|
     c.trend |   -.6072043    .2359112     -2.57    0.010     -1.069582    -.1448269
             |
   cL.xxbeer#|
   cL.xxbeer#|
     c.trend |   -.1155418    .1836966     -0.63    0.529     -.4755804     .2444969
             |
 c.Mxxpolice#|
 c.Mxxpolice#|
     c.trend |    .0138855    .0184299      0.75    0.451     -.0222364     .0500074
             |
 c.xxprison0#|
 c.xxprison0#|
     c.trend |    .0307773    .0120176      2.56    0.010      .0072232     .0543313
             |
 c.xxafdc150#|
     c.trend |   -.0110052    .0192488     -0.57    0.568     -.0487321     .0267217
             |
          c. |
  Dxxincome0#|
     c.trend |    23.70846    15.77783      1.50    0.133     -7.215512     54.63244
             |
          c. |
  Dxxafdc150#|
          c. |
  Dxxafdc150#|
     c.trend#|
     c.trend |   -.4924875    .6780526     -0.73    0.468     -1.821446     .8364712
             |
  c.Dxxbeer0#|
     c.trend |   -.4432308     .615485     -0.72    0.471     -1.649559     .7630976
             |
        year |
         89  |   -.0018837    .0074461     -0.25    0.800     -.0164778     .0127104
         90  |   -.0015543    .0078372     -0.20    0.843      -.016915     .0138064
         91  |    .0026103    .0082424      0.32    0.751     -.0135445     .0187652
         92  |   -.0383772     .007847     -4.89    0.000     -.0537572    -.0229973
         93  |   -.0286917    .0078866     -3.64    0.000      -.044149    -.0132343
         96  |   -.0532177    .0091573     -5.81    0.000     -.0711657    -.0352698
         97  |   -.0484425    .0103793     -4.67    0.000     -.0687855    -.0280995
             |
       _cons |    .1825626    .2176019      0.84    0.401     -.2439293     .6090544
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    D.efaprop
------------------------------------------------------------------------------
Options:     fe
Fixed effects transformation...
1.  (PDS/CHS) Selecting HD controls for dep var D.lpc_prop...
Selected:  cL.xxafdc15#cL.xxafdc15 cL.xxunemp#c.trend
          cL.xxunemp#cL.xxunemp#c.trend 92.year
2.  (PDS/CHS) Selecting HD controls for exog regressor D.efaprop...
Selected:  D.xxincome cD.xxprison#cD.xxunemp c.prop0#c.trend#c.trend
          c.prop0#c.prop0#c.trend#c.trend cL.xxunemp#cL.xxunemp#c.trend
          cL.xxafdc15#cL.xxafdc15#c.trend cL.xxbeer#cL.xxbeer#c.trend
          c.xxprison0#c.xxprison0#c.trend c.Dxxunemp0#c.Dxxunemp0#c.trend
          c.Dxxincome0#c.trend c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
          89.year 90.year 91.year 92.year 93.year 96.year 97.year


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      homoskedastic
Number of observations:                600
Number of fixed effects:                50
Exogenous (1):                         D.efaprop
High-dim controls (348):               prop0 c.prop0#c.prop0 Dprop0
                                       c.Dprop0#c.Dprop0 D.xxprison D.xxpolice
                                       D.xxunemp D.xxincome D.xxpover
                                       D.xxafdc15 D.xxgunlaw D.xxbeer
                                       cD.xxprison#cD.xxprison
                                       cD.xxprison#cD.xxpolice
                                       cD.xxprison#cD.xxunemp
                                       cD.xxprison#cD.xxincome
                                       cD.xxprison#cD.xxpover
                                       cD.xxprison#cD.xxafdc15
                                       cD.xxprison#cD.xxgunlaw
                                       cD.xxprison#cD.xxbeer
                                       cD.xxpolice#cD.xxpolice
                                       cD.xxpolice#cD.xxunemp
                                       cD.xxpolice#cD.xxincome
                                       cD.xxpolice#cD.xxpover
                                       cD.xxpolice#cD.xxafdc15
                                       cD.xxpolice#cD.xxgunlaw
                                       cD.xxpolice#cD.xxbeer
                                       cD.xxunemp#cD.xxunemp
                                       cD.xxunemp#cD.xxincome
                                       cD.xxunemp#cD.xxpover
                                       cD.xxunemp#cD.xxafdc15
                                       cD.xxunemp#cD.xxgunlaw
                                       cD.xxunemp#cD.xxbeer
                                       cD.xxincome#cD.xxincome
                                       cD.xxincome#cD.xxpover
                                       cD.xxincome#cD.xxafdc15
                                       cD.xxincome#cD.xxgunlaw
                                       cD.xxincome#cD.xxbeer
                                       cD.xxpover#cD.xxpover
                                       cD.xxpover#cD.xxafdc15
                                       cD.xxpover#cD.xxgunlaw
                                       cD.xxpover#cD.xxbeer
                                       cD.xxafdc15#cD.xxafdc15
                                       cD.xxafdc15#cD.xxgunlaw
                                       cD.xxafdc15#cD.xxbeer
                                       cD.xxgunlaw#cD.xxgunlaw
                                       cD.xxgunlaw#cD.xxbeer
                                       cD.xxbeer#cD.xxbeer L.xxprison
                                       cL.xxprison#cL.xxprison L.xxpolice
                                       cL.xxpolice#cL.xxpolice L.xxunemp
                                       cL.xxunemp#cL.xxunemp L.xxincome
                                       cL.xxincome#cL.xxincome L.xxpover
                                       cL.xxpover#cL.xxpover L.xxafdc15
                                       cL.xxafdc15#cL.xxafdc15 L.xxgunlaw
                                       cL.xxgunlaw#cL.xxgunlaw L.xxbeer
                                       cL.xxbeer#cL.xxbeer Mxxprison
                                       c.Mxxprison#c.Mxxprison Mxxpolice
                                       c.Mxxpolice#c.Mxxpolice Mxxunemp
                                       c.Mxxunemp#c.Mxxunemp Mxxincome
                                       c.Mxxincome#c.Mxxincome Mxxpover
                                       c.Mxxpover#c.Mxxpover Mxxafdc15
                                       c.Mxxafdc15#c.Mxxafdc15 Mxxgunlaw
                                       c.Mxxgunlaw#c.Mxxgunlaw Mxxbeer
                                       c.Mxxbeer#c.Mxxbeer xxprison0
                                       c.xxprison0#c.xxprison0 xxpolice0
                                       c.xxpolice0#c.xxpolice0 xxunemp0
                                       c.xxunemp0#c.xxunemp0 xxincome0
                                       c.xxincome0#c.xxincome0 xxpover0
                                       c.xxpover0#c.xxpover0 xxafdc150
                                       c.xxafdc150#c.xxafdc150 xxgunlaw0
                                       c.xxgunlaw0#c.xxgunlaw0 xxbeer0
                                       c.xxbeer0#c.xxbeer0 Dxxprison0
                                       c.Dxxprison0#c.Dxxprison0 Dxxpolice0
                                       c.Dxxpolice0#c.Dxxpolice0 Dxxunemp0
                                       c.Dxxunemp0#c.Dxxunemp0 Dxxincome0
                                       c.Dxxincome0#c.Dxxincome0 Dxxpover0
                                       c.Dxxpover0#c.Dxxpover0 Dxxafdc150
                                       c.Dxxafdc150#c.Dxxafdc150 Dxxgunlaw0
                                       c.Dxxgunlaw0#c.Dxxgunlaw0 Dxxbeer0
                                       c.Dxxbeer0#c.Dxxbeer0 c.prop0#c.trend
                                       c.prop0#c.trend#c.trend
                                       c.prop0#c.prop0#c.trend
                                       c.prop0#c.prop0#c.trend#c.trend
                                       c.Dprop0#c.trend
                                       c.Dprop0#c.trend#c.trend
                                       c.Dprop0#c.Dprop0#c.trend
                                       c.Dprop0#c.Dprop0#c.trend#c.trend
                                       cD.xxprison#c.trend
                                       cD.xxprison#c.trend#c.trend
                                       cD.xxpolice#c.trend
                                       cD.xxpolice#c.trend#c.trend
                                       cD.xxunemp#c.trend
                                       cD.xxunemp#c.trend#c.trend
                                       cD.xxincome#c.trend
                                       cD.xxincome#c.trend#c.trend
                                       cD.xxpover#c.trend
                                       cD.xxpover#c.trend#c.trend
                                       cD.xxafdc15#c.trend
                                       cD.xxafdc15#c.trend#c.trend
                                       cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#c.trend#c.trend
                                       cD.xxbeer#c.trend
                                       cD.xxbeer#c.trend#c.trend
                                       cD.xxprison#cD.xxprison#c.trend
                                       cD.xxprison#cD.xxprison#c.trend#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend#c.trend
                                       cD.xxprison#cD.xxincome#c.trend
                                       cD.xxprison#cD.xxincome#c.trend#c.trend
                                       cD.xxprison#cD.xxpover#c.trend
                                       cD.xxprison#cD.xxpover#c.trend#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend#c.trend
                                       cD.xxincome#cD.xxincome#c.trend
                                       cD.xxincome#cD.xxincome#c.trend#c.trend
                                       cD.xxincome#cD.xxpover#c.trend
                                       cD.xxincome#cD.xxpover#c.trend#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend#c.trend
                                       cD.xxpover#cD.xxpover#c.trend
                                       cD.xxpover#cD.xxpover#c.trend#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend#c.trend
                                       cL.xxprison#c.trend
                                       cL.xxprison#c.trend#c.trend
                                       cL.xxprison#cL.xxprison#c.trend
                                       cL.xxprison#cL.xxprison#c.trend#c.trend
                                       cL.xxpolice#c.trend
                                       cL.xxpolice#c.trend#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend#c.trend
                                       cL.xxunemp#c.trend
                                       cL.xxunemp#c.trend#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend#c.trend
                                       cL.xxincome#c.trend
                                       cL.xxincome#c.trend#c.trend
                                       cL.xxincome#cL.xxincome#c.trend
                                       cL.xxincome#cL.xxincome#c.trend#c.trend
                                       cL.xxpover#c.trend
                                       cL.xxpover#c.trend#c.trend
                                       cL.xxpover#cL.xxpover#c.trend
                                       cL.xxpover#cL.xxpover#c.trend#c.trend
                                       cL.xxafdc15#c.trend
                                       cL.xxafdc15#c.trend#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend#c.trend
                                       cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#c.trend#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend#c.trend
                                       cL.xxbeer#c.trend
                                       cL.xxbeer#c.trend#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend#c.trend
                                       c.Mxxprison#c.trend
                                       c.Mxxprison#c.trend#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend#c.trend
                                       c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.trend#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend#c.trend
                                       c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.trend#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend#c.trend
                                       c.Mxxincome#c.trend
                                       c.Mxxincome#c.trend#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend#c.trend
                                       c.Mxxpover#c.trend
                                       c.Mxxpover#c.trend#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend#c.trend
                                       c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.trend#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend#c.trend
                                       c.xxprison0#c.trend
                                       c.xxprison0#c.trend#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.xxprison0#c.xxprison0#c.trend#c.trend
                                       c.xxpolice0#c.trend
                                       c.xxpolice0#c.trend#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend#c.trend
                                       c.xxunemp0#c.trend
                                       c.xxunemp0#c.trend#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend#c.trend
                                       c.xxincome0#c.trend
                                       c.xxincome0#c.trend#c.trend
                                       c.xxincome0#c.xxincome0#c.trend
                                       c.xxincome0#c.xxincome0#c.trend#c.trend
                                       c.xxpover0#c.trend
                                       c.xxpover0#c.trend#c.trend
                                       c.xxpover0#c.xxpover0#c.trend
                                       c.xxpover0#c.xxpover0#c.trend#c.trend
                                       c.xxafdc150#c.trend
                                       c.xxafdc150#c.trend#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend#c.trend
                                       c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.trend#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend#c.trend
                                       c.xxbeer0#c.trend
                                       c.xxbeer0#c.trend#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend#c.trend
                                       c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.trend#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend#c.trend
                                       c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.trend#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend#c.trend
                                       c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.trend#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend#c.trend
                                       c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.trend#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend#c.trend
                                       86b.year 87.year 88.year 89.year 90.year
                                       91.year 92.year 93.year 94.year 95.year
                                       96.year 97.year
Selected controls (20):                D.xxincome cD.xxprison#cD.xxunemp
                                       cL.xxafdc15#cL.xxafdc15
                                       c.prop0#c.trend#c.trend
                                       c.prop0#c.prop0#c.trend#c.trend
                                       cL.xxunemp#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend
                                       c.Dxxincome0#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       89.year 90.year 91.year 92.year 93.year
                                       96.year 97.year

Structural equation (fixed effects, #groups=50):

OLS using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.1564198    .0617164     -2.53    0.011     -.2773818    -.0354578
-------------+----------------------------------------------------------------

OLS using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |    -.184829    .0751541     -2.46    0.014     -.3321284    -.0375297
-------------+----------------------------------------------------------------

OLS with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.2107865    .0756391     -2.79    0.005     -.3590364    -.0625366
             |
    xxincome |
         D1. |   -13.59428    11.57446     -1.17    0.240     -36.27981     9.091248
             |
 cD.xxprison#|
  cD.xxunemp |    4.446929    3.248478      1.37    0.171      -1.91997     10.81383
             |
 cL.xxafdc15#|
 cL.xxafdc15 |    .0131344    .0186569      0.70    0.481     -.0234325     .0497014
             |
     c.prop0#|
     c.trend#|
     c.trend |    .0494942    .1851277      0.27    0.789     -.3133495     .4123379
             |
     c.prop0#|
     c.prop0#|
     c.trend#|
     c.trend |   -.3519988    .2631329     -1.34    0.181     -.8677299     .1637323
             |
  cL.xxunemp#|
     c.trend |   -.0282544    .8961037     -0.03    0.975     -1.784585     1.728077
             |
  cL.xxunemp#|
  cL.xxunemp#|
     c.trend |   -4.940899    8.467639     -0.58    0.560     -21.53717     11.65537
             |
 cL.xxafdc15#|
 cL.xxafdc15#|
     c.trend |    .0105381     .030399      0.35    0.729     -.0490429      .070119
             |
   cL.xxbeer#|
   cL.xxbeer#|
     c.trend |    .8260327    .4004716      2.06    0.039      .0411228     1.610943
             |
 c.xxprison0#|
 c.xxprison0#|
     c.trend |   -.0051437    .0224803     -0.23    0.819     -.0492042     .0389168
             |
 c.Dxxunemp0#|
 c.Dxxunemp0#|
     c.trend |   -4.841663    96.97646     -0.05    0.960      -194.912     185.2287
             |
          c. |
  Dxxincome0#|
     c.trend |   -12.36979    36.82629     -0.34    0.737     -84.54799     59.80842
             |
          c. |
  Dxxafdc150#|
          c. |
  Dxxafdc150#|
     c.trend#|
     c.trend |   -1.304046    1.039637     -1.25    0.210     -3.341697     .7336055
             |
        year |
         89  |   -.0002653    .0079841     -0.03    0.973     -.0159139     .0153833
         90  |   -.0004137    .0084958     -0.05    0.961     -.0170651     .0162377
         91  |    .0020101    .0090243      0.22    0.824     -.0156772     .0196973
         92  |   -.0411255    .0082625     -4.98    0.000     -.0573198    -.0249313
         93  |   -.0296378    .0084574     -3.50    0.000      -.046214    -.0130616
         96  |   -.0458827    .0094947     -4.83    0.000     -.0644919    -.0272735
         97  |   -.0407131    .0121748     -3.34    0.001     -.0645752     -.016851
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    D.efaprop
------------------------------------------------------------------------------
Options:     nocons
1.  (PDS/CHS) Selecting HD controls for dep var D.lpc_prop...
Selected:  Mxxincome cL.xxunemp#c.trend c.xxafdc150#c.trend 92.year
2.  (PDS/CHS) Selecting HD controls for exog regressor D.efaprop...
Selected:  prop0 cD.xxprison#cD.xxunemp L.xxprison cL.xxpolice#cL.xxpolice
          cL.xxincome#cL.xxincome xxpover0 c.Dprop0#c.Dprop0#c.trend#c.trend
          cD.xxunemp#cD.xxunemp#c.trend cL.xxafdc15#cL.xxafdc15#c.trend
          cL.xxbeer#cL.xxbeer#c.trend c.Mxxpolice#c.Mxxpolice#c.trend
          c.xxprison0#c.xxprison0#c.trend c.Dxxincome0#c.trend
          c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend c.Dxxbeer0#c.trend 90.year
          91.year 92.year 93.year 97.year


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      homoskedastic
Number of observations:                600
Exogenous (1):                         D.efaprop
High-dim controls (348):               prop0 c.prop0#c.prop0 Dprop0
                                       c.Dprop0#c.Dprop0 D.xxprison D.xxpolice
                                       D.xxunemp D.xxincome D.xxpover
                                       D.xxafdc15 D.xxgunlaw D.xxbeer
                                       cD.xxprison#cD.xxprison
                                       cD.xxprison#cD.xxpolice
                                       cD.xxprison#cD.xxunemp
                                       cD.xxprison#cD.xxincome
                                       cD.xxprison#cD.xxpover
                                       cD.xxprison#cD.xxafdc15
                                       cD.xxprison#cD.xxgunlaw
                                       cD.xxprison#cD.xxbeer
                                       cD.xxpolice#cD.xxpolice
                                       cD.xxpolice#cD.xxunemp
                                       cD.xxpolice#cD.xxincome
                                       cD.xxpolice#cD.xxpover
                                       cD.xxpolice#cD.xxafdc15
                                       cD.xxpolice#cD.xxgunlaw
                                       cD.xxpolice#cD.xxbeer
                                       cD.xxunemp#cD.xxunemp
                                       cD.xxunemp#cD.xxincome
                                       cD.xxunemp#cD.xxpover
                                       cD.xxunemp#cD.xxafdc15
                                       cD.xxunemp#cD.xxgunlaw
                                       cD.xxunemp#cD.xxbeer
                                       cD.xxincome#cD.xxincome
                                       cD.xxincome#cD.xxpover
                                       cD.xxincome#cD.xxafdc15
                                       cD.xxincome#cD.xxgunlaw
                                       cD.xxincome#cD.xxbeer
                                       cD.xxpover#cD.xxpover
                                       cD.xxpover#cD.xxafdc15
                                       cD.xxpover#cD.xxgunlaw
                                       cD.xxpover#cD.xxbeer
                                       cD.xxafdc15#cD.xxafdc15
                                       cD.xxafdc15#cD.xxgunlaw
                                       cD.xxafdc15#cD.xxbeer
                                       cD.xxgunlaw#cD.xxgunlaw
                                       cD.xxgunlaw#cD.xxbeer
                                       cD.xxbeer#cD.xxbeer L.xxprison
                                       cL.xxprison#cL.xxprison L.xxpolice
                                       cL.xxpolice#cL.xxpolice L.xxunemp
                                       cL.xxunemp#cL.xxunemp L.xxincome
                                       cL.xxincome#cL.xxincome L.xxpover
                                       cL.xxpover#cL.xxpover L.xxafdc15
                                       cL.xxafdc15#cL.xxafdc15 L.xxgunlaw
                                       cL.xxgunlaw#cL.xxgunlaw L.xxbeer
                                       cL.xxbeer#cL.xxbeer Mxxprison
                                       c.Mxxprison#c.Mxxprison Mxxpolice
                                       c.Mxxpolice#c.Mxxpolice Mxxunemp
                                       c.Mxxunemp#c.Mxxunemp Mxxincome
                                       c.Mxxincome#c.Mxxincome Mxxpover
                                       c.Mxxpover#c.Mxxpover Mxxafdc15
                                       c.Mxxafdc15#c.Mxxafdc15 Mxxgunlaw
                                       c.Mxxgunlaw#c.Mxxgunlaw Mxxbeer
                                       c.Mxxbeer#c.Mxxbeer xxprison0
                                       c.xxprison0#c.xxprison0 xxpolice0
                                       c.xxpolice0#c.xxpolice0 xxunemp0
                                       c.xxunemp0#c.xxunemp0 xxincome0
                                       c.xxincome0#c.xxincome0 xxpover0
                                       c.xxpover0#c.xxpover0 xxafdc150
                                       c.xxafdc150#c.xxafdc150 xxgunlaw0
                                       c.xxgunlaw0#c.xxgunlaw0 xxbeer0
                                       c.xxbeer0#c.xxbeer0 Dxxprison0
                                       c.Dxxprison0#c.Dxxprison0 Dxxpolice0
                                       c.Dxxpolice0#c.Dxxpolice0 Dxxunemp0
                                       c.Dxxunemp0#c.Dxxunemp0 Dxxincome0
                                       c.Dxxincome0#c.Dxxincome0 Dxxpover0
                                       c.Dxxpover0#c.Dxxpover0 Dxxafdc150
                                       c.Dxxafdc150#c.Dxxafdc150 Dxxgunlaw0
                                       c.Dxxgunlaw0#c.Dxxgunlaw0 Dxxbeer0
                                       c.Dxxbeer0#c.Dxxbeer0 c.prop0#c.trend
                                       c.prop0#c.trend#c.trend
                                       c.prop0#c.prop0#c.trend
                                       c.prop0#c.prop0#c.trend#c.trend
                                       c.Dprop0#c.trend
                                       c.Dprop0#c.trend#c.trend
                                       c.Dprop0#c.Dprop0#c.trend
                                       c.Dprop0#c.Dprop0#c.trend#c.trend
                                       cD.xxprison#c.trend
                                       cD.xxprison#c.trend#c.trend
                                       cD.xxpolice#c.trend
                                       cD.xxpolice#c.trend#c.trend
                                       cD.xxunemp#c.trend
                                       cD.xxunemp#c.trend#c.trend
                                       cD.xxincome#c.trend
                                       cD.xxincome#c.trend#c.trend
                                       cD.xxpover#c.trend
                                       cD.xxpover#c.trend#c.trend
                                       cD.xxafdc15#c.trend
                                       cD.xxafdc15#c.trend#c.trend
                                       cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#c.trend#c.trend
                                       cD.xxbeer#c.trend
                                       cD.xxbeer#c.trend#c.trend
                                       cD.xxprison#cD.xxprison#c.trend
                                       cD.xxprison#cD.xxprison#c.trend#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend#c.trend
                                       cD.xxprison#cD.xxincome#c.trend
                                       cD.xxprison#cD.xxincome#c.trend#c.trend
                                       cD.xxprison#cD.xxpover#c.trend
                                       cD.xxprison#cD.xxpover#c.trend#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend#c.trend
                                       cD.xxincome#cD.xxincome#c.trend
                                       cD.xxincome#cD.xxincome#c.trend#c.trend
                                       cD.xxincome#cD.xxpover#c.trend
                                       cD.xxincome#cD.xxpover#c.trend#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend#c.trend
                                       cD.xxpover#cD.xxpover#c.trend
                                       cD.xxpover#cD.xxpover#c.trend#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend#c.trend
                                       cL.xxprison#c.trend
                                       cL.xxprison#c.trend#c.trend
                                       cL.xxprison#cL.xxprison#c.trend
                                       cL.xxprison#cL.xxprison#c.trend#c.trend
                                       cL.xxpolice#c.trend
                                       cL.xxpolice#c.trend#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend#c.trend
                                       cL.xxunemp#c.trend
                                       cL.xxunemp#c.trend#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend#c.trend
                                       cL.xxincome#c.trend
                                       cL.xxincome#c.trend#c.trend
                                       cL.xxincome#cL.xxincome#c.trend
                                       cL.xxincome#cL.xxincome#c.trend#c.trend
                                       cL.xxpover#c.trend
                                       cL.xxpover#c.trend#c.trend
                                       cL.xxpover#cL.xxpover#c.trend
                                       cL.xxpover#cL.xxpover#c.trend#c.trend
                                       cL.xxafdc15#c.trend
                                       cL.xxafdc15#c.trend#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend#c.trend
                                       cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#c.trend#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend#c.trend
                                       cL.xxbeer#c.trend
                                       cL.xxbeer#c.trend#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend#c.trend
                                       c.Mxxprison#c.trend
                                       c.Mxxprison#c.trend#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend#c.trend
                                       c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.trend#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend#c.trend
                                       c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.trend#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend#c.trend
                                       c.Mxxincome#c.trend
                                       c.Mxxincome#c.trend#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend#c.trend
                                       c.Mxxpover#c.trend
                                       c.Mxxpover#c.trend#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend#c.trend
                                       c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.trend#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend#c.trend
                                       c.xxprison0#c.trend
                                       c.xxprison0#c.trend#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.xxprison0#c.xxprison0#c.trend#c.trend
                                       c.xxpolice0#c.trend
                                       c.xxpolice0#c.trend#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend#c.trend
                                       c.xxunemp0#c.trend
                                       c.xxunemp0#c.trend#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend#c.trend
                                       c.xxincome0#c.trend
                                       c.xxincome0#c.trend#c.trend
                                       c.xxincome0#c.xxincome0#c.trend
                                       c.xxincome0#c.xxincome0#c.trend#c.trend
                                       c.xxpover0#c.trend
                                       c.xxpover0#c.trend#c.trend
                                       c.xxpover0#c.xxpover0#c.trend
                                       c.xxpover0#c.xxpover0#c.trend#c.trend
                                       c.xxafdc150#c.trend
                                       c.xxafdc150#c.trend#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend#c.trend
                                       c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.trend#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend#c.trend
                                       c.xxbeer0#c.trend
                                       c.xxbeer0#c.trend#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend#c.trend
                                       c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.trend#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend#c.trend
                                       c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.trend#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend#c.trend
                                       c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.trend#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend#c.trend
                                       c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.trend#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend#c.trend
                                       86b.year 87.year 88.year 89.year 90.year
                                       91.year 92.year 93.year 94.year 95.year
                                       96.year 97.year
Selected controls (23):                prop0 cD.xxprison#cD.xxunemp L.xxprison
                                       cL.xxpolice#cL.xxpolice
                                       cL.xxincome#cL.xxincome Mxxincome
                                       xxpover0
                                       c.Dprop0#c.Dprop0#c.trend#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend
                                       cL.xxunemp#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.xxafdc150#c.trend c.Dxxincome0#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxbeer0#c.trend 90.year 91.year
                                       92.year 93.year 97.year

Structural equation:

OLS using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.1319714    .0405315     -3.26    0.001     -.2114117    -.0525311
-------------+----------------------------------------------------------------

OLS using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |    -.121797     .050542     -2.41    0.016     -.2208574    -.0227365
-------------+----------------------------------------------------------------

OLS with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.1280416    .0491692     -2.60    0.009     -.2244115    -.0316717
             |
       prop0 |    .0606623    .0429506      1.41    0.158     -.0235193      .144844
             |
 cD.xxprison#|
  cD.xxunemp |    2.817717    2.998312      0.94    0.347     -3.058867       8.6943
             |
    xxprison |
         L1. |    .0051591    .0059085      0.87    0.383     -.0064214     .0167397
             |
 cL.xxpolice#|
 cL.xxpolice |   -.0080365    .0110582     -0.73    0.467     -.0297102     .0136372
             |
 cL.xxincome#|
 cL.xxincome |    25.29955    23.99588      1.05    0.292      -21.7315     72.33061
             |
   Mxxincome |   -2.386742    2.375994     -1.00    0.315     -7.043605     2.270121
    xxpover0 |      .18385    .0720426      2.55    0.011       .042649      .325051
             |
    c.Dprop0#|
    c.Dprop0#|
     c.trend#|
     c.trend |    -.961159     .360912     -2.66    0.008     -1.668533    -.2537846
             |
  cD.xxunemp#|
  cD.xxunemp#|
     c.trend |    81.24456    35.99871      2.26    0.024      10.68839     151.8007
             |
  cL.xxunemp#|
     c.trend |   -.6012786    .2442709     -2.46    0.014     -1.080041    -.1225163
             |
 cL.xxafdc15#|
 cL.xxafdc15#|
     c.trend |    .0217072     .021813      1.00    0.320     -.0210455       .06446
             |
   cL.xxbeer#|
   cL.xxbeer#|
     c.trend |   -.0499188    .1837649     -0.27    0.786     -.4100914     .3102538
             |
 c.Mxxpolice#|
 c.Mxxpolice#|
     c.trend |   -.0003914    .0198406     -0.02    0.984     -.0392782     .0384954
             |
 c.xxprison0#|
 c.xxprison0#|
     c.trend |    .0236591    .0127808      1.85    0.064     -.0013909     .0487091
             |
 c.xxafdc150#|
     c.trend |   -.0266799    .0246081     -1.08    0.278      -.074911     .0215512
             |
          c. |
  Dxxincome0#|
     c.trend |    18.38049    16.45463      1.12    0.264        -13.87     50.63098
             |
          c. |
  Dxxafdc150#|
          c. |
  Dxxafdc150#|
     c.trend#|
     c.trend |   -.0101632    .6932622     -0.01    0.988     -1.368932     1.348606
             |
  c.Dxxbeer0#|
     c.trend |   -1.018891    .6514725     -1.56    0.118     -2.295753     .2579719
             |
        year |
         90  |    .0036374    .0076653      0.47    0.635     -.0113863      .018661
         91  |    .0081383    .0080762      1.01    0.314     -.0076907     .0239673
         92  |   -.0336401    .0077828     -4.32    0.000     -.0488942     -.018386
         93  |   -.0186534    .0076627     -2.43    0.015      -.033672    -.0036347
         97  |   -.0115868    .0088234     -1.31    0.189     -.0288803     .0057067
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    D.efaprop
------------------------------------------------------------------------------
Options:   robust
1.  (PDS/CHS) Selecting HD controls for dep var D.lpc_prop...
Selected:  c.prop0#c.trend cL.xxunemp#c.trend cL.xxunemp#cL.xxunemp#c.trend
          c.Mxxpolice#c.Mxxpolice#c.trend c.xxafdc150#c.trend
          c.xxafdc150#c.xxafdc150#c.trend 92.year
2.  (PDS/CHS) Selecting HD controls for exog regressor D.efaprop...
Selected:  prop0 D.xxbeer cD.xxincome#cD.xxincome L.xxprison L.xxpolice
          L.xxincome Mxxincome cD.xxunemp#cD.xxunemp#c.trend cL.xxunemp#c.trend
          cL.xxafdc15#cL.xxafdc15#c.trend cL.xxbeer#cL.xxbeer#c.trend
          c.xxprison0#c.xxprison0#c.trend c.Dxxincome0#c.trend
          c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend c.Dxxbeer0#c.trend 87.year
          90.year 91.year 92.year 93.year 97.year


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      heteroskedastic
Number of observations:                600
Exogenous (1):                         D.efaprop
High-dim controls (348):               prop0 c.prop0#c.prop0 Dprop0
                                       c.Dprop0#c.Dprop0 D.xxprison D.xxpolice
                                       D.xxunemp D.xxincome D.xxpover
                                       D.xxafdc15 D.xxgunlaw D.xxbeer
                                       cD.xxprison#cD.xxprison
                                       cD.xxprison#cD.xxpolice
                                       cD.xxprison#cD.xxunemp
                                       cD.xxprison#cD.xxincome
                                       cD.xxprison#cD.xxpover
                                       cD.xxprison#cD.xxafdc15
                                       cD.xxprison#cD.xxgunlaw
                                       cD.xxprison#cD.xxbeer
                                       cD.xxpolice#cD.xxpolice
                                       cD.xxpolice#cD.xxunemp
                                       cD.xxpolice#cD.xxincome
                                       cD.xxpolice#cD.xxpover
                                       cD.xxpolice#cD.xxafdc15
                                       cD.xxpolice#cD.xxgunlaw
                                       cD.xxpolice#cD.xxbeer
                                       cD.xxunemp#cD.xxunemp
                                       cD.xxunemp#cD.xxincome
                                       cD.xxunemp#cD.xxpover
                                       cD.xxunemp#cD.xxafdc15
                                       cD.xxunemp#cD.xxgunlaw
                                       cD.xxunemp#cD.xxbeer
                                       cD.xxincome#cD.xxincome
                                       cD.xxincome#cD.xxpover
                                       cD.xxincome#cD.xxafdc15
                                       cD.xxincome#cD.xxgunlaw
                                       cD.xxincome#cD.xxbeer
                                       cD.xxpover#cD.xxpover
                                       cD.xxpover#cD.xxafdc15
                                       cD.xxpover#cD.xxgunlaw
                                       cD.xxpover#cD.xxbeer
                                       cD.xxafdc15#cD.xxafdc15
                                       cD.xxafdc15#cD.xxgunlaw
                                       cD.xxafdc15#cD.xxbeer
                                       cD.xxgunlaw#cD.xxgunlaw
                                       cD.xxgunlaw#cD.xxbeer
                                       cD.xxbeer#cD.xxbeer L.xxprison
                                       cL.xxprison#cL.xxprison L.xxpolice
                                       cL.xxpolice#cL.xxpolice L.xxunemp
                                       cL.xxunemp#cL.xxunemp L.xxincome
                                       cL.xxincome#cL.xxincome L.xxpover
                                       cL.xxpover#cL.xxpover L.xxafdc15
                                       cL.xxafdc15#cL.xxafdc15 L.xxgunlaw
                                       cL.xxgunlaw#cL.xxgunlaw L.xxbeer
                                       cL.xxbeer#cL.xxbeer Mxxprison
                                       c.Mxxprison#c.Mxxprison Mxxpolice
                                       c.Mxxpolice#c.Mxxpolice Mxxunemp
                                       c.Mxxunemp#c.Mxxunemp Mxxincome
                                       c.Mxxincome#c.Mxxincome Mxxpover
                                       c.Mxxpover#c.Mxxpover Mxxafdc15
                                       c.Mxxafdc15#c.Mxxafdc15 Mxxgunlaw
                                       c.Mxxgunlaw#c.Mxxgunlaw Mxxbeer
                                       c.Mxxbeer#c.Mxxbeer xxprison0
                                       c.xxprison0#c.xxprison0 xxpolice0
                                       c.xxpolice0#c.xxpolice0 xxunemp0
                                       c.xxunemp0#c.xxunemp0 xxincome0
                                       c.xxincome0#c.xxincome0 xxpover0
                                       c.xxpover0#c.xxpover0 xxafdc150
                                       c.xxafdc150#c.xxafdc150 xxgunlaw0
                                       c.xxgunlaw0#c.xxgunlaw0 xxbeer0
                                       c.xxbeer0#c.xxbeer0 Dxxprison0
                                       c.Dxxprison0#c.Dxxprison0 Dxxpolice0
                                       c.Dxxpolice0#c.Dxxpolice0 Dxxunemp0
                                       c.Dxxunemp0#c.Dxxunemp0 Dxxincome0
                                       c.Dxxincome0#c.Dxxincome0 Dxxpover0
                                       c.Dxxpover0#c.Dxxpover0 Dxxafdc150
                                       c.Dxxafdc150#c.Dxxafdc150 Dxxgunlaw0
                                       c.Dxxgunlaw0#c.Dxxgunlaw0 Dxxbeer0
                                       c.Dxxbeer0#c.Dxxbeer0 c.prop0#c.trend
                                       c.prop0#c.trend#c.trend
                                       c.prop0#c.prop0#c.trend
                                       c.prop0#c.prop0#c.trend#c.trend
                                       c.Dprop0#c.trend
                                       c.Dprop0#c.trend#c.trend
                                       c.Dprop0#c.Dprop0#c.trend
                                       c.Dprop0#c.Dprop0#c.trend#c.trend
                                       cD.xxprison#c.trend
                                       cD.xxprison#c.trend#c.trend
                                       cD.xxpolice#c.trend
                                       cD.xxpolice#c.trend#c.trend
                                       cD.xxunemp#c.trend
                                       cD.xxunemp#c.trend#c.trend
                                       cD.xxincome#c.trend
                                       cD.xxincome#c.trend#c.trend
                                       cD.xxpover#c.trend
                                       cD.xxpover#c.trend#c.trend
                                       cD.xxafdc15#c.trend
                                       cD.xxafdc15#c.trend#c.trend
                                       cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#c.trend#c.trend
                                       cD.xxbeer#c.trend
                                       cD.xxbeer#c.trend#c.trend
                                       cD.xxprison#cD.xxprison#c.trend
                                       cD.xxprison#cD.xxprison#c.trend#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend#c.trend
                                       cD.xxprison#cD.xxincome#c.trend
                                       cD.xxprison#cD.xxincome#c.trend#c.trend
                                       cD.xxprison#cD.xxpover#c.trend
                                       cD.xxprison#cD.xxpover#c.trend#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend#c.trend
                                       cD.xxincome#cD.xxincome#c.trend
                                       cD.xxincome#cD.xxincome#c.trend#c.trend
                                       cD.xxincome#cD.xxpover#c.trend
                                       cD.xxincome#cD.xxpover#c.trend#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend#c.trend
                                       cD.xxpover#cD.xxpover#c.trend
                                       cD.xxpover#cD.xxpover#c.trend#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend#c.trend
                                       cL.xxprison#c.trend
                                       cL.xxprison#c.trend#c.trend
                                       cL.xxprison#cL.xxprison#c.trend
                                       cL.xxprison#cL.xxprison#c.trend#c.trend
                                       cL.xxpolice#c.trend
                                       cL.xxpolice#c.trend#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend#c.trend
                                       cL.xxunemp#c.trend
                                       cL.xxunemp#c.trend#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend#c.trend
                                       cL.xxincome#c.trend
                                       cL.xxincome#c.trend#c.trend
                                       cL.xxincome#cL.xxincome#c.trend
                                       cL.xxincome#cL.xxincome#c.trend#c.trend
                                       cL.xxpover#c.trend
                                       cL.xxpover#c.trend#c.trend
                                       cL.xxpover#cL.xxpover#c.trend
                                       cL.xxpover#cL.xxpover#c.trend#c.trend
                                       cL.xxafdc15#c.trend
                                       cL.xxafdc15#c.trend#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend#c.trend
                                       cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#c.trend#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend#c.trend
                                       cL.xxbeer#c.trend
                                       cL.xxbeer#c.trend#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend#c.trend
                                       c.Mxxprison#c.trend
                                       c.Mxxprison#c.trend#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend#c.trend
                                       c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.trend#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend#c.trend
                                       c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.trend#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend#c.trend
                                       c.Mxxincome#c.trend
                                       c.Mxxincome#c.trend#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend#c.trend
                                       c.Mxxpover#c.trend
                                       c.Mxxpover#c.trend#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend#c.trend
                                       c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.trend#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend#c.trend
                                       c.xxprison0#c.trend
                                       c.xxprison0#c.trend#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.xxprison0#c.xxprison0#c.trend#c.trend
                                       c.xxpolice0#c.trend
                                       c.xxpolice0#c.trend#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend#c.trend
                                       c.xxunemp0#c.trend
                                       c.xxunemp0#c.trend#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend#c.trend
                                       c.xxincome0#c.trend
                                       c.xxincome0#c.trend#c.trend
                                       c.xxincome0#c.xxincome0#c.trend
                                       c.xxincome0#c.xxincome0#c.trend#c.trend
                                       c.xxpover0#c.trend
                                       c.xxpover0#c.trend#c.trend
                                       c.xxpover0#c.xxpover0#c.trend
                                       c.xxpover0#c.xxpover0#c.trend#c.trend
                                       c.xxafdc150#c.trend
                                       c.xxafdc150#c.trend#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend#c.trend
                                       c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.trend#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend#c.trend
                                       c.xxbeer0#c.trend
                                       c.xxbeer0#c.trend#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend#c.trend
                                       c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.trend#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend#c.trend
                                       c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.trend#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend#c.trend
                                       c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.trend#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend#c.trend
                                       c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.trend#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend#c.trend
                                       86b.year 87.year 88.year 89.year 90.year
                                       91.year 92.year 93.year 94.year 95.year
                                       96.year 97.year
Selected controls (26):                prop0 D.xxbeer cD.xxincome#cD.xxincome
                                       L.xxprison L.xxpolice L.xxincome
                                       Mxxincome c.prop0#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend
                                       cL.xxunemp#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.xxafdc150#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend
                                       c.Dxxincome0#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxbeer0#c.trend 87.year 90.year
                                       91.year 92.year 93.year 97.year
Unpenalized controls (1):              _cons

Structural equation:

OLS using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.1104749    .0356529     -3.10    0.002     -.1803533    -.0405964
-------------+----------------------------------------------------------------

OLS using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.0724933    .0412774     -1.76    0.079     -.1533955     .0084088
-------------+----------------------------------------------------------------

OLS with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.1078605    .0464419     -2.32    0.020      -.198885     -.016836
             |
       prop0 |    .1051237    .0426812      2.46    0.014      .0214701     .1887773
             |
      xxbeer |
         D1. |   -.1085068    .2027137     -0.54    0.592     -.5058184     .2888047
             |
 cD.xxincome#|
 cD.xxincome |   -268.9403     24935.2     -0.01    0.991     -49141.03     48603.15
             |
    xxprison |
         L1. |    .0081261     .005844      1.39    0.164      -.003328     .0195802
             |
    xxpolice |
         L1. |   -.0239673    .0196481     -1.22    0.223     -.0624768     .0145422
             |
    xxincome |
         L1. |    12.83443    8.868524      1.45    0.148     -4.547557     30.21642
             |
   Mxxincome |     -14.325    8.552621     -1.67    0.094     -31.08783      2.43783
             |
     c.prop0#|
     c.trend |   -.1913456     .063562     -3.01    0.003     -.3159249    -.0667664
             |
  cD.xxunemp#|
  cD.xxunemp#|
     c.trend |    83.26206     30.5435      2.73    0.006       23.3979     143.1262
             |
  cL.xxunemp#|
     c.trend |   -.3752772    .9161915     -0.41    0.682     -2.170979     1.420425
             |
  cL.xxunemp#|
  cL.xxunemp#|
     c.trend |   -1.542008    7.843038     -0.20    0.844     -16.91408     13.83006
             |
 cL.xxafdc15#|
 cL.xxafdc15#|
     c.trend |    .0272481    .0204591      1.33    0.183     -.0128509     .0673472
             |
   cL.xxbeer#|
   cL.xxbeer#|
     c.trend |   -.1151426    .2084873     -0.55    0.581     -.5237702      .293485
             |
 c.Mxxpolice#|
 c.Mxxpolice#|
     c.trend |    .0048057    .0173796      0.28    0.782     -.0292576      .038869
             |
 c.xxprison0#|
 c.xxprison0#|
     c.trend |    .0217297    .0119895      1.81    0.070     -.0017693     .0452286
             |
 c.xxafdc150#|
     c.trend |   -.0650272     .057338     -1.13    0.257     -.1774077     .0473532
             |
 c.xxafdc150#|
 c.xxafdc150#|
     c.trend |    .0204079    .0342507      0.60    0.551     -.0467222     .0875381
             |
          c. |
  Dxxincome0#|
     c.trend |    17.34056    16.82678      1.03    0.303     -15.63932     50.32043
             |
          c. |
  Dxxafdc150#|
          c. |
  Dxxafdc150#|
     c.trend#|
     c.trend |    .1092866    .6823705      0.16    0.873     -1.228135     1.446708
             |
  c.Dxxbeer0#|
     c.trend |   -.8376048    .6503364     -1.29    0.198     -2.112241      .437031
             |
        year |
         87  |   -.0038404    .0076007     -0.51    0.613     -.0187375     .0110567
         90  |    .0040554    .0078378      0.52    0.605     -.0113063     .0194172
         91  |    .0085694    .0090051      0.95    0.341     -.0090802     .0262191
         92  |   -.0325043    .0090462     -3.59    0.000     -.0502345    -.0147741
         93  |   -.0189694    .0079208     -2.39    0.017     -.0344938     -.003445
         97  |   -.0131792    .0081097     -1.63    0.104      -.029074     .0027155
             |
       _cons |    .2049942     .199114      1.03    0.303     -.1852621     .5952504
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    D.efaprop
------------------------------------------------------------------------------
Options:   robust fe
Fixed effects transformation...
1.  (PDS/CHS) Selecting HD controls for dep var D.lpc_prop...
Selected:  L.xxprison cL.xxafdc15#cL.xxafdc15 c.prop0#c.trend
          cL.xxunemp#c.trend cL.xxunemp#cL.xxunemp#c.trend
          c.Mxxpolice#c.Mxxpolice#c.trend 92.year
2.  (PDS/CHS) Selecting HD controls for exog regressor D.efaprop...
Selected:  D.xxincome cD.xxincome#cD.xxincome c.prop0#c.trend#c.trend
          c.prop0#c.prop0#c.trend#c.trend cL.xxunemp#cL.xxunemp#c.trend
          cL.xxafdc15#cL.xxafdc15#c.trend cL.xxbeer#cL.xxbeer#c.trend
          c.xxprison0#c.xxprison0#c.trend c.Dxxunemp0#c.Dxxunemp0#c.trend
          c.Dxxincome0#c.trend 89.year 90.year 91.year 92.year 93.year 94.year
          96.year 97.year


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      heteroskedastic
Number of observations:                600
Number of fixed effects:                50
Exogenous (1):                         D.efaprop
High-dim controls (348):               prop0 c.prop0#c.prop0 Dprop0
                                       c.Dprop0#c.Dprop0 D.xxprison D.xxpolice
                                       D.xxunemp D.xxincome D.xxpover
                                       D.xxafdc15 D.xxgunlaw D.xxbeer
                                       cD.xxprison#cD.xxprison
                                       cD.xxprison#cD.xxpolice
                                       cD.xxprison#cD.xxunemp
                                       cD.xxprison#cD.xxincome
                                       cD.xxprison#cD.xxpover
                                       cD.xxprison#cD.xxafdc15
                                       cD.xxprison#cD.xxgunlaw
                                       cD.xxprison#cD.xxbeer
                                       cD.xxpolice#cD.xxpolice
                                       cD.xxpolice#cD.xxunemp
                                       cD.xxpolice#cD.xxincome
                                       cD.xxpolice#cD.xxpover
                                       cD.xxpolice#cD.xxafdc15
                                       cD.xxpolice#cD.xxgunlaw
                                       cD.xxpolice#cD.xxbeer
                                       cD.xxunemp#cD.xxunemp
                                       cD.xxunemp#cD.xxincome
                                       cD.xxunemp#cD.xxpover
                                       cD.xxunemp#cD.xxafdc15
                                       cD.xxunemp#cD.xxgunlaw
                                       cD.xxunemp#cD.xxbeer
                                       cD.xxincome#cD.xxincome
                                       cD.xxincome#cD.xxpover
                                       cD.xxincome#cD.xxafdc15
                                       cD.xxincome#cD.xxgunlaw
                                       cD.xxincome#cD.xxbeer
                                       cD.xxpover#cD.xxpover
                                       cD.xxpover#cD.xxafdc15
                                       cD.xxpover#cD.xxgunlaw
                                       cD.xxpover#cD.xxbeer
                                       cD.xxafdc15#cD.xxafdc15
                                       cD.xxafdc15#cD.xxgunlaw
                                       cD.xxafdc15#cD.xxbeer
                                       cD.xxgunlaw#cD.xxgunlaw
                                       cD.xxgunlaw#cD.xxbeer
                                       cD.xxbeer#cD.xxbeer L.xxprison
                                       cL.xxprison#cL.xxprison L.xxpolice
                                       cL.xxpolice#cL.xxpolice L.xxunemp
                                       cL.xxunemp#cL.xxunemp L.xxincome
                                       cL.xxincome#cL.xxincome L.xxpover
                                       cL.xxpover#cL.xxpover L.xxafdc15
                                       cL.xxafdc15#cL.xxafdc15 L.xxgunlaw
                                       cL.xxgunlaw#cL.xxgunlaw L.xxbeer
                                       cL.xxbeer#cL.xxbeer Mxxprison
                                       c.Mxxprison#c.Mxxprison Mxxpolice
                                       c.Mxxpolice#c.Mxxpolice Mxxunemp
                                       c.Mxxunemp#c.Mxxunemp Mxxincome
                                       c.Mxxincome#c.Mxxincome Mxxpover
                                       c.Mxxpover#c.Mxxpover Mxxafdc15
                                       c.Mxxafdc15#c.Mxxafdc15 Mxxgunlaw
                                       c.Mxxgunlaw#c.Mxxgunlaw Mxxbeer
                                       c.Mxxbeer#c.Mxxbeer xxprison0
                                       c.xxprison0#c.xxprison0 xxpolice0
                                       c.xxpolice0#c.xxpolice0 xxunemp0
                                       c.xxunemp0#c.xxunemp0 xxincome0
                                       c.xxincome0#c.xxincome0 xxpover0
                                       c.xxpover0#c.xxpover0 xxafdc150
                                       c.xxafdc150#c.xxafdc150 xxgunlaw0
                                       c.xxgunlaw0#c.xxgunlaw0 xxbeer0
                                       c.xxbeer0#c.xxbeer0 Dxxprison0
                                       c.Dxxprison0#c.Dxxprison0 Dxxpolice0
                                       c.Dxxpolice0#c.Dxxpolice0 Dxxunemp0
                                       c.Dxxunemp0#c.Dxxunemp0 Dxxincome0
                                       c.Dxxincome0#c.Dxxincome0 Dxxpover0
                                       c.Dxxpover0#c.Dxxpover0 Dxxafdc150
                                       c.Dxxafdc150#c.Dxxafdc150 Dxxgunlaw0
                                       c.Dxxgunlaw0#c.Dxxgunlaw0 Dxxbeer0
                                       c.Dxxbeer0#c.Dxxbeer0 c.prop0#c.trend
                                       c.prop0#c.trend#c.trend
                                       c.prop0#c.prop0#c.trend
                                       c.prop0#c.prop0#c.trend#c.trend
                                       c.Dprop0#c.trend
                                       c.Dprop0#c.trend#c.trend
                                       c.Dprop0#c.Dprop0#c.trend
                                       c.Dprop0#c.Dprop0#c.trend#c.trend
                                       cD.xxprison#c.trend
                                       cD.xxprison#c.trend#c.trend
                                       cD.xxpolice#c.trend
                                       cD.xxpolice#c.trend#c.trend
                                       cD.xxunemp#c.trend
                                       cD.xxunemp#c.trend#c.trend
                                       cD.xxincome#c.trend
                                       cD.xxincome#c.trend#c.trend
                                       cD.xxpover#c.trend
                                       cD.xxpover#c.trend#c.trend
                                       cD.xxafdc15#c.trend
                                       cD.xxafdc15#c.trend#c.trend
                                       cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#c.trend#c.trend
                                       cD.xxbeer#c.trend
                                       cD.xxbeer#c.trend#c.trend
                                       cD.xxprison#cD.xxprison#c.trend
                                       cD.xxprison#cD.xxprison#c.trend#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend#c.trend
                                       cD.xxprison#cD.xxincome#c.trend
                                       cD.xxprison#cD.xxincome#c.trend#c.trend
                                       cD.xxprison#cD.xxpover#c.trend
                                       cD.xxprison#cD.xxpover#c.trend#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend#c.trend
                                       cD.xxincome#cD.xxincome#c.trend
                                       cD.xxincome#cD.xxincome#c.trend#c.trend
                                       cD.xxincome#cD.xxpover#c.trend
                                       cD.xxincome#cD.xxpover#c.trend#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend#c.trend
                                       cD.xxpover#cD.xxpover#c.trend
                                       cD.xxpover#cD.xxpover#c.trend#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend#c.trend
                                       cL.xxprison#c.trend
                                       cL.xxprison#c.trend#c.trend
                                       cL.xxprison#cL.xxprison#c.trend
                                       cL.xxprison#cL.xxprison#c.trend#c.trend
                                       cL.xxpolice#c.trend
                                       cL.xxpolice#c.trend#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend#c.trend
                                       cL.xxunemp#c.trend
                                       cL.xxunemp#c.trend#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend#c.trend
                                       cL.xxincome#c.trend
                                       cL.xxincome#c.trend#c.trend
                                       cL.xxincome#cL.xxincome#c.trend
                                       cL.xxincome#cL.xxincome#c.trend#c.trend
                                       cL.xxpover#c.trend
                                       cL.xxpover#c.trend#c.trend
                                       cL.xxpover#cL.xxpover#c.trend
                                       cL.xxpover#cL.xxpover#c.trend#c.trend
                                       cL.xxafdc15#c.trend
                                       cL.xxafdc15#c.trend#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend#c.trend
                                       cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#c.trend#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend#c.trend
                                       cL.xxbeer#c.trend
                                       cL.xxbeer#c.trend#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend#c.trend
                                       c.Mxxprison#c.trend
                                       c.Mxxprison#c.trend#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend#c.trend
                                       c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.trend#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend#c.trend
                                       c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.trend#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend#c.trend
                                       c.Mxxincome#c.trend
                                       c.Mxxincome#c.trend#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend#c.trend
                                       c.Mxxpover#c.trend
                                       c.Mxxpover#c.trend#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend#c.trend
                                       c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.trend#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend#c.trend
                                       c.xxprison0#c.trend
                                       c.xxprison0#c.trend#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.xxprison0#c.xxprison0#c.trend#c.trend
                                       c.xxpolice0#c.trend
                                       c.xxpolice0#c.trend#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend#c.trend
                                       c.xxunemp0#c.trend
                                       c.xxunemp0#c.trend#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend#c.trend
                                       c.xxincome0#c.trend
                                       c.xxincome0#c.trend#c.trend
                                       c.xxincome0#c.xxincome0#c.trend
                                       c.xxincome0#c.xxincome0#c.trend#c.trend
                                       c.xxpover0#c.trend
                                       c.xxpover0#c.trend#c.trend
                                       c.xxpover0#c.xxpover0#c.trend
                                       c.xxpover0#c.xxpover0#c.trend#c.trend
                                       c.xxafdc150#c.trend
                                       c.xxafdc150#c.trend#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend#c.trend
                                       c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.trend#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend#c.trend
                                       c.xxbeer0#c.trend
                                       c.xxbeer0#c.trend#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend#c.trend
                                       c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.trend#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend#c.trend
                                       c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.trend#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend#c.trend
                                       c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.trend#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend#c.trend
                                       c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.trend#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend#c.trend
                                       86b.year 87.year 88.year 89.year 90.year
                                       91.year 92.year 93.year 94.year 95.year
                                       96.year 97.year
Selected controls (23):                D.xxincome cD.xxincome#cD.xxincome
                                       L.xxprison cL.xxafdc15#cL.xxafdc15
                                       c.prop0#c.trend c.prop0#c.trend#c.trend
                                       c.prop0#c.prop0#c.trend#c.trend
                                       cL.xxunemp#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend
                                       c.Dxxincome0#c.trend 89.year 90.year
                                       91.year 92.year 93.year 94.year 96.year
                                       97.year

Structural equation (fixed effects, #groups=50):

OLS using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.1224896    .0505517     -2.42    0.015     -.2215691    -.0234101
-------------+----------------------------------------------------------------

OLS using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.1509495    .0615736     -2.45    0.014     -.2716314    -.0302675
-------------+----------------------------------------------------------------

OLS with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.1652394    .0647876     -2.55    0.011     -.2922208    -.0382579
             |
    xxincome |
         D1. |   -7.758859    18.35395     -0.42    0.672     -43.73194     28.21422
             |
 cD.xxincome#|
 cD.xxincome |   -29585.44    32600.09     -0.91    0.364     -93480.44     34309.56
             |
    xxprison |
         L1. |   -.0088731    .0218327     -0.41    0.684     -.0516644     .0339183
             |
 cL.xxafdc15#|
 cL.xxafdc15 |    .0153863    .0170319      0.90    0.366     -.0179955     .0487681
             |
     c.prop0#|
     c.trend |   -.3789762     .209893     -1.81    0.071     -.7903588     .0324065
             |
     c.prop0#|
     c.trend#|
     c.trend |    .3177836    .2089963      1.52    0.128     -.0918415     .7274087
             |
     c.prop0#|
     c.prop0#|
     c.trend#|
     c.trend |   -.1996753    .2144398     -0.93    0.352     -.6199696      .220619
             |
  cL.xxunemp#|
     c.trend |    .4587773     1.01516      0.45    0.651       -1.5309     2.448454
             |
  cL.xxunemp#|
  cL.xxunemp#|
     c.trend |   -9.577018    8.297946     -1.15    0.248     -25.84069     6.686657
             |
 cL.xxafdc15#|
 cL.xxafdc15#|
     c.trend |    .0314954    .0316841      0.99    0.320     -.0306043     .0935951
             |
   cL.xxbeer#|
   cL.xxbeer#|
     c.trend |    .8218488    .3606204      2.28    0.023      .1150458     1.528652
             |
 c.Mxxpolice#|
 c.Mxxpolice#|
     c.trend |   -.0179044    .0214351     -0.84    0.404     -.0599164     .0241076
             |
 c.xxprison0#|
 c.xxprison0#|
     c.trend |     .001938    .0238925      0.08    0.935     -.0448905     .0487665
             |
 c.Dxxunemp0#|
 c.Dxxunemp0#|
     c.trend |    18.34605    88.89764      0.21    0.836     -155.8901     192.5822
             |
          c. |
  Dxxincome0#|
     c.trend |   -11.25713    41.42349     -0.27    0.786     -92.44569     69.93142
             |
        year |
         89  |   -.0017234    .0071402     -0.24    0.809     -.0157179     .0122711
         90  |   -.0004734    .0088375     -0.05    0.957     -.0177946     .0168477
         91  |    .0040155    .0109942      0.37    0.715     -.0175327     .0255636
         92  |   -.0416207    .0102622     -4.06    0.000     -.0617342    -.0215073
         93  |   -.0326789    .0097531     -3.35    0.001     -.0517946    -.0135632
         94  |   -.0047294    .0090262     -0.52    0.600     -.0224204     .0129615
         96  |    -.048605    .0109767     -4.43    0.000     -.0701189    -.0270911
         97  |   -.0451808    .0127236     -3.55    0.000     -.0701186    -.0202429
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    D.efaprop
------------------------------------------------------------------------------
Options:   robust nocons
1.  (PDS/CHS) Selecting HD controls for dep var D.lpc_prop...
Selected:  c.prop0#c.trend#c.trend c.xxafdc150#c.xxafdc150#c.trend#c.trend
2.  (PDS/CHS) Selecting HD controls for exog regressor D.efaprop...
Selected:  prop0 L.xxprison cL.xxpolice#cL.xxpolice c.Mxxpolice#c.Mxxpolice
          c.xxafdc150#c.xxafdc150 Dxxincome0 cD.xxunemp#cD.xxunemp#c.trend
          cL.xxafdc15#cL.xxafdc15#c.trend cL.xxbeer#cL.xxbeer#c.trend
          c.xxprison0#c.xxprison0#c.trend c.xxbeer0#c.xxbeer0#c.trend
          c.Dxxincome0#c.trend c.Dxxincome0#c.Dxxincome0#c.trend
          c.Dxxbeer0#c.trend 87.year 89.year 90.year 91.year 92.year 93.year
          97.year


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      heteroskedastic
Number of observations:                600
Exogenous (1):                         D.efaprop
High-dim controls (348):               prop0 c.prop0#c.prop0 Dprop0
                                       c.Dprop0#c.Dprop0 D.xxprison D.xxpolice
                                       D.xxunemp D.xxincome D.xxpover
                                       D.xxafdc15 D.xxgunlaw D.xxbeer
                                       cD.xxprison#cD.xxprison
                                       cD.xxprison#cD.xxpolice
                                       cD.xxprison#cD.xxunemp
                                       cD.xxprison#cD.xxincome
                                       cD.xxprison#cD.xxpover
                                       cD.xxprison#cD.xxafdc15
                                       cD.xxprison#cD.xxgunlaw
                                       cD.xxprison#cD.xxbeer
                                       cD.xxpolice#cD.xxpolice
                                       cD.xxpolice#cD.xxunemp
                                       cD.xxpolice#cD.xxincome
                                       cD.xxpolice#cD.xxpover
                                       cD.xxpolice#cD.xxafdc15
                                       cD.xxpolice#cD.xxgunlaw
                                       cD.xxpolice#cD.xxbeer
                                       cD.xxunemp#cD.xxunemp
                                       cD.xxunemp#cD.xxincome
                                       cD.xxunemp#cD.xxpover
                                       cD.xxunemp#cD.xxafdc15
                                       cD.xxunemp#cD.xxgunlaw
                                       cD.xxunemp#cD.xxbeer
                                       cD.xxincome#cD.xxincome
                                       cD.xxincome#cD.xxpover
                                       cD.xxincome#cD.xxafdc15
                                       cD.xxincome#cD.xxgunlaw
                                       cD.xxincome#cD.xxbeer
                                       cD.xxpover#cD.xxpover
                                       cD.xxpover#cD.xxafdc15
                                       cD.xxpover#cD.xxgunlaw
                                       cD.xxpover#cD.xxbeer
                                       cD.xxafdc15#cD.xxafdc15
                                       cD.xxafdc15#cD.xxgunlaw
                                       cD.xxafdc15#cD.xxbeer
                                       cD.xxgunlaw#cD.xxgunlaw
                                       cD.xxgunlaw#cD.xxbeer
                                       cD.xxbeer#cD.xxbeer L.xxprison
                                       cL.xxprison#cL.xxprison L.xxpolice
                                       cL.xxpolice#cL.xxpolice L.xxunemp
                                       cL.xxunemp#cL.xxunemp L.xxincome
                                       cL.xxincome#cL.xxincome L.xxpover
                                       cL.xxpover#cL.xxpover L.xxafdc15
                                       cL.xxafdc15#cL.xxafdc15 L.xxgunlaw
                                       cL.xxgunlaw#cL.xxgunlaw L.xxbeer
                                       cL.xxbeer#cL.xxbeer Mxxprison
                                       c.Mxxprison#c.Mxxprison Mxxpolice
                                       c.Mxxpolice#c.Mxxpolice Mxxunemp
                                       c.Mxxunemp#c.Mxxunemp Mxxincome
                                       c.Mxxincome#c.Mxxincome Mxxpover
                                       c.Mxxpover#c.Mxxpover Mxxafdc15
                                       c.Mxxafdc15#c.Mxxafdc15 Mxxgunlaw
                                       c.Mxxgunlaw#c.Mxxgunlaw Mxxbeer
                                       c.Mxxbeer#c.Mxxbeer xxprison0
                                       c.xxprison0#c.xxprison0 xxpolice0
                                       c.xxpolice0#c.xxpolice0 xxunemp0
                                       c.xxunemp0#c.xxunemp0 xxincome0
                                       c.xxincome0#c.xxincome0 xxpover0
                                       c.xxpover0#c.xxpover0 xxafdc150
                                       c.xxafdc150#c.xxafdc150 xxgunlaw0
                                       c.xxgunlaw0#c.xxgunlaw0 xxbeer0
                                       c.xxbeer0#c.xxbeer0 Dxxprison0
                                       c.Dxxprison0#c.Dxxprison0 Dxxpolice0
                                       c.Dxxpolice0#c.Dxxpolice0 Dxxunemp0
                                       c.Dxxunemp0#c.Dxxunemp0 Dxxincome0
                                       c.Dxxincome0#c.Dxxincome0 Dxxpover0
                                       c.Dxxpover0#c.Dxxpover0 Dxxafdc150
                                       c.Dxxafdc150#c.Dxxafdc150 Dxxgunlaw0
                                       c.Dxxgunlaw0#c.Dxxgunlaw0 Dxxbeer0
                                       c.Dxxbeer0#c.Dxxbeer0 c.prop0#c.trend
                                       c.prop0#c.trend#c.trend
                                       c.prop0#c.prop0#c.trend
                                       c.prop0#c.prop0#c.trend#c.trend
                                       c.Dprop0#c.trend
                                       c.Dprop0#c.trend#c.trend
                                       c.Dprop0#c.Dprop0#c.trend
                                       c.Dprop0#c.Dprop0#c.trend#c.trend
                                       cD.xxprison#c.trend
                                       cD.xxprison#c.trend#c.trend
                                       cD.xxpolice#c.trend
                                       cD.xxpolice#c.trend#c.trend
                                       cD.xxunemp#c.trend
                                       cD.xxunemp#c.trend#c.trend
                                       cD.xxincome#c.trend
                                       cD.xxincome#c.trend#c.trend
                                       cD.xxpover#c.trend
                                       cD.xxpover#c.trend#c.trend
                                       cD.xxafdc15#c.trend
                                       cD.xxafdc15#c.trend#c.trend
                                       cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#c.trend#c.trend
                                       cD.xxbeer#c.trend
                                       cD.xxbeer#c.trend#c.trend
                                       cD.xxprison#cD.xxprison#c.trend
                                       cD.xxprison#cD.xxprison#c.trend#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend#c.trend
                                       cD.xxprison#cD.xxincome#c.trend
                                       cD.xxprison#cD.xxincome#c.trend#c.trend
                                       cD.xxprison#cD.xxpover#c.trend
                                       cD.xxprison#cD.xxpover#c.trend#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend#c.trend
                                       cD.xxincome#cD.xxincome#c.trend
                                       cD.xxincome#cD.xxincome#c.trend#c.trend
                                       cD.xxincome#cD.xxpover#c.trend
                                       cD.xxincome#cD.xxpover#c.trend#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend#c.trend
                                       cD.xxpover#cD.xxpover#c.trend
                                       cD.xxpover#cD.xxpover#c.trend#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend#c.trend
                                       cL.xxprison#c.trend
                                       cL.xxprison#c.trend#c.trend
                                       cL.xxprison#cL.xxprison#c.trend
                                       cL.xxprison#cL.xxprison#c.trend#c.trend
                                       cL.xxpolice#c.trend
                                       cL.xxpolice#c.trend#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend#c.trend
                                       cL.xxunemp#c.trend
                                       cL.xxunemp#c.trend#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend#c.trend
                                       cL.xxincome#c.trend
                                       cL.xxincome#c.trend#c.trend
                                       cL.xxincome#cL.xxincome#c.trend
                                       cL.xxincome#cL.xxincome#c.trend#c.trend
                                       cL.xxpover#c.trend
                                       cL.xxpover#c.trend#c.trend
                                       cL.xxpover#cL.xxpover#c.trend
                                       cL.xxpover#cL.xxpover#c.trend#c.trend
                                       cL.xxafdc15#c.trend
                                       cL.xxafdc15#c.trend#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend#c.trend
                                       cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#c.trend#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend#c.trend
                                       cL.xxbeer#c.trend
                                       cL.xxbeer#c.trend#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend#c.trend
                                       c.Mxxprison#c.trend
                                       c.Mxxprison#c.trend#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend#c.trend
                                       c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.trend#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend#c.trend
                                       c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.trend#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend#c.trend
                                       c.Mxxincome#c.trend
                                       c.Mxxincome#c.trend#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend#c.trend
                                       c.Mxxpover#c.trend
                                       c.Mxxpover#c.trend#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend#c.trend
                                       c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.trend#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend#c.trend
                                       c.xxprison0#c.trend
                                       c.xxprison0#c.trend#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.xxprison0#c.xxprison0#c.trend#c.trend
                                       c.xxpolice0#c.trend
                                       c.xxpolice0#c.trend#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend#c.trend
                                       c.xxunemp0#c.trend
                                       c.xxunemp0#c.trend#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend#c.trend
                                       c.xxincome0#c.trend
                                       c.xxincome0#c.trend#c.trend
                                       c.xxincome0#c.xxincome0#c.trend
                                       c.xxincome0#c.xxincome0#c.trend#c.trend
                                       c.xxpover0#c.trend
                                       c.xxpover0#c.trend#c.trend
                                       c.xxpover0#c.xxpover0#c.trend
                                       c.xxpover0#c.xxpover0#c.trend#c.trend
                                       c.xxafdc150#c.trend
                                       c.xxafdc150#c.trend#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend#c.trend
                                       c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.trend#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend#c.trend
                                       c.xxbeer0#c.trend
                                       c.xxbeer0#c.trend#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend#c.trend
                                       c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.trend#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend#c.trend
                                       c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.trend#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend#c.trend
                                       c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.trend#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend#c.trend
                                       c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.trend#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend#c.trend
                                       86b.year 87.year 88.year 89.year 90.year
                                       91.year 92.year 93.year 94.year 95.year
                                       96.year 97.year
Selected controls (23):                prop0 L.xxprison
                                       cL.xxpolice#cL.xxpolice
                                       c.Mxxpolice#c.Mxxpolice
                                       c.xxafdc150#c.xxafdc150 Dxxincome0
                                       c.prop0#c.trend#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend
                                       c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend
                                       c.Dxxbeer0#c.trend 87.year 89.year
                                       90.year 91.year 92.year 93.year 97.year

Structural equation:

OLS using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.1379155    .0367491     -3.75    0.000     -.2099425    -.0658885
-------------+----------------------------------------------------------------

OLS using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |    -.127781    .0386842     -3.30    0.001     -.2036007    -.0519613
-------------+----------------------------------------------------------------

OLS with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.1571803    .0396627     -3.96    0.000     -.2349177    -.0794429
             |
       prop0 |    .0809726    .0309528      2.62    0.009      .0203063     .1416389
             |
    xxprison |
         L1. |    .0058447    .0058761      0.99    0.320     -.0056723     .0173617
             |
 cL.xxpolice#|
 cL.xxpolice |   -.0229566    .0136082     -1.69    0.092     -.0496281      .003715
             |
 c.Mxxpolice#|
 c.Mxxpolice |    .0298425    .0142079      2.10    0.036      .0019955     .0576894
             |
 c.xxafdc150#|
 c.xxafdc150 |   -.0054622    .0100657     -0.54    0.587     -.0251906     .0142662
             |
  Dxxincome0 |    40.77151    21.74764      1.87    0.061     -1.853085     83.39611
             |
     c.prop0#|
     c.trend#|
     c.trend |   -.2090877    .0601842     -3.47    0.001     -.3270465    -.0911289
             |
  cD.xxunemp#|
  cD.xxunemp#|
     c.trend |    65.08729    27.86897      2.34    0.020      10.46512     119.7095
             |
 cL.xxafdc15#|
 cL.xxafdc15#|
     c.trend |    .0274552    .0208341      1.32    0.188      -.013379     .0682894
             |
   cL.xxbeer#|
   cL.xxbeer#|
     c.trend |    .9049256    .4188043      2.16    0.031      .0840843     1.725767
             |
 c.xxprison0#|
 c.xxprison0#|
     c.trend |    .0198886    .0128747      1.54    0.122     -.0053453     .0451225
             |
 c.xxafdc150#|
 c.xxafdc150#|
     c.trend#|
     c.trend |   -.0059352    .0157281     -0.38    0.706     -.0367618     .0248914
             |
   c.xxbeer0#|
   c.xxbeer0#|
     c.trend |   -.8847003    .3734161     -2.37    0.018     -1.616582    -.1528181
             |
          c. |
  Dxxincome0#|
     c.trend |   -9.095876    32.22346     -0.28    0.778     -72.25269     54.06094
             |
          c. |
  Dxxincome0#|
          c. |
  Dxxincome0#|
     c.trend |   -37526.69     43103.6     -0.87    0.384     -122008.2     46954.82
             |
  c.Dxxbeer0#|
     c.trend |   -.9333864    .6171046     -1.51    0.130     -2.142889     .2761164
             |
        year |
         87  |   -.0000846     .007206     -0.01    0.991      -.014208     .0140389
         89  |    .0015858    .0065448      0.24    0.809     -.0112418     .0144135
         90  |    .0082269    .0075474      1.09    0.276     -.0065658     .0230195
         91  |    .0111038    .0088349      1.26    0.209     -.0062123     .0284198
         92  |   -.0365003    .0088642     -4.12    0.000     -.0538739    -.0191268
         93  |   -.0241705    .0074442     -3.25    0.001     -.0387609      -.00958
         97  |   -.0064322    .0074624     -0.86    0.389     -.0210583     .0081939
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    D.efaprop
------------------------------------------------------------------------------
Options:   cluster(statenum)
1.  (PDS/CHS) Selecting HD controls for dep var D.lpc_prop...
Selected:  Mxxincome xxincome0 c.prop0#c.trend cL.xxunemp#cL.xxunemp#c.trend
          c.Mxxpolice#c.Mxxpolice#c.trend c.xxafdc150#c.trend
          c.xxafdc150#c.xxafdc150#c.trend 92.year
2.  (PDS/CHS) Selecting HD controls for exog regressor D.efaprop...
Selected:  prop0 cD.xxprison#cD.xxbeer L.xxincome cD.xxunemp#cD.xxunemp#c.trend
          cD.xxunemp#cD.xxincome#c.trend#c.trend cD.xxgunlaw#cD.xxbeer#c.trend
          c.Dxxincome0#c.trend 87.year 90.year 91.year 92.year 93.year 94.year
          95.year


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      cluster-lasso
Number of observations:                600
Number of clusters:                     50
Exogenous (1):                         D.efaprop
High-dim controls (348):               prop0 c.prop0#c.prop0 Dprop0
                                       c.Dprop0#c.Dprop0 D.xxprison D.xxpolice
                                       D.xxunemp D.xxincome D.xxpover
                                       D.xxafdc15 D.xxgunlaw D.xxbeer
                                       cD.xxprison#cD.xxprison
                                       cD.xxprison#cD.xxpolice
                                       cD.xxprison#cD.xxunemp
                                       cD.xxprison#cD.xxincome
                                       cD.xxprison#cD.xxpover
                                       cD.xxprison#cD.xxafdc15
                                       cD.xxprison#cD.xxgunlaw
                                       cD.xxprison#cD.xxbeer
                                       cD.xxpolice#cD.xxpolice
                                       cD.xxpolice#cD.xxunemp
                                       cD.xxpolice#cD.xxincome
                                       cD.xxpolice#cD.xxpover
                                       cD.xxpolice#cD.xxafdc15
                                       cD.xxpolice#cD.xxgunlaw
                                       cD.xxpolice#cD.xxbeer
                                       cD.xxunemp#cD.xxunemp
                                       cD.xxunemp#cD.xxincome
                                       cD.xxunemp#cD.xxpover
                                       cD.xxunemp#cD.xxafdc15
                                       cD.xxunemp#cD.xxgunlaw
                                       cD.xxunemp#cD.xxbeer
                                       cD.xxincome#cD.xxincome
                                       cD.xxincome#cD.xxpover
                                       cD.xxincome#cD.xxafdc15
                                       cD.xxincome#cD.xxgunlaw
                                       cD.xxincome#cD.xxbeer
                                       cD.xxpover#cD.xxpover
                                       cD.xxpover#cD.xxafdc15
                                       cD.xxpover#cD.xxgunlaw
                                       cD.xxpover#cD.xxbeer
                                       cD.xxafdc15#cD.xxafdc15
                                       cD.xxafdc15#cD.xxgunlaw
                                       cD.xxafdc15#cD.xxbeer
                                       cD.xxgunlaw#cD.xxgunlaw
                                       cD.xxgunlaw#cD.xxbeer
                                       cD.xxbeer#cD.xxbeer L.xxprison
                                       cL.xxprison#cL.xxprison L.xxpolice
                                       cL.xxpolice#cL.xxpolice L.xxunemp
                                       cL.xxunemp#cL.xxunemp L.xxincome
                                       cL.xxincome#cL.xxincome L.xxpover
                                       cL.xxpover#cL.xxpover L.xxafdc15
                                       cL.xxafdc15#cL.xxafdc15 L.xxgunlaw
                                       cL.xxgunlaw#cL.xxgunlaw L.xxbeer
                                       cL.xxbeer#cL.xxbeer Mxxprison
                                       c.Mxxprison#c.Mxxprison Mxxpolice
                                       c.Mxxpolice#c.Mxxpolice Mxxunemp
                                       c.Mxxunemp#c.Mxxunemp Mxxincome
                                       c.Mxxincome#c.Mxxincome Mxxpover
                                       c.Mxxpover#c.Mxxpover Mxxafdc15
                                       c.Mxxafdc15#c.Mxxafdc15 Mxxgunlaw
                                       c.Mxxgunlaw#c.Mxxgunlaw Mxxbeer
                                       c.Mxxbeer#c.Mxxbeer xxprison0
                                       c.xxprison0#c.xxprison0 xxpolice0
                                       c.xxpolice0#c.xxpolice0 xxunemp0
                                       c.xxunemp0#c.xxunemp0 xxincome0
                                       c.xxincome0#c.xxincome0 xxpover0
                                       c.xxpover0#c.xxpover0 xxafdc150
                                       c.xxafdc150#c.xxafdc150 xxgunlaw0
                                       c.xxgunlaw0#c.xxgunlaw0 xxbeer0
                                       c.xxbeer0#c.xxbeer0 Dxxprison0
                                       c.Dxxprison0#c.Dxxprison0 Dxxpolice0
                                       c.Dxxpolice0#c.Dxxpolice0 Dxxunemp0
                                       c.Dxxunemp0#c.Dxxunemp0 Dxxincome0
                                       c.Dxxincome0#c.Dxxincome0 Dxxpover0
                                       c.Dxxpover0#c.Dxxpover0 Dxxafdc150
                                       c.Dxxafdc150#c.Dxxafdc150 Dxxgunlaw0
                                       c.Dxxgunlaw0#c.Dxxgunlaw0 Dxxbeer0
                                       c.Dxxbeer0#c.Dxxbeer0 c.prop0#c.trend
                                       c.prop0#c.trend#c.trend
                                       c.prop0#c.prop0#c.trend
                                       c.prop0#c.prop0#c.trend#c.trend
                                       c.Dprop0#c.trend
                                       c.Dprop0#c.trend#c.trend
                                       c.Dprop0#c.Dprop0#c.trend
                                       c.Dprop0#c.Dprop0#c.trend#c.trend
                                       cD.xxprison#c.trend
                                       cD.xxprison#c.trend#c.trend
                                       cD.xxpolice#c.trend
                                       cD.xxpolice#c.trend#c.trend
                                       cD.xxunemp#c.trend
                                       cD.xxunemp#c.trend#c.trend
                                       cD.xxincome#c.trend
                                       cD.xxincome#c.trend#c.trend
                                       cD.xxpover#c.trend
                                       cD.xxpover#c.trend#c.trend
                                       cD.xxafdc15#c.trend
                                       cD.xxafdc15#c.trend#c.trend
                                       cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#c.trend#c.trend
                                       cD.xxbeer#c.trend
                                       cD.xxbeer#c.trend#c.trend
                                       cD.xxprison#cD.xxprison#c.trend
                                       cD.xxprison#cD.xxprison#c.trend#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend#c.trend
                                       cD.xxprison#cD.xxincome#c.trend
                                       cD.xxprison#cD.xxincome#c.trend#c.trend
                                       cD.xxprison#cD.xxpover#c.trend
                                       cD.xxprison#cD.xxpover#c.trend#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend#c.trend
                                       cD.xxincome#cD.xxincome#c.trend
                                       cD.xxincome#cD.xxincome#c.trend#c.trend
                                       cD.xxincome#cD.xxpover#c.trend
                                       cD.xxincome#cD.xxpover#c.trend#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend#c.trend
                                       cD.xxpover#cD.xxpover#c.trend
                                       cD.xxpover#cD.xxpover#c.trend#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend#c.trend
                                       cL.xxprison#c.trend
                                       cL.xxprison#c.trend#c.trend
                                       cL.xxprison#cL.xxprison#c.trend
                                       cL.xxprison#cL.xxprison#c.trend#c.trend
                                       cL.xxpolice#c.trend
                                       cL.xxpolice#c.trend#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend#c.trend
                                       cL.xxunemp#c.trend
                                       cL.xxunemp#c.trend#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend#c.trend
                                       cL.xxincome#c.trend
                                       cL.xxincome#c.trend#c.trend
                                       cL.xxincome#cL.xxincome#c.trend
                                       cL.xxincome#cL.xxincome#c.trend#c.trend
                                       cL.xxpover#c.trend
                                       cL.xxpover#c.trend#c.trend
                                       cL.xxpover#cL.xxpover#c.trend
                                       cL.xxpover#cL.xxpover#c.trend#c.trend
                                       cL.xxafdc15#c.trend
                                       cL.xxafdc15#c.trend#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend#c.trend
                                       cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#c.trend#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend#c.trend
                                       cL.xxbeer#c.trend
                                       cL.xxbeer#c.trend#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend#c.trend
                                       c.Mxxprison#c.trend
                                       c.Mxxprison#c.trend#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend#c.trend
                                       c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.trend#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend#c.trend
                                       c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.trend#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend#c.trend
                                       c.Mxxincome#c.trend
                                       c.Mxxincome#c.trend#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend#c.trend
                                       c.Mxxpover#c.trend
                                       c.Mxxpover#c.trend#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend#c.trend
                                       c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.trend#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend#c.trend
                                       c.xxprison0#c.trend
                                       c.xxprison0#c.trend#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.xxprison0#c.xxprison0#c.trend#c.trend
                                       c.xxpolice0#c.trend
                                       c.xxpolice0#c.trend#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend#c.trend
                                       c.xxunemp0#c.trend
                                       c.xxunemp0#c.trend#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend#c.trend
                                       c.xxincome0#c.trend
                                       c.xxincome0#c.trend#c.trend
                                       c.xxincome0#c.xxincome0#c.trend
                                       c.xxincome0#c.xxincome0#c.trend#c.trend
                                       c.xxpover0#c.trend
                                       c.xxpover0#c.trend#c.trend
                                       c.xxpover0#c.xxpover0#c.trend
                                       c.xxpover0#c.xxpover0#c.trend#c.trend
                                       c.xxafdc150#c.trend
                                       c.xxafdc150#c.trend#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend#c.trend
                                       c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.trend#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend#c.trend
                                       c.xxbeer0#c.trend
                                       c.xxbeer0#c.trend#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend#c.trend
                                       c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.trend#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend#c.trend
                                       c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.trend#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend#c.trend
                                       c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.trend#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend#c.trend
                                       c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.trend#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend#c.trend
                                       86b.year 87.year 88.year 89.year 90.year
                                       91.year 92.year 93.year 94.year 95.year
                                       96.year 97.year
Selected controls (21):                prop0 cD.xxprison#cD.xxbeer L.xxincome
                                       Mxxincome xxincome0 c.prop0#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend
                                       c.xxafdc150#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend
                                       c.Dxxincome0#c.trend 87.year 90.year
                                       91.year 92.year 93.year 94.year 95.year
Unpenalized controls (1):              _cons

Structural equation:

OLS using CHS lasso-orthogonalized vars
(Std. Err. adjusted for 50 clusters in statenum)
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.1089538    .0375056     -2.90    0.004     -.1824634    -.0354441
-------------+----------------------------------------------------------------

OLS using CHS post-lasso-orthogonalized vars
(Std. Err. adjusted for 50 clusters in statenum)
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.0996591    .0471049     -2.12    0.034      -.191983    -.0073352
-------------+----------------------------------------------------------------

OLS with PDS-selected variables and full regressor set
(Std. Err. adjusted for 50 clusters in statenum)
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.1222854    .0433432     -2.82    0.005     -.2072365    -.0373344
             |
       prop0 |    .0884841    .0331646      2.67    0.008      .0234827     .1534855
             |
 cD.xxprison#|
   cD.xxbeer |   -.2509887    2.537429     -0.10    0.921     -5.224259     4.722281
             |
    xxincome |
         L1. |    21.26904    6.525578      3.26    0.001      8.479141     34.05894
             |
   Mxxincome |   -4.689568     8.51237     -0.55    0.582     -21.37351     11.99437
   xxincome0 |   -15.37054    4.920162     -3.12    0.002     -25.01388    -5.727201
             |
     c.prop0#|
     c.trend |   -.1140357    .0557385     -2.05    0.041     -.2232811    -.0047903
             |
  cD.xxunemp#|
  cD.xxunemp#|
     c.trend |    93.34036    27.53644      3.39    0.001      39.36994     147.3108
             |
  cD.xxunemp#|
 cD.xxincome#|
     c.trend#|
     c.trend |    4089.957    2805.121      1.46    0.145      -1407.98     9587.893
             |
 cD.xxgunlaw#|
   cD.xxbeer#|
     c.trend |    -.328785     2.24858     -0.15    0.884     -4.735921     4.078351
             |
  cL.xxunemp#|
  cL.xxunemp#|
     c.trend |   -4.415418    1.081663     -4.08    0.000     -6.535439    -2.295397
             |
 c.Mxxpolice#|
 c.Mxxpolice#|
     c.trend |   -.0094359    .0069418     -1.36    0.174     -.0230415     .0041697
             |
 c.xxafdc150#|
     c.trend |   -.0999831    .0357175     -2.80    0.005      -.169988    -.0299781
             |
 c.xxafdc150#|
 c.xxafdc150#|
     c.trend |    .0347214    .0236827      1.47    0.143     -.0116957     .0811386
             |
          c. |
  Dxxincome0#|
     c.trend |   -27.37345    22.20388     -1.23    0.218     -70.89226     16.14536
             |
        year |
         87  |   -.0032165    .0067164     -0.48    0.632     -.0163804     .0099474
         90  |     .012448    .0081842      1.52    0.128     -.0035927     .0284887
         91  |     .020836     .007049      2.96    0.003      .0070202     .0346519
         92  |   -.0178729    .0109631     -1.63    0.103     -.0393601     .0036144
         93  |   -.0013745    .0090993     -0.15    0.880     -.0192088     .0164598
         94  |    .0337148    .0074689      4.51    0.000      .0190759     .0483536
         95  |    .0458226    .0089875      5.10    0.000      .0282073     .0634379
             |
       _cons |   -.0813763    .1515465     -0.54    0.591     -.3784021     .2156494
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    D.efaprop
------------------------------------------------------------------------------
Options:   cluster(statenum) fe
Fixed effects transformation...
1.  (PDS/CHS) Selecting HD controls for dep var D.lpc_prop...
Selected:  L.xxprison cL.xxafdc15#cL.xxafdc15 L.xxbeer
          cL.xxunemp#cL.xxunemp#c.trend
          c.Dxxincome0#c.Dxxincome0#c.trend#c.trend
2.  (PDS/CHS) Selecting HD controls for exog regressor D.efaprop...
Selected:  cD.xxincome#cD.xxincome cD.xxunemp#cD.xxincome#c.trend#c.trend
          cD.xxincome#cD.xxgunlaw#c.trend#c.trend cL.xxbeer#cL.xxbeer#c.trend
          87.year 89.year 90.year 91.year 92.year 93.year 94.year


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      cluster-lasso
Number of observations:                600
Number of clusters:                     50
Number of fixed effects:                50
Exogenous (1):                         D.efaprop
High-dim controls (348):               prop0 c.prop0#c.prop0 Dprop0
                                       c.Dprop0#c.Dprop0 D.xxprison D.xxpolice
                                       D.xxunemp D.xxincome D.xxpover
                                       D.xxafdc15 D.xxgunlaw D.xxbeer
                                       cD.xxprison#cD.xxprison
                                       cD.xxprison#cD.xxpolice
                                       cD.xxprison#cD.xxunemp
                                       cD.xxprison#cD.xxincome
                                       cD.xxprison#cD.xxpover
                                       cD.xxprison#cD.xxafdc15
                                       cD.xxprison#cD.xxgunlaw
                                       cD.xxprison#cD.xxbeer
                                       cD.xxpolice#cD.xxpolice
                                       cD.xxpolice#cD.xxunemp
                                       cD.xxpolice#cD.xxincome
                                       cD.xxpolice#cD.xxpover
                                       cD.xxpolice#cD.xxafdc15
                                       cD.xxpolice#cD.xxgunlaw
                                       cD.xxpolice#cD.xxbeer
                                       cD.xxunemp#cD.xxunemp
                                       cD.xxunemp#cD.xxincome
                                       cD.xxunemp#cD.xxpover
                                       cD.xxunemp#cD.xxafdc15
                                       cD.xxunemp#cD.xxgunlaw
                                       cD.xxunemp#cD.xxbeer
                                       cD.xxincome#cD.xxincome
                                       cD.xxincome#cD.xxpover
                                       cD.xxincome#cD.xxafdc15
                                       cD.xxincome#cD.xxgunlaw
                                       cD.xxincome#cD.xxbeer
                                       cD.xxpover#cD.xxpover
                                       cD.xxpover#cD.xxafdc15
                                       cD.xxpover#cD.xxgunlaw
                                       cD.xxpover#cD.xxbeer
                                       cD.xxafdc15#cD.xxafdc15
                                       cD.xxafdc15#cD.xxgunlaw
                                       cD.xxafdc15#cD.xxbeer
                                       cD.xxgunlaw#cD.xxgunlaw
                                       cD.xxgunlaw#cD.xxbeer
                                       cD.xxbeer#cD.xxbeer L.xxprison
                                       cL.xxprison#cL.xxprison L.xxpolice
                                       cL.xxpolice#cL.xxpolice L.xxunemp
                                       cL.xxunemp#cL.xxunemp L.xxincome
                                       cL.xxincome#cL.xxincome L.xxpover
                                       cL.xxpover#cL.xxpover L.xxafdc15
                                       cL.xxafdc15#cL.xxafdc15 L.xxgunlaw
                                       cL.xxgunlaw#cL.xxgunlaw L.xxbeer
                                       cL.xxbeer#cL.xxbeer Mxxprison
                                       c.Mxxprison#c.Mxxprison Mxxpolice
                                       c.Mxxpolice#c.Mxxpolice Mxxunemp
                                       c.Mxxunemp#c.Mxxunemp Mxxincome
                                       c.Mxxincome#c.Mxxincome Mxxpover
                                       c.Mxxpover#c.Mxxpover Mxxafdc15
                                       c.Mxxafdc15#c.Mxxafdc15 Mxxgunlaw
                                       c.Mxxgunlaw#c.Mxxgunlaw Mxxbeer
                                       c.Mxxbeer#c.Mxxbeer xxprison0
                                       c.xxprison0#c.xxprison0 xxpolice0
                                       c.xxpolice0#c.xxpolice0 xxunemp0
                                       c.xxunemp0#c.xxunemp0 xxincome0
                                       c.xxincome0#c.xxincome0 xxpover0
                                       c.xxpover0#c.xxpover0 xxafdc150
                                       c.xxafdc150#c.xxafdc150 xxgunlaw0
                                       c.xxgunlaw0#c.xxgunlaw0 xxbeer0
                                       c.xxbeer0#c.xxbeer0 Dxxprison0
                                       c.Dxxprison0#c.Dxxprison0 Dxxpolice0
                                       c.Dxxpolice0#c.Dxxpolice0 Dxxunemp0
                                       c.Dxxunemp0#c.Dxxunemp0 Dxxincome0
                                       c.Dxxincome0#c.Dxxincome0 Dxxpover0
                                       c.Dxxpover0#c.Dxxpover0 Dxxafdc150
                                       c.Dxxafdc150#c.Dxxafdc150 Dxxgunlaw0
                                       c.Dxxgunlaw0#c.Dxxgunlaw0 Dxxbeer0
                                       c.Dxxbeer0#c.Dxxbeer0 c.prop0#c.trend
                                       c.prop0#c.trend#c.trend
                                       c.prop0#c.prop0#c.trend
                                       c.prop0#c.prop0#c.trend#c.trend
                                       c.Dprop0#c.trend
                                       c.Dprop0#c.trend#c.trend
                                       c.Dprop0#c.Dprop0#c.trend
                                       c.Dprop0#c.Dprop0#c.trend#c.trend
                                       cD.xxprison#c.trend
                                       cD.xxprison#c.trend#c.trend
                                       cD.xxpolice#c.trend
                                       cD.xxpolice#c.trend#c.trend
                                       cD.xxunemp#c.trend
                                       cD.xxunemp#c.trend#c.trend
                                       cD.xxincome#c.trend
                                       cD.xxincome#c.trend#c.trend
                                       cD.xxpover#c.trend
                                       cD.xxpover#c.trend#c.trend
                                       cD.xxafdc15#c.trend
                                       cD.xxafdc15#c.trend#c.trend
                                       cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#c.trend#c.trend
                                       cD.xxbeer#c.trend
                                       cD.xxbeer#c.trend#c.trend
                                       cD.xxprison#cD.xxprison#c.trend
                                       cD.xxprison#cD.xxprison#c.trend#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend#c.trend
                                       cD.xxprison#cD.xxincome#c.trend
                                       cD.xxprison#cD.xxincome#c.trend#c.trend
                                       cD.xxprison#cD.xxpover#c.trend
                                       cD.xxprison#cD.xxpover#c.trend#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend#c.trend
                                       cD.xxincome#cD.xxincome#c.trend
                                       cD.xxincome#cD.xxincome#c.trend#c.trend
                                       cD.xxincome#cD.xxpover#c.trend
                                       cD.xxincome#cD.xxpover#c.trend#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend#c.trend
                                       cD.xxpover#cD.xxpover#c.trend
                                       cD.xxpover#cD.xxpover#c.trend#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend#c.trend
                                       cL.xxprison#c.trend
                                       cL.xxprison#c.trend#c.trend
                                       cL.xxprison#cL.xxprison#c.trend
                                       cL.xxprison#cL.xxprison#c.trend#c.trend
                                       cL.xxpolice#c.trend
                                       cL.xxpolice#c.trend#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend#c.trend
                                       cL.xxunemp#c.trend
                                       cL.xxunemp#c.trend#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend#c.trend
                                       cL.xxincome#c.trend
                                       cL.xxincome#c.trend#c.trend
                                       cL.xxincome#cL.xxincome#c.trend
                                       cL.xxincome#cL.xxincome#c.trend#c.trend
                                       cL.xxpover#c.trend
                                       cL.xxpover#c.trend#c.trend
                                       cL.xxpover#cL.xxpover#c.trend
                                       cL.xxpover#cL.xxpover#c.trend#c.trend
                                       cL.xxafdc15#c.trend
                                       cL.xxafdc15#c.trend#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend#c.trend
                                       cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#c.trend#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend#c.trend
                                       cL.xxbeer#c.trend
                                       cL.xxbeer#c.trend#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend#c.trend
                                       c.Mxxprison#c.trend
                                       c.Mxxprison#c.trend#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend#c.trend
                                       c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.trend#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend#c.trend
                                       c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.trend#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend#c.trend
                                       c.Mxxincome#c.trend
                                       c.Mxxincome#c.trend#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend#c.trend
                                       c.Mxxpover#c.trend
                                       c.Mxxpover#c.trend#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend#c.trend
                                       c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.trend#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend#c.trend
                                       c.xxprison0#c.trend
                                       c.xxprison0#c.trend#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.xxprison0#c.xxprison0#c.trend#c.trend
                                       c.xxpolice0#c.trend
                                       c.xxpolice0#c.trend#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend#c.trend
                                       c.xxunemp0#c.trend
                                       c.xxunemp0#c.trend#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend#c.trend
                                       c.xxincome0#c.trend
                                       c.xxincome0#c.trend#c.trend
                                       c.xxincome0#c.xxincome0#c.trend
                                       c.xxincome0#c.xxincome0#c.trend#c.trend
                                       c.xxpover0#c.trend
                                       c.xxpover0#c.trend#c.trend
                                       c.xxpover0#c.xxpover0#c.trend
                                       c.xxpover0#c.xxpover0#c.trend#c.trend
                                       c.xxafdc150#c.trend
                                       c.xxafdc150#c.trend#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend#c.trend
                                       c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.trend#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend#c.trend
                                       c.xxbeer0#c.trend
                                       c.xxbeer0#c.trend#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend#c.trend
                                       c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.trend#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend#c.trend
                                       c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.trend#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend#c.trend
                                       c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.trend#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend#c.trend
                                       c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.trend#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend#c.trend
                                       86b.year 87.year 88.year 89.year 90.year
                                       91.year 92.year 93.year 94.year 95.year
                                       96.year 97.year
Selected controls (16):                cD.xxincome#cD.xxincome L.xxprison
                                       cL.xxafdc15#cL.xxafdc15 L.xxbeer
                                       cD.xxunemp#cD.xxincome#c.trend#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend#c.trend
                                       87.year 89.year 90.year 91.year 92.year
                                       93.year 94.year

Structural equation (fixed effects, #groups=50):

OLS using CHS lasso-orthogonalized vars
(Std. Err. adjusted for 50 clusters in statenum)
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.0900702     .059069     -1.52    0.127     -.2058433      .025703
-------------+----------------------------------------------------------------

OLS using CHS post-lasso-orthogonalized vars
(Std. Err. adjusted for 50 clusters in statenum)
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.0558052    .0614682     -0.91    0.364     -.1762807     .0646704
-------------+----------------------------------------------------------------

OLS with PDS-selected variables and full regressor set
(Std. Err. adjusted for 50 clusters in statenum)
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.0544084    .0591521     -0.92    0.358     -.1703443     .0615275
             |
 cD.xxincome#|
 cD.xxincome |   -17962.61       26306     -0.68    0.495     -69521.42     33596.21
             |
    xxprison |
         L1. |   -.0286856    .0170242     -1.68    0.092     -.0620524     .0046813
             |
 cL.xxafdc15#|
 cL.xxafdc15 |    .0239262    .0101867      2.35    0.019      .0039606     .0438917
             |
      xxbeer |
         L1. |    .0888455     .171222      0.52    0.604     -.2467436     .4244345
             |
  cD.xxunemp#|
 cD.xxincome#|
     c.trend#|
     c.trend |   -3637.457    3271.587     -1.11    0.266     -10049.65     2774.735
             |
 cD.xxincome#|
 cD.xxgunlaw#|
     c.trend#|
     c.trend |    11.70052    65.62844      0.18    0.858     -116.9289     140.3299
             |
  cL.xxunemp#|
  cL.xxunemp#|
     c.trend |    -6.80752    3.025821     -2.25    0.024     -12.73802     -.877019
             |
   cL.xxbeer#|
   cL.xxbeer#|
     c.trend |    .4021752    .2822715      1.42    0.154     -.1510668     .9554171
             |
          c. |
  Dxxincome0#|
          c. |
  Dxxincome0#|
     c.trend#|
     c.trend |   -84372.67    49683.06     -1.70    0.089     -181749.7     13004.33
             |
        year |
         87  |   -.0026751    .0070967     -0.38    0.706     -.0165843     .0112341
         89  |    -.003843    .0066131     -0.58    0.561     -.0168045     .0091185
         90  |    .0004309     .008929      0.05    0.962     -.0170696     .0179315
         91  |    .0085252    .0095245      0.90    0.371     -.0101424     .0271928
         92  |    -.032907    .0109432     -3.01    0.003     -.0543552    -.0114588
         93  |   -.0179099     .009053     -1.98    0.048     -.0356534    -.0001664
         94  |    .0097781    .0085537      1.14    0.253     -.0069869     .0265432
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    D.efaprop
------------------------------------------------------------------------------
Options:   cluster(statenum) nocons
1.  (PDS/CHS) Selecting HD controls for dep var D.lpc_prop...
Selected:  c.prop0#c.prop0#c.trend#c.trend
          cL.xxpolice#cL.xxpolice#c.trend#c.trend
          c.xxafdc150#c.xxafdc150#c.trend#c.trend
          c.Dxxincome0#c.Dxxincome0#c.trend#c.trend
2.  (PDS/CHS) Selecting HD controls for exog regressor D.efaprop...
Selected:  prop0 L.xxprison cL.xxpolice#cL.xxpolice cL.xxafdc15#cL.xxafdc15
          Dxxincome0 c.Dxxincome0#c.Dxxincome0 cD.xxprison#c.trend
          cD.xxprison#cD.xxprison#c.trend
          cD.xxprison#cD.xxincome#c.trend#c.trend cD.xxunemp#cD.xxunemp#c.trend
          c.xxbeer0#c.trend c.Dxxincome0#c.trend
          c.Dxxincome0#c.Dxxincome0#c.trend 89.year 90.year 91.year 92.year
          93.year 94.year 95.year


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      cluster-lasso
Number of observations:                600
Number of clusters:                     50
Exogenous (1):                         D.efaprop
High-dim controls (348):               prop0 c.prop0#c.prop0 Dprop0
                                       c.Dprop0#c.Dprop0 D.xxprison D.xxpolice
                                       D.xxunemp D.xxincome D.xxpover
                                       D.xxafdc15 D.xxgunlaw D.xxbeer
                                       cD.xxprison#cD.xxprison
                                       cD.xxprison#cD.xxpolice
                                       cD.xxprison#cD.xxunemp
                                       cD.xxprison#cD.xxincome
                                       cD.xxprison#cD.xxpover
                                       cD.xxprison#cD.xxafdc15
                                       cD.xxprison#cD.xxgunlaw
                                       cD.xxprison#cD.xxbeer
                                       cD.xxpolice#cD.xxpolice
                                       cD.xxpolice#cD.xxunemp
                                       cD.xxpolice#cD.xxincome
                                       cD.xxpolice#cD.xxpover
                                       cD.xxpolice#cD.xxafdc15
                                       cD.xxpolice#cD.xxgunlaw
                                       cD.xxpolice#cD.xxbeer
                                       cD.xxunemp#cD.xxunemp
                                       cD.xxunemp#cD.xxincome
                                       cD.xxunemp#cD.xxpover
                                       cD.xxunemp#cD.xxafdc15
                                       cD.xxunemp#cD.xxgunlaw
                                       cD.xxunemp#cD.xxbeer
                                       cD.xxincome#cD.xxincome
                                       cD.xxincome#cD.xxpover
                                       cD.xxincome#cD.xxafdc15
                                       cD.xxincome#cD.xxgunlaw
                                       cD.xxincome#cD.xxbeer
                                       cD.xxpover#cD.xxpover
                                       cD.xxpover#cD.xxafdc15
                                       cD.xxpover#cD.xxgunlaw
                                       cD.xxpover#cD.xxbeer
                                       cD.xxafdc15#cD.xxafdc15
                                       cD.xxafdc15#cD.xxgunlaw
                                       cD.xxafdc15#cD.xxbeer
                                       cD.xxgunlaw#cD.xxgunlaw
                                       cD.xxgunlaw#cD.xxbeer
                                       cD.xxbeer#cD.xxbeer L.xxprison
                                       cL.xxprison#cL.xxprison L.xxpolice
                                       cL.xxpolice#cL.xxpolice L.xxunemp
                                       cL.xxunemp#cL.xxunemp L.xxincome
                                       cL.xxincome#cL.xxincome L.xxpover
                                       cL.xxpover#cL.xxpover L.xxafdc15
                                       cL.xxafdc15#cL.xxafdc15 L.xxgunlaw
                                       cL.xxgunlaw#cL.xxgunlaw L.xxbeer
                                       cL.xxbeer#cL.xxbeer Mxxprison
                                       c.Mxxprison#c.Mxxprison Mxxpolice
                                       c.Mxxpolice#c.Mxxpolice Mxxunemp
                                       c.Mxxunemp#c.Mxxunemp Mxxincome
                                       c.Mxxincome#c.Mxxincome Mxxpover
                                       c.Mxxpover#c.Mxxpover Mxxafdc15
                                       c.Mxxafdc15#c.Mxxafdc15 Mxxgunlaw
                                       c.Mxxgunlaw#c.Mxxgunlaw Mxxbeer
                                       c.Mxxbeer#c.Mxxbeer xxprison0
                                       c.xxprison0#c.xxprison0 xxpolice0
                                       c.xxpolice0#c.xxpolice0 xxunemp0
                                       c.xxunemp0#c.xxunemp0 xxincome0
                                       c.xxincome0#c.xxincome0 xxpover0
                                       c.xxpover0#c.xxpover0 xxafdc150
                                       c.xxafdc150#c.xxafdc150 xxgunlaw0
                                       c.xxgunlaw0#c.xxgunlaw0 xxbeer0
                                       c.xxbeer0#c.xxbeer0 Dxxprison0
                                       c.Dxxprison0#c.Dxxprison0 Dxxpolice0
                                       c.Dxxpolice0#c.Dxxpolice0 Dxxunemp0
                                       c.Dxxunemp0#c.Dxxunemp0 Dxxincome0
                                       c.Dxxincome0#c.Dxxincome0 Dxxpover0
                                       c.Dxxpover0#c.Dxxpover0 Dxxafdc150
                                       c.Dxxafdc150#c.Dxxafdc150 Dxxgunlaw0
                                       c.Dxxgunlaw0#c.Dxxgunlaw0 Dxxbeer0
                                       c.Dxxbeer0#c.Dxxbeer0 c.prop0#c.trend
                                       c.prop0#c.trend#c.trend
                                       c.prop0#c.prop0#c.trend
                                       c.prop0#c.prop0#c.trend#c.trend
                                       c.Dprop0#c.trend
                                       c.Dprop0#c.trend#c.trend
                                       c.Dprop0#c.Dprop0#c.trend
                                       c.Dprop0#c.Dprop0#c.trend#c.trend
                                       cD.xxprison#c.trend
                                       cD.xxprison#c.trend#c.trend
                                       cD.xxpolice#c.trend
                                       cD.xxpolice#c.trend#c.trend
                                       cD.xxunemp#c.trend
                                       cD.xxunemp#c.trend#c.trend
                                       cD.xxincome#c.trend
                                       cD.xxincome#c.trend#c.trend
                                       cD.xxpover#c.trend
                                       cD.xxpover#c.trend#c.trend
                                       cD.xxafdc15#c.trend
                                       cD.xxafdc15#c.trend#c.trend
                                       cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#c.trend#c.trend
                                       cD.xxbeer#c.trend
                                       cD.xxbeer#c.trend#c.trend
                                       cD.xxprison#cD.xxprison#c.trend
                                       cD.xxprison#cD.xxprison#c.trend#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend#c.trend
                                       cD.xxprison#cD.xxincome#c.trend
                                       cD.xxprison#cD.xxincome#c.trend#c.trend
                                       cD.xxprison#cD.xxpover#c.trend
                                       cD.xxprison#cD.xxpover#c.trend#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend#c.trend
                                       cD.xxincome#cD.xxincome#c.trend
                                       cD.xxincome#cD.xxincome#c.trend#c.trend
                                       cD.xxincome#cD.xxpover#c.trend
                                       cD.xxincome#cD.xxpover#c.trend#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend#c.trend
                                       cD.xxpover#cD.xxpover#c.trend
                                       cD.xxpover#cD.xxpover#c.trend#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend#c.trend
                                       cL.xxprison#c.trend
                                       cL.xxprison#c.trend#c.trend
                                       cL.xxprison#cL.xxprison#c.trend
                                       cL.xxprison#cL.xxprison#c.trend#c.trend
                                       cL.xxpolice#c.trend
                                       cL.xxpolice#c.trend#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend#c.trend
                                       cL.xxunemp#c.trend
                                       cL.xxunemp#c.trend#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend#c.trend
                                       cL.xxincome#c.trend
                                       cL.xxincome#c.trend#c.trend
                                       cL.xxincome#cL.xxincome#c.trend
                                       cL.xxincome#cL.xxincome#c.trend#c.trend
                                       cL.xxpover#c.trend
                                       cL.xxpover#c.trend#c.trend
                                       cL.xxpover#cL.xxpover#c.trend
                                       cL.xxpover#cL.xxpover#c.trend#c.trend
                                       cL.xxafdc15#c.trend
                                       cL.xxafdc15#c.trend#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend#c.trend
                                       cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#c.trend#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend#c.trend
                                       cL.xxbeer#c.trend
                                       cL.xxbeer#c.trend#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend#c.trend
                                       c.Mxxprison#c.trend
                                       c.Mxxprison#c.trend#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend#c.trend
                                       c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.trend#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend#c.trend
                                       c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.trend#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend#c.trend
                                       c.Mxxincome#c.trend
                                       c.Mxxincome#c.trend#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend#c.trend
                                       c.Mxxpover#c.trend
                                       c.Mxxpover#c.trend#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend#c.trend
                                       c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.trend#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend#c.trend
                                       c.xxprison0#c.trend
                                       c.xxprison0#c.trend#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.xxprison0#c.xxprison0#c.trend#c.trend
                                       c.xxpolice0#c.trend
                                       c.xxpolice0#c.trend#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend#c.trend
                                       c.xxunemp0#c.trend
                                       c.xxunemp0#c.trend#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend#c.trend
                                       c.xxincome0#c.trend
                                       c.xxincome0#c.trend#c.trend
                                       c.xxincome0#c.xxincome0#c.trend
                                       c.xxincome0#c.xxincome0#c.trend#c.trend
                                       c.xxpover0#c.trend
                                       c.xxpover0#c.trend#c.trend
                                       c.xxpover0#c.xxpover0#c.trend
                                       c.xxpover0#c.xxpover0#c.trend#c.trend
                                       c.xxafdc150#c.trend
                                       c.xxafdc150#c.trend#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend#c.trend
                                       c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.trend#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend#c.trend
                                       c.xxbeer0#c.trend
                                       c.xxbeer0#c.trend#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend#c.trend
                                       c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.trend#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend#c.trend
                                       c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.trend#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend#c.trend
                                       c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.trend#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend#c.trend
                                       c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.trend#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend#c.trend
                                       86b.year 87.year 88.year 89.year 90.year
                                       91.year 92.year 93.year 94.year 95.year
                                       96.year 97.year
Selected controls (24):                prop0 L.xxprison
                                       cL.xxpolice#cL.xxpolice
                                       cL.xxafdc15#cL.xxafdc15 Dxxincome0
                                       c.Dxxincome0#c.Dxxincome0
                                       c.prop0#c.prop0#c.trend#c.trend
                                       cD.xxprison#c.trend
                                       cD.xxprison#cD.xxprison#c.trend
                                       cD.xxprison#cD.xxincome#c.trend#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend#c.trend
                                       c.xxbeer0#c.trend c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend#c.trend
                                       89.year 90.year 91.year 92.year 93.year
                                       94.year 95.year

Structural equation:

OLS using CHS lasso-orthogonalized vars
(Std. Err. adjusted for 50 clusters in statenum)
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.1416696     .039261     -3.61    0.000     -.2186197    -.0647195
-------------+----------------------------------------------------------------

OLS using CHS post-lasso-orthogonalized vars
(Std. Err. adjusted for 50 clusters in statenum)
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.1675371    .0486207     -3.45    0.001     -.2628319    -.0722422
-------------+----------------------------------------------------------------

OLS with PDS-selected variables and full regressor set
(Std. Err. adjusted for 50 clusters in statenum)
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.1932367    .0494116     -3.91    0.000     -.2900816    -.0963917
             |
       prop0 |    .0939875    .0322455      2.91    0.004      .0307874     .1571876
             |
    xxprison |
         L1. |    .0114699    .0049899      2.30    0.022      .0016899       .02125
             |
 cL.xxpolice#|
 cL.xxpolice |     .006824    .0066037      1.03    0.301      -.006119     .0197669
             |
 cL.xxafdc15#|
 cL.xxafdc15 |   -.0008023    .0075164     -0.11    0.915     -.0155342     .0139297
             |
  Dxxincome0 |    42.06664    18.49959      2.27    0.023      5.808098     78.32517
             |
          c. |
  Dxxincome0#|
c.Dxxincome0 |    50367.24    64398.06      0.78    0.434     -75850.64     176585.1
             |
     c.prop0#|
     c.prop0#|
     c.trend#|
     c.trend |   -.2999405    .0777424     -3.86    0.000     -.4523127    -.1475683
             |
 cD.xxprison#|
     c.trend |   -.0207715    .1326011     -0.16    0.876      -.280665     .2391219
             |
 cD.xxprison#|
 cD.xxprison#|
     c.trend |    .3917216    .3127317      1.25    0.210     -.2212214     1.004665
             |
 cD.xxprison#|
 cD.xxincome#|
     c.trend#|
     c.trend |    -214.356     121.668     -1.76    0.078     -452.8209     24.10895
             |
  cD.xxunemp#|
  cD.xxunemp#|
     c.trend |    64.43873    27.24299      2.37    0.018      11.04345      117.834
             |
 cL.xxpolice#|
 cL.xxpolice#|
     c.trend#|
     c.trend |      -.0089    .0089711     -0.99    0.321     -.0264829      .008683
             |
 c.xxafdc150#|
 c.xxafdc150#|
     c.trend#|
     c.trend |   -.0139055    .0104702     -1.33    0.184     -.0344267     .0066157
             |
   c.xxbeer0#|
     c.trend |   -.0322219    .0493942     -0.65    0.514     -.1290327     .0645889
             |
          c. |
  Dxxincome0#|
     c.trend |   -14.99039    34.17169     -0.44    0.661     -81.96568     51.98489
             |
          c. |
  Dxxincome0#|
          c. |
  Dxxincome0#|
     c.trend |   -244318.4    221494.4     -1.10    0.270     -678439.5     189802.7
             |
          c. |
  Dxxincome0#|
          c. |
  Dxxincome0#|
     c.trend#|
     c.trend |    150386.9    189248.5      0.79    0.427     -220533.4     521307.1
             |
        year |
         89  |    .0120375    .0063568      1.89    0.058     -.0004217     .0244967
         90  |    .0203866    .0088701      2.30    0.022      .0030015     .0377718
         91  |    .0275378    .0084799      3.25    0.001      .0109174     .0441581
         92  |   -.0179638    .0108221     -1.66    0.097     -.0391746     .0032471
         93  |   -.0061075    .0105631     -0.58    0.563     -.0268109     .0145959
         94  |    .0244948    .0075461      3.25    0.001      .0097047      .039285
         95  |    .0394779    .0091007      4.34    0.000      .0216409     .0573149
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    D.efaprop
------------------------------------------------------------------------------
Options: partial(i.year)
Partialling out unpenalized controls...
1.  (PDS/CHS) Selecting HD controls for dep var D.lpc_prop...
Selected:  c.Mxxincome#c.Mxxincome#c.trend#c.trend c.xxincome0#c.trend
2.  (PDS/CHS) Selecting HD controls for exog regressor D.efaprop...
Selected:  prop0 L.xxincome Mxxpolice Mxxincome Dxxincome0
          c.Dprop0#c.Dprop0#c.trend#c.trend cL.xxpolice#c.trend
          cL.xxbeer#cL.xxbeer#c.trend#c.trend c.xxprison0#c.xxprison0#c.trend
          c.xxprison0#c.xxprison0#c.trend#c.trend c.Dxxincome0#c.trend
          c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend c.Dxxbeer0#c.trend


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      homoskedastic
Number of observations:                600
Exogenous (1):                         D.efaprop
High-dim controls (336):               prop0 c.prop0#c.prop0 Dprop0
                                       c.Dprop0#c.Dprop0 D.xxprison D.xxpolice
                                       D.xxunemp D.xxincome D.xxpover
                                       D.xxafdc15 D.xxgunlaw D.xxbeer
                                       cD.xxprison#cD.xxprison
                                       cD.xxprison#cD.xxpolice
                                       cD.xxprison#cD.xxunemp
                                       cD.xxprison#cD.xxincome
                                       cD.xxprison#cD.xxpover
                                       cD.xxprison#cD.xxafdc15
                                       cD.xxprison#cD.xxgunlaw
                                       cD.xxprison#cD.xxbeer
                                       cD.xxpolice#cD.xxpolice
                                       cD.xxpolice#cD.xxunemp
                                       cD.xxpolice#cD.xxincome
                                       cD.xxpolice#cD.xxpover
                                       cD.xxpolice#cD.xxafdc15
                                       cD.xxpolice#cD.xxgunlaw
                                       cD.xxpolice#cD.xxbeer
                                       cD.xxunemp#cD.xxunemp
                                       cD.xxunemp#cD.xxincome
                                       cD.xxunemp#cD.xxpover
                                       cD.xxunemp#cD.xxafdc15
                                       cD.xxunemp#cD.xxgunlaw
                                       cD.xxunemp#cD.xxbeer
                                       cD.xxincome#cD.xxincome
                                       cD.xxincome#cD.xxpover
                                       cD.xxincome#cD.xxafdc15
                                       cD.xxincome#cD.xxgunlaw
                                       cD.xxincome#cD.xxbeer
                                       cD.xxpover#cD.xxpover
                                       cD.xxpover#cD.xxafdc15
                                       cD.xxpover#cD.xxgunlaw
                                       cD.xxpover#cD.xxbeer
                                       cD.xxafdc15#cD.xxafdc15
                                       cD.xxafdc15#cD.xxgunlaw
                                       cD.xxafdc15#cD.xxbeer
                                       cD.xxgunlaw#cD.xxgunlaw
                                       cD.xxgunlaw#cD.xxbeer
                                       cD.xxbeer#cD.xxbeer L.xxprison
                                       cL.xxprison#cL.xxprison L.xxpolice
                                       cL.xxpolice#cL.xxpolice L.xxunemp
                                       cL.xxunemp#cL.xxunemp L.xxincome
                                       cL.xxincome#cL.xxincome L.xxpover
                                       cL.xxpover#cL.xxpover L.xxafdc15
                                       cL.xxafdc15#cL.xxafdc15 L.xxgunlaw
                                       cL.xxgunlaw#cL.xxgunlaw L.xxbeer
                                       cL.xxbeer#cL.xxbeer Mxxprison
                                       c.Mxxprison#c.Mxxprison Mxxpolice
                                       c.Mxxpolice#c.Mxxpolice Mxxunemp
                                       c.Mxxunemp#c.Mxxunemp Mxxincome
                                       c.Mxxincome#c.Mxxincome Mxxpover
                                       c.Mxxpover#c.Mxxpover Mxxafdc15
                                       c.Mxxafdc15#c.Mxxafdc15 Mxxgunlaw
                                       c.Mxxgunlaw#c.Mxxgunlaw Mxxbeer
                                       c.Mxxbeer#c.Mxxbeer xxprison0
                                       c.xxprison0#c.xxprison0 xxpolice0
                                       c.xxpolice0#c.xxpolice0 xxunemp0
                                       c.xxunemp0#c.xxunemp0 xxincome0
                                       c.xxincome0#c.xxincome0 xxpover0
                                       c.xxpover0#c.xxpover0 xxafdc150
                                       c.xxafdc150#c.xxafdc150 xxgunlaw0
                                       c.xxgunlaw0#c.xxgunlaw0 xxbeer0
                                       c.xxbeer0#c.xxbeer0 Dxxprison0
                                       c.Dxxprison0#c.Dxxprison0 Dxxpolice0
                                       c.Dxxpolice0#c.Dxxpolice0 Dxxunemp0
                                       c.Dxxunemp0#c.Dxxunemp0 Dxxincome0
                                       c.Dxxincome0#c.Dxxincome0 Dxxpover0
                                       c.Dxxpover0#c.Dxxpover0 Dxxafdc150
                                       c.Dxxafdc150#c.Dxxafdc150 Dxxgunlaw0
                                       c.Dxxgunlaw0#c.Dxxgunlaw0 Dxxbeer0
                                       c.Dxxbeer0#c.Dxxbeer0 c.prop0#c.trend
                                       c.prop0#c.trend#c.trend
                                       c.prop0#c.prop0#c.trend
                                       c.prop0#c.prop0#c.trend#c.trend
                                       c.Dprop0#c.trend
                                       c.Dprop0#c.trend#c.trend
                                       c.Dprop0#c.Dprop0#c.trend
                                       c.Dprop0#c.Dprop0#c.trend#c.trend
                                       cD.xxprison#c.trend
                                       cD.xxprison#c.trend#c.trend
                                       cD.xxpolice#c.trend
                                       cD.xxpolice#c.trend#c.trend
                                       cD.xxunemp#c.trend
                                       cD.xxunemp#c.trend#c.trend
                                       cD.xxincome#c.trend
                                       cD.xxincome#c.trend#c.trend
                                       cD.xxpover#c.trend
                                       cD.xxpover#c.trend#c.trend
                                       cD.xxafdc15#c.trend
                                       cD.xxafdc15#c.trend#c.trend
                                       cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#c.trend#c.trend
                                       cD.xxbeer#c.trend
                                       cD.xxbeer#c.trend#c.trend
                                       cD.xxprison#cD.xxprison#c.trend
                                       cD.xxprison#cD.xxprison#c.trend#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend#c.trend
                                       cD.xxprison#cD.xxincome#c.trend
                                       cD.xxprison#cD.xxincome#c.trend#c.trend
                                       cD.xxprison#cD.xxpover#c.trend
                                       cD.xxprison#cD.xxpover#c.trend#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend#c.trend
                                       cD.xxincome#cD.xxincome#c.trend
                                       cD.xxincome#cD.xxincome#c.trend#c.trend
                                       cD.xxincome#cD.xxpover#c.trend
                                       cD.xxincome#cD.xxpover#c.trend#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend#c.trend
                                       cD.xxpover#cD.xxpover#c.trend
                                       cD.xxpover#cD.xxpover#c.trend#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend#c.trend
                                       cL.xxprison#c.trend
                                       cL.xxprison#c.trend#c.trend
                                       cL.xxprison#cL.xxprison#c.trend
                                       cL.xxprison#cL.xxprison#c.trend#c.trend
                                       cL.xxpolice#c.trend
                                       cL.xxpolice#c.trend#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend#c.trend
                                       cL.xxunemp#c.trend
                                       cL.xxunemp#c.trend#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend#c.trend
                                       cL.xxincome#c.trend
                                       cL.xxincome#c.trend#c.trend
                                       cL.xxincome#cL.xxincome#c.trend
                                       cL.xxincome#cL.xxincome#c.trend#c.trend
                                       cL.xxpover#c.trend
                                       cL.xxpover#c.trend#c.trend
                                       cL.xxpover#cL.xxpover#c.trend
                                       cL.xxpover#cL.xxpover#c.trend#c.trend
                                       cL.xxafdc15#c.trend
                                       cL.xxafdc15#c.trend#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend#c.trend
                                       cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#c.trend#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend#c.trend
                                       cL.xxbeer#c.trend
                                       cL.xxbeer#c.trend#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend#c.trend
                                       c.Mxxprison#c.trend
                                       c.Mxxprison#c.trend#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend#c.trend
                                       c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.trend#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend#c.trend
                                       c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.trend#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend#c.trend
                                       c.Mxxincome#c.trend
                                       c.Mxxincome#c.trend#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend#c.trend
                                       c.Mxxpover#c.trend
                                       c.Mxxpover#c.trend#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend#c.trend
                                       c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.trend#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend#c.trend
                                       c.xxprison0#c.trend
                                       c.xxprison0#c.trend#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.xxprison0#c.xxprison0#c.trend#c.trend
                                       c.xxpolice0#c.trend
                                       c.xxpolice0#c.trend#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend#c.trend
                                       c.xxunemp0#c.trend
                                       c.xxunemp0#c.trend#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend#c.trend
                                       c.xxincome0#c.trend
                                       c.xxincome0#c.trend#c.trend
                                       c.xxincome0#c.xxincome0#c.trend
                                       c.xxincome0#c.xxincome0#c.trend#c.trend
                                       c.xxpover0#c.trend
                                       c.xxpover0#c.trend#c.trend
                                       c.xxpover0#c.xxpover0#c.trend
                                       c.xxpover0#c.xxpover0#c.trend#c.trend
                                       c.xxafdc150#c.trend
                                       c.xxafdc150#c.trend#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend#c.trend
                                       c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.trend#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend#c.trend
                                       c.xxbeer0#c.trend
                                       c.xxbeer0#c.trend#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend#c.trend
                                       c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.trend#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend#c.trend
                                       c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.trend#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend#c.trend
                                       c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.trend#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend#c.trend
                                       c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.trend#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend#c.trend
Selected controls (15):                prop0 L.xxincome Mxxpolice Mxxincome
                                       Dxxincome0
                                       c.Dprop0#c.Dprop0#c.trend#c.trend
                                       cL.xxpolice#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.xxprison0#c.xxprison0#c.trend#c.trend
                                       c.xxincome0#c.trend c.Dxxincome0#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxbeer0#c.trend
Partialled-out controls (12):          86b.year 87.year 88.year 89.year
                                       90.year 91.year 92.year 93.year 94.year
                                       95.year 96.year 97.year

Structural equation:

OLS using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.1058101    .0471259     -2.25    0.025     -.1981751    -.0134451
-------------+----------------------------------------------------------------

OLS using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.1318373     .054116     -2.44    0.015     -.2379027    -.0257719
-------------+----------------------------------------------------------------

OLS with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.1485247    .0530277     -2.80    0.005     -.2524571    -.0445923
             |
       prop0 |    .0875487    .0405131      2.16    0.031      .0081444     .1669529
             |
    xxincome |
         L1. |    37.32675    8.437745      4.42    0.000      20.78908     53.86443
             |
   Mxxpolice |    .0324316    .0220702      1.47    0.142     -.0108252     .0756884
   Mxxincome |   -42.81143     10.0703     -4.25    0.000     -62.54886      -23.074
  Dxxincome0 |    54.85267    17.47566      3.14    0.002      20.60101     89.10432
             |
    c.Dprop0#|
    c.Dprop0#|
     c.trend#|
     c.trend |   -1.025082     .341323     -3.00    0.003     -1.694063    -.3561011
             |
 cL.xxpolice#|
     c.trend |    -.043136    .0291179     -1.48    0.138     -.1002061     .0139341
             |
   cL.xxbeer#|
   cL.xxbeer#|
     c.trend#|
     c.trend |   -.0774695    .2399111     -0.32    0.747     -.5476866     .3927476
             |
 c.Mxxincome#|
 c.Mxxincome#|
     c.trend#|
     c.trend |   -4.051596    53.60579     -0.08    0.940      -109.117     101.0138
             |
 c.xxprison0#|
 c.xxprison0#|
     c.trend |    .0436978    .0328321      1.33    0.183      -.020652     .1080476
             |
 c.xxprison0#|
 c.xxprison0#|
     c.trend#|
     c.trend |   -.0170239    .0408409     -0.42    0.677     -.0970705     .0630227
             |
 c.xxincome0#|
     c.trend |    3.663581    10.87781      0.34    0.736     -17.65654      24.9837
             |
          c. |
  Dxxincome0#|
     c.trend |   -45.72307    31.95131     -1.43    0.152     -108.3465     16.90036
             |
          c. |
  Dxxafdc150#|
          c. |
  Dxxafdc150#|
     c.trend#|
     c.trend |   -.2559563     .618171     -0.41    0.679     -1.467549     .9556366
             |
  c.Dxxbeer0#|
     c.trend |   -.6758118    .6022485     -1.12    0.262     -1.856197     .5045736
             |
        year |
         87  |   -.0517003    .0806348     -0.64    0.521     -.2097416     .1063409
         88  |   -.0959424    .1537809     -0.62    0.533     -.3973474     .2054627
         89  |   -.1090876    .2207728     -0.49    0.621     -.5417943     .3236192
         90  |   -.1343578    .2818049     -0.48    0.634     -.6866853     .4179696
         91  |   -.1526918    .3365201     -0.45    0.650      -.812259     .5068754
         92  |   -.2244485    .3853981     -0.58    0.560     -.9798149     .5309178
         93  |   -.2424421    .4293773     -0.56    0.572     -1.084006     .5991219
         94  |    -.237294    .4679259     -0.51    0.612     -1.154412      .679824
         95  |   -.2568836    .5022178     -0.51    0.609     -1.241212     .7274451
         96  |   -.3350883    .5325294     -0.63    0.529     -1.378827     .7086502
         97  |   -.3509993    .5586521     -0.63    0.530     -1.445937     .7439387
             |
       _cons |    .5454645    .3035513      1.80    0.072     -.0494851     1.140414
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    D.efaprop
------------------------------------------------------------------------------
Options: partial(i.year)   fe
Fixed effects transformation...
1.  (PDS/CHS) Selecting HD controls for dep var D.lpc_prop...
Selected:  L.xxunemp
2.  (PDS/CHS) Selecting HD controls for exog regressor D.efaprop...
Selected:  D.xxincome L.xxunemp c.prop0#c.trend#c.trend c.prop0#c.prop0#c.trend
          cL.xxincome#c.trend c.Mxxincome#c.Mxxincome#c.trend
          c.Mxxbeer#c.Mxxbeer#c.trend c.xxprison0#c.xxprison0#c.trend
          c.Dxxincome0#c.trend c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
          c.Dxxbeer0#c.trend


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      homoskedastic
Number of observations:                600
Number of fixed effects:                50
Exogenous (1):                         D.efaprop
High-dim controls (336):               prop0 c.prop0#c.prop0 Dprop0
                                       c.Dprop0#c.Dprop0 D.xxprison D.xxpolice
                                       D.xxunemp D.xxincome D.xxpover
                                       D.xxafdc15 D.xxgunlaw D.xxbeer
                                       cD.xxprison#cD.xxprison
                                       cD.xxprison#cD.xxpolice
                                       cD.xxprison#cD.xxunemp
                                       cD.xxprison#cD.xxincome
                                       cD.xxprison#cD.xxpover
                                       cD.xxprison#cD.xxafdc15
                                       cD.xxprison#cD.xxgunlaw
                                       cD.xxprison#cD.xxbeer
                                       cD.xxpolice#cD.xxpolice
                                       cD.xxpolice#cD.xxunemp
                                       cD.xxpolice#cD.xxincome
                                       cD.xxpolice#cD.xxpover
                                       cD.xxpolice#cD.xxafdc15
                                       cD.xxpolice#cD.xxgunlaw
                                       cD.xxpolice#cD.xxbeer
                                       cD.xxunemp#cD.xxunemp
                                       cD.xxunemp#cD.xxincome
                                       cD.xxunemp#cD.xxpover
                                       cD.xxunemp#cD.xxafdc15
                                       cD.xxunemp#cD.xxgunlaw
                                       cD.xxunemp#cD.xxbeer
                                       cD.xxincome#cD.xxincome
                                       cD.xxincome#cD.xxpover
                                       cD.xxincome#cD.xxafdc15
                                       cD.xxincome#cD.xxgunlaw
                                       cD.xxincome#cD.xxbeer
                                       cD.xxpover#cD.xxpover
                                       cD.xxpover#cD.xxafdc15
                                       cD.xxpover#cD.xxgunlaw
                                       cD.xxpover#cD.xxbeer
                                       cD.xxafdc15#cD.xxafdc15
                                       cD.xxafdc15#cD.xxgunlaw
                                       cD.xxafdc15#cD.xxbeer
                                       cD.xxgunlaw#cD.xxgunlaw
                                       cD.xxgunlaw#cD.xxbeer
                                       cD.xxbeer#cD.xxbeer L.xxprison
                                       cL.xxprison#cL.xxprison L.xxpolice
                                       cL.xxpolice#cL.xxpolice L.xxunemp
                                       cL.xxunemp#cL.xxunemp L.xxincome
                                       cL.xxincome#cL.xxincome L.xxpover
                                       cL.xxpover#cL.xxpover L.xxafdc15
                                       cL.xxafdc15#cL.xxafdc15 L.xxgunlaw
                                       cL.xxgunlaw#cL.xxgunlaw L.xxbeer
                                       cL.xxbeer#cL.xxbeer Mxxprison
                                       c.Mxxprison#c.Mxxprison Mxxpolice
                                       c.Mxxpolice#c.Mxxpolice Mxxunemp
                                       c.Mxxunemp#c.Mxxunemp Mxxincome
                                       c.Mxxincome#c.Mxxincome Mxxpover
                                       c.Mxxpover#c.Mxxpover Mxxafdc15
                                       c.Mxxafdc15#c.Mxxafdc15 Mxxgunlaw
                                       c.Mxxgunlaw#c.Mxxgunlaw Mxxbeer
                                       c.Mxxbeer#c.Mxxbeer xxprison0
                                       c.xxprison0#c.xxprison0 xxpolice0
                                       c.xxpolice0#c.xxpolice0 xxunemp0
                                       c.xxunemp0#c.xxunemp0 xxincome0
                                       c.xxincome0#c.xxincome0 xxpover0
                                       c.xxpover0#c.xxpover0 xxafdc150
                                       c.xxafdc150#c.xxafdc150 xxgunlaw0
                                       c.xxgunlaw0#c.xxgunlaw0 xxbeer0
                                       c.xxbeer0#c.xxbeer0 Dxxprison0
                                       c.Dxxprison0#c.Dxxprison0 Dxxpolice0
                                       c.Dxxpolice0#c.Dxxpolice0 Dxxunemp0
                                       c.Dxxunemp0#c.Dxxunemp0 Dxxincome0
                                       c.Dxxincome0#c.Dxxincome0 Dxxpover0
                                       c.Dxxpover0#c.Dxxpover0 Dxxafdc150
                                       c.Dxxafdc150#c.Dxxafdc150 Dxxgunlaw0
                                       c.Dxxgunlaw0#c.Dxxgunlaw0 Dxxbeer0
                                       c.Dxxbeer0#c.Dxxbeer0 c.prop0#c.trend
                                       c.prop0#c.trend#c.trend
                                       c.prop0#c.prop0#c.trend
                                       c.prop0#c.prop0#c.trend#c.trend
                                       c.Dprop0#c.trend
                                       c.Dprop0#c.trend#c.trend
                                       c.Dprop0#c.Dprop0#c.trend
                                       c.Dprop0#c.Dprop0#c.trend#c.trend
                                       cD.xxprison#c.trend
                                       cD.xxprison#c.trend#c.trend
                                       cD.xxpolice#c.trend
                                       cD.xxpolice#c.trend#c.trend
                                       cD.xxunemp#c.trend
                                       cD.xxunemp#c.trend#c.trend
                                       cD.xxincome#c.trend
                                       cD.xxincome#c.trend#c.trend
                                       cD.xxpover#c.trend
                                       cD.xxpover#c.trend#c.trend
                                       cD.xxafdc15#c.trend
                                       cD.xxafdc15#c.trend#c.trend
                                       cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#c.trend#c.trend
                                       cD.xxbeer#c.trend
                                       cD.xxbeer#c.trend#c.trend
                                       cD.xxprison#cD.xxprison#c.trend
                                       cD.xxprison#cD.xxprison#c.trend#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend#c.trend
                                       cD.xxprison#cD.xxincome#c.trend
                                       cD.xxprison#cD.xxincome#c.trend#c.trend
                                       cD.xxprison#cD.xxpover#c.trend
                                       cD.xxprison#cD.xxpover#c.trend#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend#c.trend
                                       cD.xxincome#cD.xxincome#c.trend
                                       cD.xxincome#cD.xxincome#c.trend#c.trend
                                       cD.xxincome#cD.xxpover#c.trend
                                       cD.xxincome#cD.xxpover#c.trend#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend#c.trend
                                       cD.xxpover#cD.xxpover#c.trend
                                       cD.xxpover#cD.xxpover#c.trend#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend#c.trend
                                       cL.xxprison#c.trend
                                       cL.xxprison#c.trend#c.trend
                                       cL.xxprison#cL.xxprison#c.trend
                                       cL.xxprison#cL.xxprison#c.trend#c.trend
                                       cL.xxpolice#c.trend
                                       cL.xxpolice#c.trend#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend#c.trend
                                       cL.xxunemp#c.trend
                                       cL.xxunemp#c.trend#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend#c.trend
                                       cL.xxincome#c.trend
                                       cL.xxincome#c.trend#c.trend
                                       cL.xxincome#cL.xxincome#c.trend
                                       cL.xxincome#cL.xxincome#c.trend#c.trend
                                       cL.xxpover#c.trend
                                       cL.xxpover#c.trend#c.trend
                                       cL.xxpover#cL.xxpover#c.trend
                                       cL.xxpover#cL.xxpover#c.trend#c.trend
                                       cL.xxafdc15#c.trend
                                       cL.xxafdc15#c.trend#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend#c.trend
                                       cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#c.trend#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend#c.trend
                                       cL.xxbeer#c.trend
                                       cL.xxbeer#c.trend#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend#c.trend
                                       c.Mxxprison#c.trend
                                       c.Mxxprison#c.trend#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend#c.trend
                                       c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.trend#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend#c.trend
                                       c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.trend#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend#c.trend
                                       c.Mxxincome#c.trend
                                       c.Mxxincome#c.trend#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend#c.trend
                                       c.Mxxpover#c.trend
                                       c.Mxxpover#c.trend#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend#c.trend
                                       c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.trend#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend#c.trend
                                       c.xxprison0#c.trend
                                       c.xxprison0#c.trend#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.xxprison0#c.xxprison0#c.trend#c.trend
                                       c.xxpolice0#c.trend
                                       c.xxpolice0#c.trend#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend#c.trend
                                       c.xxunemp0#c.trend
                                       c.xxunemp0#c.trend#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend#c.trend
                                       c.xxincome0#c.trend
                                       c.xxincome0#c.trend#c.trend
                                       c.xxincome0#c.xxincome0#c.trend
                                       c.xxincome0#c.xxincome0#c.trend#c.trend
                                       c.xxpover0#c.trend
                                       c.xxpover0#c.trend#c.trend
                                       c.xxpover0#c.xxpover0#c.trend
                                       c.xxpover0#c.xxpover0#c.trend#c.trend
                                       c.xxafdc150#c.trend
                                       c.xxafdc150#c.trend#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend#c.trend
                                       c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.trend#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend#c.trend
                                       c.xxbeer0#c.trend
                                       c.xxbeer0#c.trend#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend#c.trend
                                       c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.trend#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend#c.trend
                                       c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.trend#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend#c.trend
                                       c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.trend#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend#c.trend
                                       c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.trend#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend#c.trend
Selected controls (11):                D.xxincome L.xxunemp
                                       c.prop0#c.trend#c.trend
                                       c.prop0#c.prop0#c.trend
                                       cL.xxincome#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.Dxxincome0#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxbeer0#c.trend
Partialled-out controls (12):          86b.year 87.year 88.year 89.year
                                       90.year 91.year 92.year 93.year 94.year
                                       95.year 96.year 97.year

Structural equation (fixed effects, #groups=50):

OLS using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |    -.087322    .0716592     -1.22    0.223     -.2277714     .0531273
-------------+----------------------------------------------------------------

OLS using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.0873263    .0789462     -1.11    0.269     -.2420581     .0674054
-------------+----------------------------------------------------------------

OLS with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.0873263    .0777244     -1.12    0.261     -.2396633     .0650106
             |
    xxincome |
         D1. |   -14.84713    12.53389     -1.18    0.236      -39.4131     9.718839
             |
     xxunemp |
         L1. |   -.6872977     .259856     -2.64    0.008     -1.196606    -.1779894
             |
     c.prop0#|
     c.trend#|
     c.trend |    .1171882    .1647577      0.71    0.477     -.2057309     .4401073
             |
     c.prop0#|
     c.prop0#|
     c.trend |   -.4023849    .2538944     -1.58    0.113     -.9000089      .095239
             |
 cL.xxincome#|
     c.trend |    48.42856    18.53102      2.61    0.009      12.10842     84.74869
             |
 c.Mxxincome#|
 c.Mxxincome#|
     c.trend |   -228.2286    95.68554     -2.39    0.017     -415.7688    -40.68842
             |
   c.Mxxbeer#|
   c.Mxxbeer#|
     c.trend |    .5671674    .3855607      1.47    0.141     -.1885178     1.322853
             |
 c.xxprison0#|
 c.xxprison0#|
     c.trend |    .0018339    .0204301      0.09    0.928     -.0382083     .0418761
             |
          c. |
  Dxxincome0#|
     c.trend |   -11.15665    32.43505     -0.34    0.731     -74.72817     52.41487
             |
          c. |
  Dxxafdc150#|
          c. |
  Dxxafdc150#|
     c.trend#|
     c.trend |   -.6639184    .9904958     -0.67    0.503     -2.605255     1.277418
             |
  c.Dxxbeer0#|
     c.trend |   -1.013086    1.314351     -0.77    0.441     -3.589168     1.562995
             |
        year |
         87  |   -.2346428    .0820309     -2.86    0.004     -.3954204    -.0738653
         88  |   -.4693528    .1643793     -2.86    0.004     -.7915303    -.1471752
         89  |   -.6752619    .2473985     -2.73    0.006     -1.160154    -.1903698
         90  |    -.893982    .3305068     -2.70    0.007     -1.541763    -.2462005
         91  |   -1.105742    .4133368     -2.68    0.007     -1.915867    -.2956169
         92  |   -1.361006    .4974702     -2.74    0.006      -2.33603    -.3859828
         93  |   -1.571732    .5822853     -2.70    0.007     -2.712991    -.4304742
         94  |   -1.762021    .6670801     -2.64    0.008     -3.069474    -.4545683
         95  |   -1.982157    .7546974     -2.63    0.009     -3.461336    -.5029768
         96  |   -2.266987    .8435839     -2.69    0.007     -3.920381    -.6135925
         97  |   -2.491206    .9306118     -2.68    0.007     -4.315172    -.6672406
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    D.efaprop
------------------------------------------------------------------------------
Options: partial(i.year)   nocons
error: incompatible options, partial and nocons
Options: partial(i.year) robust
Partialling out unpenalized controls...
1.  (PDS/CHS) Selecting HD controls for dep var D.lpc_prop...
Selected:  xxafdc150 c.prop0#c.trend#c.trend
          c.Mxxincome#c.Mxxincome#c.trend#c.trend
          c.xxincome0#c.xxincome0#c.trend#c.trend
2.  (PDS/CHS) Selecting HD controls for exog regressor D.efaprop...
Selected:  prop0 L.xxprison L.xxpolice L.xxincome Mxxincome Dxxincome0
          c.xxprison0#c.xxprison0#c.trend#c.trend
          c.xxbeer0#c.xxbeer0#c.trend#c.trend c.Dxxincome0#c.trend
          c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend c.Dxxbeer0#c.trend


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      heteroskedastic
Number of observations:                600
Exogenous (1):                         D.efaprop
High-dim controls (336):               prop0 c.prop0#c.prop0 Dprop0
                                       c.Dprop0#c.Dprop0 D.xxprison D.xxpolice
                                       D.xxunemp D.xxincome D.xxpover
                                       D.xxafdc15 D.xxgunlaw D.xxbeer
                                       cD.xxprison#cD.xxprison
                                       cD.xxprison#cD.xxpolice
                                       cD.xxprison#cD.xxunemp
                                       cD.xxprison#cD.xxincome
                                       cD.xxprison#cD.xxpover
                                       cD.xxprison#cD.xxafdc15
                                       cD.xxprison#cD.xxgunlaw
                                       cD.xxprison#cD.xxbeer
                                       cD.xxpolice#cD.xxpolice
                                       cD.xxpolice#cD.xxunemp
                                       cD.xxpolice#cD.xxincome
                                       cD.xxpolice#cD.xxpover
                                       cD.xxpolice#cD.xxafdc15
                                       cD.xxpolice#cD.xxgunlaw
                                       cD.xxpolice#cD.xxbeer
                                       cD.xxunemp#cD.xxunemp
                                       cD.xxunemp#cD.xxincome
                                       cD.xxunemp#cD.xxpover
                                       cD.xxunemp#cD.xxafdc15
                                       cD.xxunemp#cD.xxgunlaw
                                       cD.xxunemp#cD.xxbeer
                                       cD.xxincome#cD.xxincome
                                       cD.xxincome#cD.xxpover
                                       cD.xxincome#cD.xxafdc15
                                       cD.xxincome#cD.xxgunlaw
                                       cD.xxincome#cD.xxbeer
                                       cD.xxpover#cD.xxpover
                                       cD.xxpover#cD.xxafdc15
                                       cD.xxpover#cD.xxgunlaw
                                       cD.xxpover#cD.xxbeer
                                       cD.xxafdc15#cD.xxafdc15
                                       cD.xxafdc15#cD.xxgunlaw
                                       cD.xxafdc15#cD.xxbeer
                                       cD.xxgunlaw#cD.xxgunlaw
                                       cD.xxgunlaw#cD.xxbeer
                                       cD.xxbeer#cD.xxbeer L.xxprison
                                       cL.xxprison#cL.xxprison L.xxpolice
                                       cL.xxpolice#cL.xxpolice L.xxunemp
                                       cL.xxunemp#cL.xxunemp L.xxincome
                                       cL.xxincome#cL.xxincome L.xxpover
                                       cL.xxpover#cL.xxpover L.xxafdc15
                                       cL.xxafdc15#cL.xxafdc15 L.xxgunlaw
                                       cL.xxgunlaw#cL.xxgunlaw L.xxbeer
                                       cL.xxbeer#cL.xxbeer Mxxprison
                                       c.Mxxprison#c.Mxxprison Mxxpolice
                                       c.Mxxpolice#c.Mxxpolice Mxxunemp
                                       c.Mxxunemp#c.Mxxunemp Mxxincome
                                       c.Mxxincome#c.Mxxincome Mxxpover
                                       c.Mxxpover#c.Mxxpover Mxxafdc15
                                       c.Mxxafdc15#c.Mxxafdc15 Mxxgunlaw
                                       c.Mxxgunlaw#c.Mxxgunlaw Mxxbeer
                                       c.Mxxbeer#c.Mxxbeer xxprison0
                                       c.xxprison0#c.xxprison0 xxpolice0
                                       c.xxpolice0#c.xxpolice0 xxunemp0
                                       c.xxunemp0#c.xxunemp0 xxincome0
                                       c.xxincome0#c.xxincome0 xxpover0
                                       c.xxpover0#c.xxpover0 xxafdc150
                                       c.xxafdc150#c.xxafdc150 xxgunlaw0
                                       c.xxgunlaw0#c.xxgunlaw0 xxbeer0
                                       c.xxbeer0#c.xxbeer0 Dxxprison0
                                       c.Dxxprison0#c.Dxxprison0 Dxxpolice0
                                       c.Dxxpolice0#c.Dxxpolice0 Dxxunemp0
                                       c.Dxxunemp0#c.Dxxunemp0 Dxxincome0
                                       c.Dxxincome0#c.Dxxincome0 Dxxpover0
                                       c.Dxxpover0#c.Dxxpover0 Dxxafdc150
                                       c.Dxxafdc150#c.Dxxafdc150 Dxxgunlaw0
                                       c.Dxxgunlaw0#c.Dxxgunlaw0 Dxxbeer0
                                       c.Dxxbeer0#c.Dxxbeer0 c.prop0#c.trend
                                       c.prop0#c.trend#c.trend
                                       c.prop0#c.prop0#c.trend
                                       c.prop0#c.prop0#c.trend#c.trend
                                       c.Dprop0#c.trend
                                       c.Dprop0#c.trend#c.trend
                                       c.Dprop0#c.Dprop0#c.trend
                                       c.Dprop0#c.Dprop0#c.trend#c.trend
                                       cD.xxprison#c.trend
                                       cD.xxprison#c.trend#c.trend
                                       cD.xxpolice#c.trend
                                       cD.xxpolice#c.trend#c.trend
                                       cD.xxunemp#c.trend
                                       cD.xxunemp#c.trend#c.trend
                                       cD.xxincome#c.trend
                                       cD.xxincome#c.trend#c.trend
                                       cD.xxpover#c.trend
                                       cD.xxpover#c.trend#c.trend
                                       cD.xxafdc15#c.trend
                                       cD.xxafdc15#c.trend#c.trend
                                       cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#c.trend#c.trend
                                       cD.xxbeer#c.trend
                                       cD.xxbeer#c.trend#c.trend
                                       cD.xxprison#cD.xxprison#c.trend
                                       cD.xxprison#cD.xxprison#c.trend#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend#c.trend
                                       cD.xxprison#cD.xxincome#c.trend
                                       cD.xxprison#cD.xxincome#c.trend#c.trend
                                       cD.xxprison#cD.xxpover#c.trend
                                       cD.xxprison#cD.xxpover#c.trend#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend#c.trend
                                       cD.xxincome#cD.xxincome#c.trend
                                       cD.xxincome#cD.xxincome#c.trend#c.trend
                                       cD.xxincome#cD.xxpover#c.trend
                                       cD.xxincome#cD.xxpover#c.trend#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend#c.trend
                                       cD.xxpover#cD.xxpover#c.trend
                                       cD.xxpover#cD.xxpover#c.trend#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend#c.trend
                                       cL.xxprison#c.trend
                                       cL.xxprison#c.trend#c.trend
                                       cL.xxprison#cL.xxprison#c.trend
                                       cL.xxprison#cL.xxprison#c.trend#c.trend
                                       cL.xxpolice#c.trend
                                       cL.xxpolice#c.trend#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend#c.trend
                                       cL.xxunemp#c.trend
                                       cL.xxunemp#c.trend#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend#c.trend
                                       cL.xxincome#c.trend
                                       cL.xxincome#c.trend#c.trend
                                       cL.xxincome#cL.xxincome#c.trend
                                       cL.xxincome#cL.xxincome#c.trend#c.trend
                                       cL.xxpover#c.trend
                                       cL.xxpover#c.trend#c.trend
                                       cL.xxpover#cL.xxpover#c.trend
                                       cL.xxpover#cL.xxpover#c.trend#c.trend
                                       cL.xxafdc15#c.trend
                                       cL.xxafdc15#c.trend#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend#c.trend
                                       cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#c.trend#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend#c.trend
                                       cL.xxbeer#c.trend
                                       cL.xxbeer#c.trend#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend#c.trend
                                       c.Mxxprison#c.trend
                                       c.Mxxprison#c.trend#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend#c.trend
                                       c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.trend#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend#c.trend
                                       c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.trend#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend#c.trend
                                       c.Mxxincome#c.trend
                                       c.Mxxincome#c.trend#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend#c.trend
                                       c.Mxxpover#c.trend
                                       c.Mxxpover#c.trend#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend#c.trend
                                       c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.trend#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend#c.trend
                                       c.xxprison0#c.trend
                                       c.xxprison0#c.trend#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.xxprison0#c.xxprison0#c.trend#c.trend
                                       c.xxpolice0#c.trend
                                       c.xxpolice0#c.trend#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend#c.trend
                                       c.xxunemp0#c.trend
                                       c.xxunemp0#c.trend#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend#c.trend
                                       c.xxincome0#c.trend
                                       c.xxincome0#c.trend#c.trend
                                       c.xxincome0#c.xxincome0#c.trend
                                       c.xxincome0#c.xxincome0#c.trend#c.trend
                                       c.xxpover0#c.trend
                                       c.xxpover0#c.trend#c.trend
                                       c.xxpover0#c.xxpover0#c.trend
                                       c.xxpover0#c.xxpover0#c.trend#c.trend
                                       c.xxafdc150#c.trend
                                       c.xxafdc150#c.trend#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend#c.trend
                                       c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.trend#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend#c.trend
                                       c.xxbeer0#c.trend
                                       c.xxbeer0#c.trend#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend#c.trend
                                       c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.trend#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend#c.trend
                                       c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.trend#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend#c.trend
                                       c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.trend#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend#c.trend
                                       c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.trend#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend#c.trend
Selected controls (15):                prop0 L.xxprison L.xxpolice L.xxincome
                                       Mxxincome xxafdc150 Dxxincome0
                                       c.prop0#c.trend#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend#c.trend
                                       c.xxprison0#c.xxprison0#c.trend#c.trend
                                       c.xxincome0#c.xxincome0#c.trend#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend#c.trend
                                       c.Dxxincome0#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxbeer0#c.trend
Partialled-out controls (12):          86b.year 87.year 88.year 89.year
                                       90.year 91.year 92.year 93.year 94.year
                                       95.year 96.year 97.year

Structural equation:

OLS using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.0902033    .0371022     -2.43    0.015     -.1629224    -.0174843
-------------+----------------------------------------------------------------

OLS using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |    -.091017    .0415284     -2.19    0.028     -.1724112    -.0096228
-------------+----------------------------------------------------------------

OLS with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.1165891    .0478653     -2.44    0.015     -.2104034    -.0227748
             |
       prop0 |    .0689451    .0344955      2.00    0.046      .0013351     .1365551
             |
    xxprison |
         L1. |    .0079409    .0061451      1.29    0.196     -.0041032      .019985
             |
    xxpolice |
         L1. |   -.0169025    .0135663     -1.25    0.213     -.0434919     .0096868
             |
    xxincome |
         L1. |     35.2682    8.847264      3.99    0.000      17.92788     52.60851
             |
   Mxxincome |   -36.33527    9.829714     -3.70    0.000     -55.60116    -17.06938
   xxafdc150 |   -.0105727      .01313     -0.81    0.421     -.0363069     .0151616
  Dxxincome0 |    44.11038    24.38356      1.81    0.070     -3.680525     91.90129
             |
     c.prop0#|
     c.trend#|
     c.trend |   -.1597065    .0578214     -2.76    0.006     -.2730345    -.0463786
             |
 c.Mxxincome#|
 c.Mxxincome#|
     c.trend#|
     c.trend |    6.155479    87.16722      0.07    0.944     -164.6891     177.0001
             |
 c.xxprison0#|
 c.xxprison0#|
     c.trend#|
     c.trend |    .0215152    .0113952      1.89    0.059      -.000819     .0438493
             |
 c.xxincome0#|
 c.xxincome0#|
     c.trend#|
     c.trend |    .6278846    82.42895      0.01    0.994     -160.9299     162.1857
             |
   c.xxbeer0#|
   c.xxbeer0#|
     c.trend#|
     c.trend |   -.0558255    .1989873     -0.28    0.779     -.4458335     .3341825
             |
          c. |
  Dxxincome0#|
     c.trend |   -43.31658    45.90922     -0.94    0.345      -133.297     46.66384
             |
          c. |
  Dxxafdc150#|
          c. |
  Dxxafdc150#|
     c.trend#|
     c.trend |    .3427324    .5515613      0.62    0.534     -.7383079     1.423773
             |
  c.Dxxbeer0#|
     c.trend |   -.6689544    .5846521     -1.14    0.253     -1.814851     .4769426
             |
        year |
         87  |    -.027038    .0099011     -2.73    0.006     -.0464437    -.0076322
         88  |     -.04791    .0152192     -3.15    0.002     -.0777391     -.018081
         89  |   -.0397733    .0242629     -1.64    0.101     -.0873277      .007781
         90  |   -.0449808    .0378032     -1.19    0.234     -.1190737      .029112
         91  |   -.0456322    .0535942     -0.85    0.395      -.150675     .0594106
         92  |   -.1005797    .0723983     -1.39    0.165     -.2424778     .0413185
         93  |   -.1027098     .095531     -1.08    0.282     -.2899471     .0845274
         94  |   -.0832507    .1215047     -0.69    0.493     -.3213954     .1548941
         95  |   -.0898544    .1509125     -0.60    0.552     -.3856375     .2059288
         96  |   -.1569828     .183804     -0.85    0.393     -.5172321     .2032664
         97  |   -.1637816    .2180882     -0.75    0.453     -.5912265     .2636634
             |
       _cons |    .1849996    .2991491      0.62    0.536     -.4013219     .7713211
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    D.efaprop
------------------------------------------------------------------------------
Options: partial(i.year) robust fe
Fixed effects transformation...
1.  (PDS/CHS) Selecting HD controls for dep var D.lpc_prop...
Selected:  L.xxunemp
2.  (PDS/CHS) Selecting HD controls for exog regressor D.efaprop...
Selected:  D.xxincome L.xxunemp c.prop0#c.trend#c.trend
          c.Mxxbeer#c.Mxxbeer#c.trend c.xxprison0#c.xxprison0#c.trend
          c.Dxxunemp0#c.Dxxunemp0#c.trend#c.trend c.Dxxincome0#c.trend
          c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      heteroskedastic
Number of observations:                600
Number of fixed effects:                50
Exogenous (1):                         D.efaprop
High-dim controls (336):               prop0 c.prop0#c.prop0 Dprop0
                                       c.Dprop0#c.Dprop0 D.xxprison D.xxpolice
                                       D.xxunemp D.xxincome D.xxpover
                                       D.xxafdc15 D.xxgunlaw D.xxbeer
                                       cD.xxprison#cD.xxprison
                                       cD.xxprison#cD.xxpolice
                                       cD.xxprison#cD.xxunemp
                                       cD.xxprison#cD.xxincome
                                       cD.xxprison#cD.xxpover
                                       cD.xxprison#cD.xxafdc15
                                       cD.xxprison#cD.xxgunlaw
                                       cD.xxprison#cD.xxbeer
                                       cD.xxpolice#cD.xxpolice
                                       cD.xxpolice#cD.xxunemp
                                       cD.xxpolice#cD.xxincome
                                       cD.xxpolice#cD.xxpover
                                       cD.xxpolice#cD.xxafdc15
                                       cD.xxpolice#cD.xxgunlaw
                                       cD.xxpolice#cD.xxbeer
                                       cD.xxunemp#cD.xxunemp
                                       cD.xxunemp#cD.xxincome
                                       cD.xxunemp#cD.xxpover
                                       cD.xxunemp#cD.xxafdc15
                                       cD.xxunemp#cD.xxgunlaw
                                       cD.xxunemp#cD.xxbeer
                                       cD.xxincome#cD.xxincome
                                       cD.xxincome#cD.xxpover
                                       cD.xxincome#cD.xxafdc15
                                       cD.xxincome#cD.xxgunlaw
                                       cD.xxincome#cD.xxbeer
                                       cD.xxpover#cD.xxpover
                                       cD.xxpover#cD.xxafdc15
                                       cD.xxpover#cD.xxgunlaw
                                       cD.xxpover#cD.xxbeer
                                       cD.xxafdc15#cD.xxafdc15
                                       cD.xxafdc15#cD.xxgunlaw
                                       cD.xxafdc15#cD.xxbeer
                                       cD.xxgunlaw#cD.xxgunlaw
                                       cD.xxgunlaw#cD.xxbeer
                                       cD.xxbeer#cD.xxbeer L.xxprison
                                       cL.xxprison#cL.xxprison L.xxpolice
                                       cL.xxpolice#cL.xxpolice L.xxunemp
                                       cL.xxunemp#cL.xxunemp L.xxincome
                                       cL.xxincome#cL.xxincome L.xxpover
                                       cL.xxpover#cL.xxpover L.xxafdc15
                                       cL.xxafdc15#cL.xxafdc15 L.xxgunlaw
                                       cL.xxgunlaw#cL.xxgunlaw L.xxbeer
                                       cL.xxbeer#cL.xxbeer Mxxprison
                                       c.Mxxprison#c.Mxxprison Mxxpolice
                                       c.Mxxpolice#c.Mxxpolice Mxxunemp
                                       c.Mxxunemp#c.Mxxunemp Mxxincome
                                       c.Mxxincome#c.Mxxincome Mxxpover
                                       c.Mxxpover#c.Mxxpover Mxxafdc15
                                       c.Mxxafdc15#c.Mxxafdc15 Mxxgunlaw
                                       c.Mxxgunlaw#c.Mxxgunlaw Mxxbeer
                                       c.Mxxbeer#c.Mxxbeer xxprison0
                                       c.xxprison0#c.xxprison0 xxpolice0
                                       c.xxpolice0#c.xxpolice0 xxunemp0
                                       c.xxunemp0#c.xxunemp0 xxincome0
                                       c.xxincome0#c.xxincome0 xxpover0
                                       c.xxpover0#c.xxpover0 xxafdc150
                                       c.xxafdc150#c.xxafdc150 xxgunlaw0
                                       c.xxgunlaw0#c.xxgunlaw0 xxbeer0
                                       c.xxbeer0#c.xxbeer0 Dxxprison0
                                       c.Dxxprison0#c.Dxxprison0 Dxxpolice0
                                       c.Dxxpolice0#c.Dxxpolice0 Dxxunemp0
                                       c.Dxxunemp0#c.Dxxunemp0 Dxxincome0
                                       c.Dxxincome0#c.Dxxincome0 Dxxpover0
                                       c.Dxxpover0#c.Dxxpover0 Dxxafdc150
                                       c.Dxxafdc150#c.Dxxafdc150 Dxxgunlaw0
                                       c.Dxxgunlaw0#c.Dxxgunlaw0 Dxxbeer0
                                       c.Dxxbeer0#c.Dxxbeer0 c.prop0#c.trend
                                       c.prop0#c.trend#c.trend
                                       c.prop0#c.prop0#c.trend
                                       c.prop0#c.prop0#c.trend#c.trend
                                       c.Dprop0#c.trend
                                       c.Dprop0#c.trend#c.trend
                                       c.Dprop0#c.Dprop0#c.trend
                                       c.Dprop0#c.Dprop0#c.trend#c.trend
                                       cD.xxprison#c.trend
                                       cD.xxprison#c.trend#c.trend
                                       cD.xxpolice#c.trend
                                       cD.xxpolice#c.trend#c.trend
                                       cD.xxunemp#c.trend
                                       cD.xxunemp#c.trend#c.trend
                                       cD.xxincome#c.trend
                                       cD.xxincome#c.trend#c.trend
                                       cD.xxpover#c.trend
                                       cD.xxpover#c.trend#c.trend
                                       cD.xxafdc15#c.trend
                                       cD.xxafdc15#c.trend#c.trend
                                       cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#c.trend#c.trend
                                       cD.xxbeer#c.trend
                                       cD.xxbeer#c.trend#c.trend
                                       cD.xxprison#cD.xxprison#c.trend
                                       cD.xxprison#cD.xxprison#c.trend#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend#c.trend
                                       cD.xxprison#cD.xxincome#c.trend
                                       cD.xxprison#cD.xxincome#c.trend#c.trend
                                       cD.xxprison#cD.xxpover#c.trend
                                       cD.xxprison#cD.xxpover#c.trend#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend#c.trend
                                       cD.xxincome#cD.xxincome#c.trend
                                       cD.xxincome#cD.xxincome#c.trend#c.trend
                                       cD.xxincome#cD.xxpover#c.trend
                                       cD.xxincome#cD.xxpover#c.trend#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend#c.trend
                                       cD.xxpover#cD.xxpover#c.trend
                                       cD.xxpover#cD.xxpover#c.trend#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend#c.trend
                                       cL.xxprison#c.trend
                                       cL.xxprison#c.trend#c.trend
                                       cL.xxprison#cL.xxprison#c.trend
                                       cL.xxprison#cL.xxprison#c.trend#c.trend
                                       cL.xxpolice#c.trend
                                       cL.xxpolice#c.trend#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend#c.trend
                                       cL.xxunemp#c.trend
                                       cL.xxunemp#c.trend#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend#c.trend
                                       cL.xxincome#c.trend
                                       cL.xxincome#c.trend#c.trend
                                       cL.xxincome#cL.xxincome#c.trend
                                       cL.xxincome#cL.xxincome#c.trend#c.trend
                                       cL.xxpover#c.trend
                                       cL.xxpover#c.trend#c.trend
                                       cL.xxpover#cL.xxpover#c.trend
                                       cL.xxpover#cL.xxpover#c.trend#c.trend
                                       cL.xxafdc15#c.trend
                                       cL.xxafdc15#c.trend#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend#c.trend
                                       cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#c.trend#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend#c.trend
                                       cL.xxbeer#c.trend
                                       cL.xxbeer#c.trend#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend#c.trend
                                       c.Mxxprison#c.trend
                                       c.Mxxprison#c.trend#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend#c.trend
                                       c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.trend#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend#c.trend
                                       c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.trend#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend#c.trend
                                       c.Mxxincome#c.trend
                                       c.Mxxincome#c.trend#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend#c.trend
                                       c.Mxxpover#c.trend
                                       c.Mxxpover#c.trend#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend#c.trend
                                       c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.trend#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend#c.trend
                                       c.xxprison0#c.trend
                                       c.xxprison0#c.trend#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.xxprison0#c.xxprison0#c.trend#c.trend
                                       c.xxpolice0#c.trend
                                       c.xxpolice0#c.trend#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend#c.trend
                                       c.xxunemp0#c.trend
                                       c.xxunemp0#c.trend#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend#c.trend
                                       c.xxincome0#c.trend
                                       c.xxincome0#c.trend#c.trend
                                       c.xxincome0#c.xxincome0#c.trend
                                       c.xxincome0#c.xxincome0#c.trend#c.trend
                                       c.xxpover0#c.trend
                                       c.xxpover0#c.trend#c.trend
                                       c.xxpover0#c.xxpover0#c.trend
                                       c.xxpover0#c.xxpover0#c.trend#c.trend
                                       c.xxafdc150#c.trend
                                       c.xxafdc150#c.trend#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend#c.trend
                                       c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.trend#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend#c.trend
                                       c.xxbeer0#c.trend
                                       c.xxbeer0#c.trend#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend#c.trend
                                       c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.trend#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend#c.trend
                                       c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.trend#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend#c.trend
                                       c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.trend#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend#c.trend
                                       c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.trend#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend#c.trend
Selected controls (8):                 D.xxincome L.xxunemp
                                       c.prop0#c.trend#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxincome0#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
Partialled-out controls (12):          86b.year 87.year 88.year 89.year
                                       90.year 91.year 92.year 93.year 94.year
                                       95.year 96.year 97.year

Structural equation (fixed effects, #groups=50):

OLS using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.0546072    .0609766     -0.90    0.370     -.1741192     .0649047
-------------+----------------------------------------------------------------

OLS using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.0708728     .066728     -1.06    0.288     -.2016574     .0599117
-------------+----------------------------------------------------------------

OLS with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.0708728    .0655627     -1.08    0.280     -.1993734     .0576277
             |
    xxincome |
         D1. |   -27.59272    13.83443     -1.99    0.046     -54.70771    -.4777299
             |
     xxunemp |
         L1. |   -.8351233     .215151     -3.88    0.000     -1.256811    -.4134351
             |
     c.prop0#|
     c.trend#|
     c.trend |   -.0947974    .0576251     -1.65    0.100     -.2077406     .0181457
             |
   c.Mxxbeer#|
   c.Mxxbeer#|
     c.trend |    .6889324    .3605034      1.91    0.056     -.0176413     1.395506
             |
 c.xxprison0#|
 c.xxprison0#|
     c.trend |   -.0046991    .0166347     -0.28    0.778     -.0373025     .0279044
             |
 c.Dxxunemp0#|
 c.Dxxunemp0#|
     c.trend#|
     c.trend |   -78.31638    72.66661     -1.08    0.281     -220.7403     64.10756
             |
          c. |
  Dxxincome0#|
     c.trend |   -28.25837    39.22787     -0.72    0.471     -105.1436     48.62685
             |
          c. |
  Dxxafdc150#|
          c. |
  Dxxafdc150#|
     c.trend#|
     c.trend |   -.5932685    .8528173     -0.70    0.487      -2.26476     1.078223
             |
        year |
         87  |   -.0266762    .0087537     -3.05    0.002     -.0438332    -.0095193
         88  |   -.0499206    .0099531     -5.02    0.000     -.0694283     -.030413
         89  |   -.0428834    .0131407     -3.26    0.001     -.0686387    -.0171281
         90  |   -.0478202    .0161614     -2.96    0.003      -.079496    -.0161445
         91  |   -.0462237     .018521     -2.50    0.013     -.0825242    -.0099232
         92  |   -.0842623    .0183434     -4.59    0.000     -.1202147      -.04831
         93  |   -.0752757    .0185256     -4.06    0.000     -.1115851    -.0389663
         94  |   -.0457316     .019393     -2.36    0.018     -.0837411     -.007722
         95  |   -.0378468    .0220703     -1.71    0.086     -.0811037     .0054102
         96  |   -.0906559    .0224875     -4.03    0.000     -.1347307    -.0465811
         97  |   -.0875697    .0248299     -3.53    0.000     -.1362354    -.0389039
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    D.efaprop
------------------------------------------------------------------------------
Options: partial(i.year) robust nocons
error: incompatible options, partial and nocons
Options: partial(i.year) cluster(statenum)
Partialling out unpenalized controls...
1.  (PDS/CHS) Selecting HD controls for dep var D.lpc_prop...
Selected:  xxincome0 xxafdc150 c.Mxxincome#c.trend
2.  (PDS/CHS) Selecting HD controls for exog regressor D.efaprop...
Selected:  prop0 cD.xxprison#cD.xxbeer L.xxincome


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      cluster-lasso
Number of observations:                600
Number of clusters:                     50
Exogenous (1):                         D.efaprop
High-dim controls (336):               prop0 c.prop0#c.prop0 Dprop0
                                       c.Dprop0#c.Dprop0 D.xxprison D.xxpolice
                                       D.xxunemp D.xxincome D.xxpover
                                       D.xxafdc15 D.xxgunlaw D.xxbeer
                                       cD.xxprison#cD.xxprison
                                       cD.xxprison#cD.xxpolice
                                       cD.xxprison#cD.xxunemp
                                       cD.xxprison#cD.xxincome
                                       cD.xxprison#cD.xxpover
                                       cD.xxprison#cD.xxafdc15
                                       cD.xxprison#cD.xxgunlaw
                                       cD.xxprison#cD.xxbeer
                                       cD.xxpolice#cD.xxpolice
                                       cD.xxpolice#cD.xxunemp
                                       cD.xxpolice#cD.xxincome
                                       cD.xxpolice#cD.xxpover
                                       cD.xxpolice#cD.xxafdc15
                                       cD.xxpolice#cD.xxgunlaw
                                       cD.xxpolice#cD.xxbeer
                                       cD.xxunemp#cD.xxunemp
                                       cD.xxunemp#cD.xxincome
                                       cD.xxunemp#cD.xxpover
                                       cD.xxunemp#cD.xxafdc15
                                       cD.xxunemp#cD.xxgunlaw
                                       cD.xxunemp#cD.xxbeer
                                       cD.xxincome#cD.xxincome
                                       cD.xxincome#cD.xxpover
                                       cD.xxincome#cD.xxafdc15
                                       cD.xxincome#cD.xxgunlaw
                                       cD.xxincome#cD.xxbeer
                                       cD.xxpover#cD.xxpover
                                       cD.xxpover#cD.xxafdc15
                                       cD.xxpover#cD.xxgunlaw
                                       cD.xxpover#cD.xxbeer
                                       cD.xxafdc15#cD.xxafdc15
                                       cD.xxafdc15#cD.xxgunlaw
                                       cD.xxafdc15#cD.xxbeer
                                       cD.xxgunlaw#cD.xxgunlaw
                                       cD.xxgunlaw#cD.xxbeer
                                       cD.xxbeer#cD.xxbeer L.xxprison
                                       cL.xxprison#cL.xxprison L.xxpolice
                                       cL.xxpolice#cL.xxpolice L.xxunemp
                                       cL.xxunemp#cL.xxunemp L.xxincome
                                       cL.xxincome#cL.xxincome L.xxpover
                                       cL.xxpover#cL.xxpover L.xxafdc15
                                       cL.xxafdc15#cL.xxafdc15 L.xxgunlaw
                                       cL.xxgunlaw#cL.xxgunlaw L.xxbeer
                                       cL.xxbeer#cL.xxbeer Mxxprison
                                       c.Mxxprison#c.Mxxprison Mxxpolice
                                       c.Mxxpolice#c.Mxxpolice Mxxunemp
                                       c.Mxxunemp#c.Mxxunemp Mxxincome
                                       c.Mxxincome#c.Mxxincome Mxxpover
                                       c.Mxxpover#c.Mxxpover Mxxafdc15
                                       c.Mxxafdc15#c.Mxxafdc15 Mxxgunlaw
                                       c.Mxxgunlaw#c.Mxxgunlaw Mxxbeer
                                       c.Mxxbeer#c.Mxxbeer xxprison0
                                       c.xxprison0#c.xxprison0 xxpolice0
                                       c.xxpolice0#c.xxpolice0 xxunemp0
                                       c.xxunemp0#c.xxunemp0 xxincome0
                                       c.xxincome0#c.xxincome0 xxpover0
                                       c.xxpover0#c.xxpover0 xxafdc150
                                       c.xxafdc150#c.xxafdc150 xxgunlaw0
                                       c.xxgunlaw0#c.xxgunlaw0 xxbeer0
                                       c.xxbeer0#c.xxbeer0 Dxxprison0
                                       c.Dxxprison0#c.Dxxprison0 Dxxpolice0
                                       c.Dxxpolice0#c.Dxxpolice0 Dxxunemp0
                                       c.Dxxunemp0#c.Dxxunemp0 Dxxincome0
                                       c.Dxxincome0#c.Dxxincome0 Dxxpover0
                                       c.Dxxpover0#c.Dxxpover0 Dxxafdc150
                                       c.Dxxafdc150#c.Dxxafdc150 Dxxgunlaw0
                                       c.Dxxgunlaw0#c.Dxxgunlaw0 Dxxbeer0
                                       c.Dxxbeer0#c.Dxxbeer0 c.prop0#c.trend
                                       c.prop0#c.trend#c.trend
                                       c.prop0#c.prop0#c.trend
                                       c.prop0#c.prop0#c.trend#c.trend
                                       c.Dprop0#c.trend
                                       c.Dprop0#c.trend#c.trend
                                       c.Dprop0#c.Dprop0#c.trend
                                       c.Dprop0#c.Dprop0#c.trend#c.trend
                                       cD.xxprison#c.trend
                                       cD.xxprison#c.trend#c.trend
                                       cD.xxpolice#c.trend
                                       cD.xxpolice#c.trend#c.trend
                                       cD.xxunemp#c.trend
                                       cD.xxunemp#c.trend#c.trend
                                       cD.xxincome#c.trend
                                       cD.xxincome#c.trend#c.trend
                                       cD.xxpover#c.trend
                                       cD.xxpover#c.trend#c.trend
                                       cD.xxafdc15#c.trend
                                       cD.xxafdc15#c.trend#c.trend
                                       cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#c.trend#c.trend
                                       cD.xxbeer#c.trend
                                       cD.xxbeer#c.trend#c.trend
                                       cD.xxprison#cD.xxprison#c.trend
                                       cD.xxprison#cD.xxprison#c.trend#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend#c.trend
                                       cD.xxprison#cD.xxincome#c.trend
                                       cD.xxprison#cD.xxincome#c.trend#c.trend
                                       cD.xxprison#cD.xxpover#c.trend
                                       cD.xxprison#cD.xxpover#c.trend#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend#c.trend
                                       cD.xxincome#cD.xxincome#c.trend
                                       cD.xxincome#cD.xxincome#c.trend#c.trend
                                       cD.xxincome#cD.xxpover#c.trend
                                       cD.xxincome#cD.xxpover#c.trend#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend#c.trend
                                       cD.xxpover#cD.xxpover#c.trend
                                       cD.xxpover#cD.xxpover#c.trend#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend#c.trend
                                       cL.xxprison#c.trend
                                       cL.xxprison#c.trend#c.trend
                                       cL.xxprison#cL.xxprison#c.trend
                                       cL.xxprison#cL.xxprison#c.trend#c.trend
                                       cL.xxpolice#c.trend
                                       cL.xxpolice#c.trend#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend#c.trend
                                       cL.xxunemp#c.trend
                                       cL.xxunemp#c.trend#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend#c.trend
                                       cL.xxincome#c.trend
                                       cL.xxincome#c.trend#c.trend
                                       cL.xxincome#cL.xxincome#c.trend
                                       cL.xxincome#cL.xxincome#c.trend#c.trend
                                       cL.xxpover#c.trend
                                       cL.xxpover#c.trend#c.trend
                                       cL.xxpover#cL.xxpover#c.trend
                                       cL.xxpover#cL.xxpover#c.trend#c.trend
                                       cL.xxafdc15#c.trend
                                       cL.xxafdc15#c.trend#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend#c.trend
                                       cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#c.trend#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend#c.trend
                                       cL.xxbeer#c.trend
                                       cL.xxbeer#c.trend#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend#c.trend
                                       c.Mxxprison#c.trend
                                       c.Mxxprison#c.trend#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend#c.trend
                                       c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.trend#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend#c.trend
                                       c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.trend#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend#c.trend
                                       c.Mxxincome#c.trend
                                       c.Mxxincome#c.trend#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend#c.trend
                                       c.Mxxpover#c.trend
                                       c.Mxxpover#c.trend#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend#c.trend
                                       c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.trend#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend#c.trend
                                       c.xxprison0#c.trend
                                       c.xxprison0#c.trend#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.xxprison0#c.xxprison0#c.trend#c.trend
                                       c.xxpolice0#c.trend
                                       c.xxpolice0#c.trend#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend#c.trend
                                       c.xxunemp0#c.trend
                                       c.xxunemp0#c.trend#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend#c.trend
                                       c.xxincome0#c.trend
                                       c.xxincome0#c.trend#c.trend
                                       c.xxincome0#c.xxincome0#c.trend
                                       c.xxincome0#c.xxincome0#c.trend#c.trend
                                       c.xxpover0#c.trend
                                       c.xxpover0#c.trend#c.trend
                                       c.xxpover0#c.xxpover0#c.trend
                                       c.xxpover0#c.xxpover0#c.trend#c.trend
                                       c.xxafdc150#c.trend
                                       c.xxafdc150#c.trend#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend#c.trend
                                       c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.trend#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend#c.trend
                                       c.xxbeer0#c.trend
                                       c.xxbeer0#c.trend#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend#c.trend
                                       c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.trend#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend#c.trend
                                       c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.trend#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend#c.trend
                                       c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.trend#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend#c.trend
                                       c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.trend#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend#c.trend
Selected controls (6):                 prop0 cD.xxprison#cD.xxbeer L.xxincome
                                       xxincome0 xxafdc150 c.Mxxincome#c.trend
Partialled-out controls (12):          86b.year 87.year 88.year 89.year
                                       90.year 91.year 92.year 93.year 94.year
                                       95.year 96.year 97.year

Structural equation:

OLS using CHS lasso-orthogonalized vars
(Std. Err. adjusted for 50 clusters in statenum)
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.0645541     .044142     -1.46    0.144     -.1510708     .0219626
-------------+----------------------------------------------------------------

OLS using CHS post-lasso-orthogonalized vars
(Std. Err. adjusted for 50 clusters in statenum)
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.0628553    .0481347     -1.31    0.192     -.1571975      .031487
-------------+----------------------------------------------------------------

OLS with PDS-selected variables and full regressor set
(Std. Err. adjusted for 50 clusters in statenum)
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.0897886     .056477     -1.59    0.112     -.2004815     .0209043
             |
       prop0 |    .0088669    .0253529      0.35    0.727     -.0408239     .0585577
             |
 cD.xxprison#|
   cD.xxbeer |   -.1947112    2.542185     -0.08    0.939     -5.177302      4.78788
             |
    xxincome |
         L1. |    21.28066    4.650744      4.58    0.000      12.16537     30.39595
             |
   xxincome0 |   -15.71353    4.354251     -3.61    0.000     -24.24771    -7.179358
   xxafdc150 |   -.0264625    .0074138     -3.57    0.000     -.0409932    -.0119318
             |
 c.Mxxincome#|
     c.trend |   -9.449333     4.21689     -2.24    0.025     -17.71429     -1.18438
             |
        year |
         87  |    .0551684    .0357699      1.54    0.123     -.0149394     .1252762
         88  |    .1144515    .0698399      1.64    0.101     -.0224323     .2513353
         89  |    .2042385    .1017077      2.01    0.045       .004895      .403582
         90  |    .2827328    .1363043      2.07    0.038      .0155812     .5498844
         91  |    .3645207    .1675923      2.18    0.030      .0360458     .6929955
         92  |    .3915994    .2067296      1.89    0.058     -.0135831     .7967819
         93  |    .4761361    .2398321      1.99    0.047      .0060738     .9461985
         94  |      .58132    .2744475      2.12    0.034      .0434128     1.119227
         95  |    .6640497    .3108557      2.14    0.033      .0547837     1.273316
         96  |     .689488    .3448339      2.00    0.046      .0136261      1.36535
         97  |    .7730275    .3812726      2.03    0.043       .025747     1.520308
             |
       _cons |   -.4087512    .2016963     -2.03    0.043     -.8040687    -.0134338
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    D.efaprop
------------------------------------------------------------------------------
Options: partial(i.year) cluster(statenum) fe
Fixed effects transformation...
1.  (PDS/CHS) Selecting HD controls for dep var D.lpc_prop...
Selected:  L.xxunemp
2.  (PDS/CHS) Selecting HD controls for exog regressor D.efaprop...
Selected:  D.xxincome L.xxunemp c.prop0#c.prop0#c.trend
          c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      cluster-lasso
Number of observations:                600
Number of clusters:                     50
Number of fixed effects:                50
Exogenous (1):                         D.efaprop
High-dim controls (336):               prop0 c.prop0#c.prop0 Dprop0
                                       c.Dprop0#c.Dprop0 D.xxprison D.xxpolice
                                       D.xxunemp D.xxincome D.xxpover
                                       D.xxafdc15 D.xxgunlaw D.xxbeer
                                       cD.xxprison#cD.xxprison
                                       cD.xxprison#cD.xxpolice
                                       cD.xxprison#cD.xxunemp
                                       cD.xxprison#cD.xxincome
                                       cD.xxprison#cD.xxpover
                                       cD.xxprison#cD.xxafdc15
                                       cD.xxprison#cD.xxgunlaw
                                       cD.xxprison#cD.xxbeer
                                       cD.xxpolice#cD.xxpolice
                                       cD.xxpolice#cD.xxunemp
                                       cD.xxpolice#cD.xxincome
                                       cD.xxpolice#cD.xxpover
                                       cD.xxpolice#cD.xxafdc15
                                       cD.xxpolice#cD.xxgunlaw
                                       cD.xxpolice#cD.xxbeer
                                       cD.xxunemp#cD.xxunemp
                                       cD.xxunemp#cD.xxincome
                                       cD.xxunemp#cD.xxpover
                                       cD.xxunemp#cD.xxafdc15
                                       cD.xxunemp#cD.xxgunlaw
                                       cD.xxunemp#cD.xxbeer
                                       cD.xxincome#cD.xxincome
                                       cD.xxincome#cD.xxpover
                                       cD.xxincome#cD.xxafdc15
                                       cD.xxincome#cD.xxgunlaw
                                       cD.xxincome#cD.xxbeer
                                       cD.xxpover#cD.xxpover
                                       cD.xxpover#cD.xxafdc15
                                       cD.xxpover#cD.xxgunlaw
                                       cD.xxpover#cD.xxbeer
                                       cD.xxafdc15#cD.xxafdc15
                                       cD.xxafdc15#cD.xxgunlaw
                                       cD.xxafdc15#cD.xxbeer
                                       cD.xxgunlaw#cD.xxgunlaw
                                       cD.xxgunlaw#cD.xxbeer
                                       cD.xxbeer#cD.xxbeer L.xxprison
                                       cL.xxprison#cL.xxprison L.xxpolice
                                       cL.xxpolice#cL.xxpolice L.xxunemp
                                       cL.xxunemp#cL.xxunemp L.xxincome
                                       cL.xxincome#cL.xxincome L.xxpover
                                       cL.xxpover#cL.xxpover L.xxafdc15
                                       cL.xxafdc15#cL.xxafdc15 L.xxgunlaw
                                       cL.xxgunlaw#cL.xxgunlaw L.xxbeer
                                       cL.xxbeer#cL.xxbeer Mxxprison
                                       c.Mxxprison#c.Mxxprison Mxxpolice
                                       c.Mxxpolice#c.Mxxpolice Mxxunemp
                                       c.Mxxunemp#c.Mxxunemp Mxxincome
                                       c.Mxxincome#c.Mxxincome Mxxpover
                                       c.Mxxpover#c.Mxxpover Mxxafdc15
                                       c.Mxxafdc15#c.Mxxafdc15 Mxxgunlaw
                                       c.Mxxgunlaw#c.Mxxgunlaw Mxxbeer
                                       c.Mxxbeer#c.Mxxbeer xxprison0
                                       c.xxprison0#c.xxprison0 xxpolice0
                                       c.xxpolice0#c.xxpolice0 xxunemp0
                                       c.xxunemp0#c.xxunemp0 xxincome0
                                       c.xxincome0#c.xxincome0 xxpover0
                                       c.xxpover0#c.xxpover0 xxafdc150
                                       c.xxafdc150#c.xxafdc150 xxgunlaw0
                                       c.xxgunlaw0#c.xxgunlaw0 xxbeer0
                                       c.xxbeer0#c.xxbeer0 Dxxprison0
                                       c.Dxxprison0#c.Dxxprison0 Dxxpolice0
                                       c.Dxxpolice0#c.Dxxpolice0 Dxxunemp0
                                       c.Dxxunemp0#c.Dxxunemp0 Dxxincome0
                                       c.Dxxincome0#c.Dxxincome0 Dxxpover0
                                       c.Dxxpover0#c.Dxxpover0 Dxxafdc150
                                       c.Dxxafdc150#c.Dxxafdc150 Dxxgunlaw0
                                       c.Dxxgunlaw0#c.Dxxgunlaw0 Dxxbeer0
                                       c.Dxxbeer0#c.Dxxbeer0 c.prop0#c.trend
                                       c.prop0#c.trend#c.trend
                                       c.prop0#c.prop0#c.trend
                                       c.prop0#c.prop0#c.trend#c.trend
                                       c.Dprop0#c.trend
                                       c.Dprop0#c.trend#c.trend
                                       c.Dprop0#c.Dprop0#c.trend
                                       c.Dprop0#c.Dprop0#c.trend#c.trend
                                       cD.xxprison#c.trend
                                       cD.xxprison#c.trend#c.trend
                                       cD.xxpolice#c.trend
                                       cD.xxpolice#c.trend#c.trend
                                       cD.xxunemp#c.trend
                                       cD.xxunemp#c.trend#c.trend
                                       cD.xxincome#c.trend
                                       cD.xxincome#c.trend#c.trend
                                       cD.xxpover#c.trend
                                       cD.xxpover#c.trend#c.trend
                                       cD.xxafdc15#c.trend
                                       cD.xxafdc15#c.trend#c.trend
                                       cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#c.trend#c.trend
                                       cD.xxbeer#c.trend
                                       cD.xxbeer#c.trend#c.trend
                                       cD.xxprison#cD.xxprison#c.trend
                                       cD.xxprison#cD.xxprison#c.trend#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend#c.trend
                                       cD.xxprison#cD.xxincome#c.trend
                                       cD.xxprison#cD.xxincome#c.trend#c.trend
                                       cD.xxprison#cD.xxpover#c.trend
                                       cD.xxprison#cD.xxpover#c.trend#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend#c.trend
                                       cD.xxincome#cD.xxincome#c.trend
                                       cD.xxincome#cD.xxincome#c.trend#c.trend
                                       cD.xxincome#cD.xxpover#c.trend
                                       cD.xxincome#cD.xxpover#c.trend#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend#c.trend
                                       cD.xxpover#cD.xxpover#c.trend
                                       cD.xxpover#cD.xxpover#c.trend#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend#c.trend
                                       cL.xxprison#c.trend
                                       cL.xxprison#c.trend#c.trend
                                       cL.xxprison#cL.xxprison#c.trend
                                       cL.xxprison#cL.xxprison#c.trend#c.trend
                                       cL.xxpolice#c.trend
                                       cL.xxpolice#c.trend#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend#c.trend
                                       cL.xxunemp#c.trend
                                       cL.xxunemp#c.trend#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend#c.trend
                                       cL.xxincome#c.trend
                                       cL.xxincome#c.trend#c.trend
                                       cL.xxincome#cL.xxincome#c.trend
                                       cL.xxincome#cL.xxincome#c.trend#c.trend
                                       cL.xxpover#c.trend
                                       cL.xxpover#c.trend#c.trend
                                       cL.xxpover#cL.xxpover#c.trend
                                       cL.xxpover#cL.xxpover#c.trend#c.trend
                                       cL.xxafdc15#c.trend
                                       cL.xxafdc15#c.trend#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend#c.trend
                                       cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#c.trend#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend#c.trend
                                       cL.xxbeer#c.trend
                                       cL.xxbeer#c.trend#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend#c.trend
                                       c.Mxxprison#c.trend
                                       c.Mxxprison#c.trend#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend#c.trend
                                       c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.trend#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend#c.trend
                                       c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.trend#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend#c.trend
                                       c.Mxxincome#c.trend
                                       c.Mxxincome#c.trend#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend#c.trend
                                       c.Mxxpover#c.trend
                                       c.Mxxpover#c.trend#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend#c.trend
                                       c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.trend#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend#c.trend
                                       c.xxprison0#c.trend
                                       c.xxprison0#c.trend#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.xxprison0#c.xxprison0#c.trend#c.trend
                                       c.xxpolice0#c.trend
                                       c.xxpolice0#c.trend#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend#c.trend
                                       c.xxunemp0#c.trend
                                       c.xxunemp0#c.trend#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend#c.trend
                                       c.xxincome0#c.trend
                                       c.xxincome0#c.trend#c.trend
                                       c.xxincome0#c.xxincome0#c.trend
                                       c.xxincome0#c.xxincome0#c.trend#c.trend
                                       c.xxpover0#c.trend
                                       c.xxpover0#c.trend#c.trend
                                       c.xxpover0#c.xxpover0#c.trend
                                       c.xxpover0#c.xxpover0#c.trend#c.trend
                                       c.xxafdc150#c.trend
                                       c.xxafdc150#c.trend#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend#c.trend
                                       c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.trend#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend#c.trend
                                       c.xxbeer0#c.trend
                                       c.xxbeer0#c.trend#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend#c.trend
                                       c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.trend#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend#c.trend
                                       c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.trend#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend#c.trend
                                       c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.trend#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend#c.trend
                                       c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.trend#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend#c.trend
Selected controls (4):                 D.xxincome L.xxunemp
                                       c.prop0#c.prop0#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
Partialled-out controls (12):          86b.year 87.year 88.year 89.year
                                       90.year 91.year 92.year 93.year 94.year
                                       95.year 96.year 97.year

Structural equation (fixed effects, #groups=50):

OLS using CHS lasso-orthogonalized vars
(Std. Err. adjusted for 50 clusters in statenum)
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.0932012    .0668382     -1.39    0.163     -.2242017     .0377993
-------------+----------------------------------------------------------------

OLS using CHS post-lasso-orthogonalized vars
(Std. Err. adjusted for 50 clusters in statenum)
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.0829405    .0748093     -1.11    0.268      -.229564      .063683
-------------+----------------------------------------------------------------

OLS with PDS-selected variables and full regressor set
(Std. Err. adjusted for 50 clusters in statenum)
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.0829405    .0721085     -1.15    0.250     -.2242706     .0583896
             |
    xxincome |
         D1. |   -27.37665    15.67586     -1.75    0.081     -58.10078     3.347475
             |
     xxunemp |
         L1. |   -.8423193    .2004038     -4.20    0.000     -1.235104     -.449535
             |
     c.prop0#|
     c.prop0#|
     c.trend |    -.229436    .0804544     -2.85    0.004     -.3871238    -.0717483
             |
          c. |
  Dxxafdc150#|
          c. |
  Dxxafdc150#|
     c.trend#|
     c.trend |   -.6779636    .7268227     -0.93    0.351      -2.10251     .7465828
             |
        year |
         87  |    -.023664    .0088252     -2.68    0.007     -.0409612    -.0063669
         88  |   -.0444541    .0090865     -4.89    0.000     -.0622634    -.0266449
         89  |   -.0349657    .0102283     -3.42    0.001     -.0550128    -.0149186
         90  |   -.0377691    .0133733     -2.82    0.005     -.0639803    -.0115579
         91  |   -.0342581    .0143935     -2.38    0.017     -.0624689    -.0060472
         92  |   -.0708148    .0151894     -4.66    0.000     -.1005854    -.0410443
         93  |   -.0605907    .0144438     -4.19    0.000     -.0889001    -.0322813
         94  |   -.0302278    .0142542     -2.12    0.034     -.0581655    -.0022901
         95  |   -.0217481     .015333     -1.42    0.156     -.0518002     .0083039
         96  |   -.0741265    .0139363     -5.32    0.000     -.1014413    -.0468118
         97  |   -.0707745    .0147365     -4.80    0.000     -.0996576    -.0418914
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    D.efaprop
------------------------------------------------------------------------------
Options: partial(i.year) cluster(statenum) nocons
error: incompatible options, partial and nocons
Options: pnotpen(i.year)
1.  (PDS/CHS) Selecting HD controls for dep var D.lpc_prop...
Selected:  c.Mxxincome#c.trend#c.trend c.Mxxincome#c.Mxxincome#c.trend#c.trend
          c.xxincome0#c.trend c.xxincome0#c.xxincome0#c.trend
Also inc:  86b.year 87.year 88.year 89.year 90.year 91.year 92.year 93.year
          94.year 95.year 96.year 97.year
2.  (PDS/CHS) Selecting HD controls for exog regressor D.efaprop...
Selected:  prop0 L.xxincome Mxxpolice Mxxincome Dxxincome0
          c.Dprop0#c.Dprop0#c.trend#c.trend cL.xxpolice#c.trend
          cL.xxincome#c.trend cL.xxbeer#cL.xxbeer#c.trend#c.trend
          c.Mxxincome#c.trend c.xxprison0#c.xxprison0#c.trend
          c.xxprison0#c.xxprison0#c.trend#c.trend c.Dxxincome0#c.trend
          c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend c.Dxxbeer0#c.trend
Also inc:  86b.year 87.year 88.year 89.year 90.year 91.year 92.year 93.year
          94.year 95.year 96.year 97.year


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      homoskedastic
Number of observations:                600
Exogenous (1):                         D.efaprop
High-dim controls (336):               prop0 c.prop0#c.prop0 Dprop0
                                       c.Dprop0#c.Dprop0 D.xxprison D.xxpolice
                                       D.xxunemp D.xxincome D.xxpover
                                       D.xxafdc15 D.xxgunlaw D.xxbeer
                                       cD.xxprison#cD.xxprison
                                       cD.xxprison#cD.xxpolice
                                       cD.xxprison#cD.xxunemp
                                       cD.xxprison#cD.xxincome
                                       cD.xxprison#cD.xxpover
                                       cD.xxprison#cD.xxafdc15
                                       cD.xxprison#cD.xxgunlaw
                                       cD.xxprison#cD.xxbeer
                                       cD.xxpolice#cD.xxpolice
                                       cD.xxpolice#cD.xxunemp
                                       cD.xxpolice#cD.xxincome
                                       cD.xxpolice#cD.xxpover
                                       cD.xxpolice#cD.xxafdc15
                                       cD.xxpolice#cD.xxgunlaw
                                       cD.xxpolice#cD.xxbeer
                                       cD.xxunemp#cD.xxunemp
                                       cD.xxunemp#cD.xxincome
                                       cD.xxunemp#cD.xxpover
                                       cD.xxunemp#cD.xxafdc15
                                       cD.xxunemp#cD.xxgunlaw
                                       cD.xxunemp#cD.xxbeer
                                       cD.xxincome#cD.xxincome
                                       cD.xxincome#cD.xxpover
                                       cD.xxincome#cD.xxafdc15
                                       cD.xxincome#cD.xxgunlaw
                                       cD.xxincome#cD.xxbeer
                                       cD.xxpover#cD.xxpover
                                       cD.xxpover#cD.xxafdc15
                                       cD.xxpover#cD.xxgunlaw
                                       cD.xxpover#cD.xxbeer
                                       cD.xxafdc15#cD.xxafdc15
                                       cD.xxafdc15#cD.xxgunlaw
                                       cD.xxafdc15#cD.xxbeer
                                       cD.xxgunlaw#cD.xxgunlaw
                                       cD.xxgunlaw#cD.xxbeer
                                       cD.xxbeer#cD.xxbeer L.xxprison
                                       cL.xxprison#cL.xxprison L.xxpolice
                                       cL.xxpolice#cL.xxpolice L.xxunemp
                                       cL.xxunemp#cL.xxunemp L.xxincome
                                       cL.xxincome#cL.xxincome L.xxpover
                                       cL.xxpover#cL.xxpover L.xxafdc15
                                       cL.xxafdc15#cL.xxafdc15 L.xxgunlaw
                                       cL.xxgunlaw#cL.xxgunlaw L.xxbeer
                                       cL.xxbeer#cL.xxbeer Mxxprison
                                       c.Mxxprison#c.Mxxprison Mxxpolice
                                       c.Mxxpolice#c.Mxxpolice Mxxunemp
                                       c.Mxxunemp#c.Mxxunemp Mxxincome
                                       c.Mxxincome#c.Mxxincome Mxxpover
                                       c.Mxxpover#c.Mxxpover Mxxafdc15
                                       c.Mxxafdc15#c.Mxxafdc15 Mxxgunlaw
                                       c.Mxxgunlaw#c.Mxxgunlaw Mxxbeer
                                       c.Mxxbeer#c.Mxxbeer xxprison0
                                       c.xxprison0#c.xxprison0 xxpolice0
                                       c.xxpolice0#c.xxpolice0 xxunemp0
                                       c.xxunemp0#c.xxunemp0 xxincome0
                                       c.xxincome0#c.xxincome0 xxpover0
                                       c.xxpover0#c.xxpover0 xxafdc150
                                       c.xxafdc150#c.xxafdc150 xxgunlaw0
                                       c.xxgunlaw0#c.xxgunlaw0 xxbeer0
                                       c.xxbeer0#c.xxbeer0 Dxxprison0
                                       c.Dxxprison0#c.Dxxprison0 Dxxpolice0
                                       c.Dxxpolice0#c.Dxxpolice0 Dxxunemp0
                                       c.Dxxunemp0#c.Dxxunemp0 Dxxincome0
                                       c.Dxxincome0#c.Dxxincome0 Dxxpover0
                                       c.Dxxpover0#c.Dxxpover0 Dxxafdc150
                                       c.Dxxafdc150#c.Dxxafdc150 Dxxgunlaw0
                                       c.Dxxgunlaw0#c.Dxxgunlaw0 Dxxbeer0
                                       c.Dxxbeer0#c.Dxxbeer0 c.prop0#c.trend
                                       c.prop0#c.trend#c.trend
                                       c.prop0#c.prop0#c.trend
                                       c.prop0#c.prop0#c.trend#c.trend
                                       c.Dprop0#c.trend
                                       c.Dprop0#c.trend#c.trend
                                       c.Dprop0#c.Dprop0#c.trend
                                       c.Dprop0#c.Dprop0#c.trend#c.trend
                                       cD.xxprison#c.trend
                                       cD.xxprison#c.trend#c.trend
                                       cD.xxpolice#c.trend
                                       cD.xxpolice#c.trend#c.trend
                                       cD.xxunemp#c.trend
                                       cD.xxunemp#c.trend#c.trend
                                       cD.xxincome#c.trend
                                       cD.xxincome#c.trend#c.trend
                                       cD.xxpover#c.trend
                                       cD.xxpover#c.trend#c.trend
                                       cD.xxafdc15#c.trend
                                       cD.xxafdc15#c.trend#c.trend
                                       cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#c.trend#c.trend
                                       cD.xxbeer#c.trend
                                       cD.xxbeer#c.trend#c.trend
                                       cD.xxprison#cD.xxprison#c.trend
                                       cD.xxprison#cD.xxprison#c.trend#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend#c.trend
                                       cD.xxprison#cD.xxincome#c.trend
                                       cD.xxprison#cD.xxincome#c.trend#c.trend
                                       cD.xxprison#cD.xxpover#c.trend
                                       cD.xxprison#cD.xxpover#c.trend#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend#c.trend
                                       cD.xxincome#cD.xxincome#c.trend
                                       cD.xxincome#cD.xxincome#c.trend#c.trend
                                       cD.xxincome#cD.xxpover#c.trend
                                       cD.xxincome#cD.xxpover#c.trend#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend#c.trend
                                       cD.xxpover#cD.xxpover#c.trend
                                       cD.xxpover#cD.xxpover#c.trend#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend#c.trend
                                       cL.xxprison#c.trend
                                       cL.xxprison#c.trend#c.trend
                                       cL.xxprison#cL.xxprison#c.trend
                                       cL.xxprison#cL.xxprison#c.trend#c.trend
                                       cL.xxpolice#c.trend
                                       cL.xxpolice#c.trend#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend#c.trend
                                       cL.xxunemp#c.trend
                                       cL.xxunemp#c.trend#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend#c.trend
                                       cL.xxincome#c.trend
                                       cL.xxincome#c.trend#c.trend
                                       cL.xxincome#cL.xxincome#c.trend
                                       cL.xxincome#cL.xxincome#c.trend#c.trend
                                       cL.xxpover#c.trend
                                       cL.xxpover#c.trend#c.trend
                                       cL.xxpover#cL.xxpover#c.trend
                                       cL.xxpover#cL.xxpover#c.trend#c.trend
                                       cL.xxafdc15#c.trend
                                       cL.xxafdc15#c.trend#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend#c.trend
                                       cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#c.trend#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend#c.trend
                                       cL.xxbeer#c.trend
                                       cL.xxbeer#c.trend#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend#c.trend
                                       c.Mxxprison#c.trend
                                       c.Mxxprison#c.trend#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend#c.trend
                                       c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.trend#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend#c.trend
                                       c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.trend#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend#c.trend
                                       c.Mxxincome#c.trend
                                       c.Mxxincome#c.trend#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend#c.trend
                                       c.Mxxpover#c.trend
                                       c.Mxxpover#c.trend#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend#c.trend
                                       c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.trend#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend#c.trend
                                       c.xxprison0#c.trend
                                       c.xxprison0#c.trend#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.xxprison0#c.xxprison0#c.trend#c.trend
                                       c.xxpolice0#c.trend
                                       c.xxpolice0#c.trend#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend#c.trend
                                       c.xxunemp0#c.trend
                                       c.xxunemp0#c.trend#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend#c.trend
                                       c.xxincome0#c.trend
                                       c.xxincome0#c.trend#c.trend
                                       c.xxincome0#c.xxincome0#c.trend
                                       c.xxincome0#c.xxincome0#c.trend#c.trend
                                       c.xxpover0#c.trend
                                       c.xxpover0#c.trend#c.trend
                                       c.xxpover0#c.xxpover0#c.trend
                                       c.xxpover0#c.xxpover0#c.trend#c.trend
                                       c.xxafdc150#c.trend
                                       c.xxafdc150#c.trend#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend#c.trend
                                       c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.trend#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend#c.trend
                                       c.xxbeer0#c.trend
                                       c.xxbeer0#c.trend#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend#c.trend
                                       c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.trend#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend#c.trend
                                       c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.trend#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend#c.trend
                                       c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.trend#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend#c.trend
                                       c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.trend#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend#c.trend
Selected controls (31):                prop0 L.xxincome Mxxpolice Mxxincome
                                       Dxxincome0
                                       c.Dprop0#c.Dprop0#c.trend#c.trend
                                       cL.xxpolice#c.trend cL.xxincome#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend#c.trend
                                       c.Mxxincome#c.trend
                                       c.Mxxincome#c.trend#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.xxprison0#c.xxprison0#c.trend#c.trend
                                       c.xxincome0#c.trend
                                       c.xxincome0#c.xxincome0#c.trend
                                       c.Dxxincome0#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxbeer0#c.trend 86b.year 87.year
                                       88.year 89.year 90.year 91.year 92.year
                                       93.year 94.year 95.year 96.year 97.year
Unpenalized controls (13):             86b.year 87.year 88.year 89.year
                                       90.year 91.year 92.year 93.year 94.year
                                       95.year 96.year 97.year _cons

Structural equation:

OLS using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.1067739    .0472176     -2.26    0.024     -.1993187    -.0142292
-------------+----------------------------------------------------------------

OLS using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.1268865    .0546463     -2.32    0.020     -.2339913    -.0197817
-------------+----------------------------------------------------------------

OLS with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.1728596    .0574296     -3.01    0.003     -.2854197    -.0602996
             |
       prop0 |    .1026287    .0428657      2.39    0.017      .0186135      .186644
             |
    xxincome |
         L1. |    19.56633    14.36782      1.36    0.173     -8.594085     47.72675
             |
   Mxxpolice |    .0375522    .0220835      1.70    0.089     -.0057307      .080835
   Mxxincome |   -31.84808      15.698     -2.03    0.042     -62.61559    -1.080566
  Dxxincome0 |    52.47514    17.62393      2.98    0.003      17.93286     87.01741
             |
    c.Dprop0#|
    c.Dprop0#|
     c.trend#|
     c.trend |   -1.111321    .3500555     -3.17    0.001     -1.797417    -.4252249
             |
 cL.xxpolice#|
     c.trend |   -.0498707    .0294311     -1.69    0.090     -.1075546     .0078132
             |
 cL.xxincome#|
     c.trend |    37.24459    28.30769      1.32    0.188     -18.23747     92.72664
             |
   cL.xxbeer#|
   cL.xxbeer#|
     c.trend#|
     c.trend |   -.0418365    .2466999     -0.17    0.865     -.5253595     .4416865
             |
 c.Mxxincome#|
     c.trend |    7.073985    44.38234      0.16    0.873      -79.9138     94.06177
             |
 c.Mxxincome#|
     c.trend#|
     c.trend |      159.48    368.1366      0.43    0.665     -562.0545     881.0145
             |
 c.Mxxincome#|
 c.Mxxincome#|
     c.trend#|
     c.trend |   -944.0782    1830.385     -0.52    0.606     -4531.568     2643.411
             |
 c.xxprison0#|
 c.xxprison0#|
     c.trend |     .044902    .0326739      1.37    0.169     -.0191377     .1089417
             |
 c.xxprison0#|
 c.xxprison0#|
     c.trend#|
     c.trend |   -.0164335    .0406557     -0.40    0.686     -.0961172     .0632503
             |
 c.xxincome0#|
     c.trend |    -153.205    311.8693     -0.49    0.623     -764.4576     458.0476
             |
 c.xxincome0#|
 c.xxincome0#|
     c.trend |    742.9428    1573.194      0.47    0.637     -2340.462     3826.347
             |
          c. |
  Dxxincome0#|
     c.trend |   -53.76938    35.21785     -1.53    0.127     -122.7951     15.25633
             |
          c. |
  Dxxafdc150#|
          c. |
  Dxxafdc150#|
     c.trend#|
     c.trend |   -.3918105    .6258541     -0.63    0.531     -1.618462     .8348411
             |
  c.Dxxbeer0#|
     c.trend |   -.6351553     .608999     -1.04    0.297     -1.828771     .5584607
             |
        year |
         87  |    .1383663    1.054689      0.13    0.896     -1.928787      2.20552
         88  |    .1889731    1.973558      0.10    0.924      -3.67913     4.057076
         89  |    .1800043     2.79522      0.06    0.949     -5.298526     5.658535
         90  |    .0665982    3.568466      0.02    0.985     -6.927467     7.060663
         91  |   -.1321502    4.349634     -0.03    0.976     -8.657277     8.392976
         92  |   -.4754596      5.1993     -0.09    0.927      -10.6659     9.714982
         93  |   -.8576275    6.175082     -0.14    0.890     -12.96057     11.24531
         94  |   -1.307582    7.326238     -0.18    0.858     -15.66674     13.05158
         95  |   -1.876572    8.689928     -0.22    0.829     -18.90852     15.15537
         96  |   -2.598514    10.29137     -0.25    0.801     -22.76922      17.5722
         97  |   -3.348461    12.14548     -0.28    0.783     -27.15316     20.45624
             |
       _cons |    1.479413    1.242699      1.19    0.234     -.9562326     3.915059
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    D.efaprop
------------------------------------------------------------------------------
Options: pnotpen(i.year)   fe
Fixed effects transformation...
1.  (PDS/CHS) Selecting HD controls for dep var D.lpc_prop...
Selected:  L.xxunemp
Also inc:  86b.year 87.year 88.year 89.year 90.year 91.year 92.year 93.year
          94.year 95.year 96.year 97.year
2.  (PDS/CHS) Selecting HD controls for exog regressor D.efaprop...
Selected:  D.xxincome L.xxunemp c.prop0#c.trend#c.trend c.prop0#c.prop0#c.trend
          cL.xxincome#c.trend cL.xxincome#cL.xxincome#c.trend
          c.Mxxincome#c.trend c.Mxxincome#c.Mxxincome#c.trend
          c.Mxxbeer#c.Mxxbeer#c.trend c.xxprison0#c.xxprison0#c.trend
          c.Dxxunemp0#c.Dxxunemp0#c.trend#c.trend c.Dxxincome0#c.trend
          c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend c.Dxxbeer0#c.trend
Also inc:  86b.year 87.year 88.year 89.year 90.year 91.year 92.year 93.year
          94.year 95.year 96.year 97.year


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      homoskedastic
Number of observations:                600
Number of fixed effects:                50
Exogenous (1):                         D.efaprop
High-dim controls (336):               prop0 c.prop0#c.prop0 Dprop0
                                       c.Dprop0#c.Dprop0 D.xxprison D.xxpolice
                                       D.xxunemp D.xxincome D.xxpover
                                       D.xxafdc15 D.xxgunlaw D.xxbeer
                                       cD.xxprison#cD.xxprison
                                       cD.xxprison#cD.xxpolice
                                       cD.xxprison#cD.xxunemp
                                       cD.xxprison#cD.xxincome
                                       cD.xxprison#cD.xxpover
                                       cD.xxprison#cD.xxafdc15
                                       cD.xxprison#cD.xxgunlaw
                                       cD.xxprison#cD.xxbeer
                                       cD.xxpolice#cD.xxpolice
                                       cD.xxpolice#cD.xxunemp
                                       cD.xxpolice#cD.xxincome
                                       cD.xxpolice#cD.xxpover
                                       cD.xxpolice#cD.xxafdc15
                                       cD.xxpolice#cD.xxgunlaw
                                       cD.xxpolice#cD.xxbeer
                                       cD.xxunemp#cD.xxunemp
                                       cD.xxunemp#cD.xxincome
                                       cD.xxunemp#cD.xxpover
                                       cD.xxunemp#cD.xxafdc15
                                       cD.xxunemp#cD.xxgunlaw
                                       cD.xxunemp#cD.xxbeer
                                       cD.xxincome#cD.xxincome
                                       cD.xxincome#cD.xxpover
                                       cD.xxincome#cD.xxafdc15
                                       cD.xxincome#cD.xxgunlaw
                                       cD.xxincome#cD.xxbeer
                                       cD.xxpover#cD.xxpover
                                       cD.xxpover#cD.xxafdc15
                                       cD.xxpover#cD.xxgunlaw
                                       cD.xxpover#cD.xxbeer
                                       cD.xxafdc15#cD.xxafdc15
                                       cD.xxafdc15#cD.xxgunlaw
                                       cD.xxafdc15#cD.xxbeer
                                       cD.xxgunlaw#cD.xxgunlaw
                                       cD.xxgunlaw#cD.xxbeer
                                       cD.xxbeer#cD.xxbeer L.xxprison
                                       cL.xxprison#cL.xxprison L.xxpolice
                                       cL.xxpolice#cL.xxpolice L.xxunemp
                                       cL.xxunemp#cL.xxunemp L.xxincome
                                       cL.xxincome#cL.xxincome L.xxpover
                                       cL.xxpover#cL.xxpover L.xxafdc15
                                       cL.xxafdc15#cL.xxafdc15 L.xxgunlaw
                                       cL.xxgunlaw#cL.xxgunlaw L.xxbeer
                                       cL.xxbeer#cL.xxbeer Mxxprison
                                       c.Mxxprison#c.Mxxprison Mxxpolice
                                       c.Mxxpolice#c.Mxxpolice Mxxunemp
                                       c.Mxxunemp#c.Mxxunemp Mxxincome
                                       c.Mxxincome#c.Mxxincome Mxxpover
                                       c.Mxxpover#c.Mxxpover Mxxafdc15
                                       c.Mxxafdc15#c.Mxxafdc15 Mxxgunlaw
                                       c.Mxxgunlaw#c.Mxxgunlaw Mxxbeer
                                       c.Mxxbeer#c.Mxxbeer xxprison0
                                       c.xxprison0#c.xxprison0 xxpolice0
                                       c.xxpolice0#c.xxpolice0 xxunemp0
                                       c.xxunemp0#c.xxunemp0 xxincome0
                                       c.xxincome0#c.xxincome0 xxpover0
                                       c.xxpover0#c.xxpover0 xxafdc150
                                       c.xxafdc150#c.xxafdc150 xxgunlaw0
                                       c.xxgunlaw0#c.xxgunlaw0 xxbeer0
                                       c.xxbeer0#c.xxbeer0 Dxxprison0
                                       c.Dxxprison0#c.Dxxprison0 Dxxpolice0
                                       c.Dxxpolice0#c.Dxxpolice0 Dxxunemp0
                                       c.Dxxunemp0#c.Dxxunemp0 Dxxincome0
                                       c.Dxxincome0#c.Dxxincome0 Dxxpover0
                                       c.Dxxpover0#c.Dxxpover0 Dxxafdc150
                                       c.Dxxafdc150#c.Dxxafdc150 Dxxgunlaw0
                                       c.Dxxgunlaw0#c.Dxxgunlaw0 Dxxbeer0
                                       c.Dxxbeer0#c.Dxxbeer0 c.prop0#c.trend
                                       c.prop0#c.trend#c.trend
                                       c.prop0#c.prop0#c.trend
                                       c.prop0#c.prop0#c.trend#c.trend
                                       c.Dprop0#c.trend
                                       c.Dprop0#c.trend#c.trend
                                       c.Dprop0#c.Dprop0#c.trend
                                       c.Dprop0#c.Dprop0#c.trend#c.trend
                                       cD.xxprison#c.trend
                                       cD.xxprison#c.trend#c.trend
                                       cD.xxpolice#c.trend
                                       cD.xxpolice#c.trend#c.trend
                                       cD.xxunemp#c.trend
                                       cD.xxunemp#c.trend#c.trend
                                       cD.xxincome#c.trend
                                       cD.xxincome#c.trend#c.trend
                                       cD.xxpover#c.trend
                                       cD.xxpover#c.trend#c.trend
                                       cD.xxafdc15#c.trend
                                       cD.xxafdc15#c.trend#c.trend
                                       cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#c.trend#c.trend
                                       cD.xxbeer#c.trend
                                       cD.xxbeer#c.trend#c.trend
                                       cD.xxprison#cD.xxprison#c.trend
                                       cD.xxprison#cD.xxprison#c.trend#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend#c.trend
                                       cD.xxprison#cD.xxincome#c.trend
                                       cD.xxprison#cD.xxincome#c.trend#c.trend
                                       cD.xxprison#cD.xxpover#c.trend
                                       cD.xxprison#cD.xxpover#c.trend#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend#c.trend
                                       cD.xxincome#cD.xxincome#c.trend
                                       cD.xxincome#cD.xxincome#c.trend#c.trend
                                       cD.xxincome#cD.xxpover#c.trend
                                       cD.xxincome#cD.xxpover#c.trend#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend#c.trend
                                       cD.xxpover#cD.xxpover#c.trend
                                       cD.xxpover#cD.xxpover#c.trend#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend#c.trend
                                       cL.xxprison#c.trend
                                       cL.xxprison#c.trend#c.trend
                                       cL.xxprison#cL.xxprison#c.trend
                                       cL.xxprison#cL.xxprison#c.trend#c.trend
                                       cL.xxpolice#c.trend
                                       cL.xxpolice#c.trend#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend#c.trend
                                       cL.xxunemp#c.trend
                                       cL.xxunemp#c.trend#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend#c.trend
                                       cL.xxincome#c.trend
                                       cL.xxincome#c.trend#c.trend
                                       cL.xxincome#cL.xxincome#c.trend
                                       cL.xxincome#cL.xxincome#c.trend#c.trend
                                       cL.xxpover#c.trend
                                       cL.xxpover#c.trend#c.trend
                                       cL.xxpover#cL.xxpover#c.trend
                                       cL.xxpover#cL.xxpover#c.trend#c.trend
                                       cL.xxafdc15#c.trend
                                       cL.xxafdc15#c.trend#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend#c.trend
                                       cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#c.trend#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend#c.trend
                                       cL.xxbeer#c.trend
                                       cL.xxbeer#c.trend#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend#c.trend
                                       c.Mxxprison#c.trend
                                       c.Mxxprison#c.trend#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend#c.trend
                                       c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.trend#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend#c.trend
                                       c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.trend#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend#c.trend
                                       c.Mxxincome#c.trend
                                       c.Mxxincome#c.trend#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend#c.trend
                                       c.Mxxpover#c.trend
                                       c.Mxxpover#c.trend#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend#c.trend
                                       c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.trend#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend#c.trend
                                       c.xxprison0#c.trend
                                       c.xxprison0#c.trend#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.xxprison0#c.xxprison0#c.trend#c.trend
                                       c.xxpolice0#c.trend
                                       c.xxpolice0#c.trend#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend#c.trend
                                       c.xxunemp0#c.trend
                                       c.xxunemp0#c.trend#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend#c.trend
                                       c.xxincome0#c.trend
                                       c.xxincome0#c.trend#c.trend
                                       c.xxincome0#c.xxincome0#c.trend
                                       c.xxincome0#c.xxincome0#c.trend#c.trend
                                       c.xxpover0#c.trend
                                       c.xxpover0#c.trend#c.trend
                                       c.xxpover0#c.xxpover0#c.trend
                                       c.xxpover0#c.xxpover0#c.trend#c.trend
                                       c.xxafdc150#c.trend
                                       c.xxafdc150#c.trend#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend#c.trend
                                       c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.trend#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend#c.trend
                                       c.xxbeer0#c.trend
                                       c.xxbeer0#c.trend#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend#c.trend
                                       c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.trend#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend#c.trend
                                       c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.trend#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend#c.trend
                                       c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.trend#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend#c.trend
                                       c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.trend#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend#c.trend
Selected controls (26):                D.xxincome L.xxunemp
                                       c.prop0#c.trend#c.trend
                                       c.prop0#c.prop0#c.trend
                                       cL.xxincome#c.trend
                                       cL.xxincome#cL.xxincome#c.trend
                                       c.Mxxincome#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxincome0#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxbeer0#c.trend 86b.year 87.year
                                       88.year 89.year 90.year 91.year 92.year
                                       93.year 94.year 95.year 96.year 97.year
Unpenalized controls (12):             86b.year 87.year 88.year 89.year
                                       90.year 91.year 92.year 93.year 94.year
                                       95.year 96.year 97.year

Structural equation (fixed effects, #groups=50):

OLS using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.0871637    .0723066     -1.21    0.228      -.228882     .0545546
-------------+----------------------------------------------------------------

OLS using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.1025096    .0827982     -1.24    0.216     -.2647912     .0597719
-------------+----------------------------------------------------------------

OLS with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.0729045    .0786758     -0.93    0.354     -.2271061     .0812971
             |
    xxincome |
         D1. |   -14.60938    12.51701     -1.17    0.243     -39.14226     9.923508
             |
     xxunemp |
         L1. |   -.7110401    .2600578     -2.73    0.006     -1.220744    -.2013362
             |
     c.prop0#|
     c.trend#|
     c.trend |    .0920079    .1678091      0.55    0.583     -.2368918     .4209077
             |
     c.prop0#|
     c.prop0#|
     c.trend |    -.363906    .2595176     -1.40    0.161     -.8725512     .1447393
             |
 cL.xxincome#|
     c.trend |    51.62493    18.66532      2.77    0.006      15.04158     88.20829
             |
 cL.xxincome#|
 cL.xxincome#|
     c.trend |           0   (omitted)
             |
 c.Mxxincome#|
     c.trend |   -108.6107    365.1861     -0.30    0.766     -824.3624     607.1409
             |
 c.Mxxincome#|
 c.Mxxincome#|
     c.trend |    310.1159    1825.701      0.17    0.865     -3268.192     3888.424
             |
   c.Mxxbeer#|
   c.Mxxbeer#|
     c.trend |    .7763312    .4203205      1.85    0.065     -.0474819     1.600144
             |
 c.xxprison0#|
 c.xxprison0#|
     c.trend |    .0032496    .0204516      0.16    0.874     -.0368348      .043334
             |
 c.Dxxunemp0#|
 c.Dxxunemp0#|
     c.trend#|
     c.trend |   -116.2684    87.91857     -1.32    0.186     -288.5856     56.04883
             |
          c. |
  Dxxincome0#|
     c.trend |   -40.45634      39.281     -1.03    0.303     -117.4457       36.533
             |
          c. |
  Dxxafdc150#|
          c. |
  Dxxafdc150#|
     c.trend#|
     c.trend |   -.8082388    .9947438     -0.81    0.416     -2.757901     1.141423
             |
  c.Dxxbeer0#|
     c.trend |   -.9943418    1.312486     -0.76    0.449     -3.566768     1.578084
             |
        year |
         87  |    .1945084    1.525988      0.13    0.899     -2.796373      3.18539
         88  |    .3892071    3.051888      0.13    0.899     -5.592383     6.370797
         89  |    .6124882     4.57787      0.13    0.894     -8.359972     9.584948
         90  |    .8233655    6.103752      0.13    0.893     -11.13977      12.7865
         91  |    1.041693    7.629618      0.14    0.891     -13.91208     15.99547
         92  |    1.217202    9.155563      0.13    0.894     -16.72737     19.16178
         93  |    1.436931    10.68139      0.13    0.893     -19.49821     22.37207
         94  |    1.677285    12.20717      0.14    0.891     -22.24832     25.60289
         95  |     1.88738    13.73305      0.14    0.891      -25.0289     28.80366
         96  |    2.032644    15.25894      0.13    0.894     -27.87432     31.93961
         97  |    2.239108     16.7847      0.13    0.894      -30.6583     35.13652
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    D.efaprop
------------------------------------------------------------------------------
Options: pnotpen(i.year)   nocons
1.  (PDS/CHS) Selecting HD controls for dep var D.lpc_prop...
Selected:  xxpover0
Also inc:  86b.year 87.year 88.year 89.year 90.year 91.year 92.year 93.year
          94.year 95.year 96.year 97.year
2.  (PDS/CHS) Selecting HD controls for exog regressor D.efaprop...
Selected:  prop0 cL.xxpolice#cL.xxpolice c.xxpover0#c.xxpover0 Dxxincome0
          Dxxpover0 Dxxbeer0 c.Dprop0#c.Dprop0#c.trend#c.trend
          cL.xxincome#c.trend#c.trend cL.xxincome#cL.xxincome#c.trend#c.trend
          cL.xxbeer#cL.xxbeer#c.trend#c.trend c.Mxxpolice#c.trend
          c.Mxxpolice#c.Mxxpolice#c.trend
          c.Mxxincome#c.Mxxincome#c.trend#c.trend
          c.xxprison0#c.xxprison0#c.trend c.xxpover0#c.trend
          c.Dxxunemp0#c.Dxxunemp0#c.trend#c.trend c.Dxxincome0#c.trend
          c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend c.Dxxbeer0#c.trend
Also inc:  86b.year 87.year 88.year 89.year 90.year 91.year 92.year 93.year
          94.year 95.year 96.year 97.year


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      homoskedastic
Number of observations:                600
Exogenous (1):                         D.efaprop
High-dim controls (336):               prop0 c.prop0#c.prop0 Dprop0
                                       c.Dprop0#c.Dprop0 D.xxprison D.xxpolice
                                       D.xxunemp D.xxincome D.xxpover
                                       D.xxafdc15 D.xxgunlaw D.xxbeer
                                       cD.xxprison#cD.xxprison
                                       cD.xxprison#cD.xxpolice
                                       cD.xxprison#cD.xxunemp
                                       cD.xxprison#cD.xxincome
                                       cD.xxprison#cD.xxpover
                                       cD.xxprison#cD.xxafdc15
                                       cD.xxprison#cD.xxgunlaw
                                       cD.xxprison#cD.xxbeer
                                       cD.xxpolice#cD.xxpolice
                                       cD.xxpolice#cD.xxunemp
                                       cD.xxpolice#cD.xxincome
                                       cD.xxpolice#cD.xxpover
                                       cD.xxpolice#cD.xxafdc15
                                       cD.xxpolice#cD.xxgunlaw
                                       cD.xxpolice#cD.xxbeer
                                       cD.xxunemp#cD.xxunemp
                                       cD.xxunemp#cD.xxincome
                                       cD.xxunemp#cD.xxpover
                                       cD.xxunemp#cD.xxafdc15
                                       cD.xxunemp#cD.xxgunlaw
                                       cD.xxunemp#cD.xxbeer
                                       cD.xxincome#cD.xxincome
                                       cD.xxincome#cD.xxpover
                                       cD.xxincome#cD.xxafdc15
                                       cD.xxincome#cD.xxgunlaw
                                       cD.xxincome#cD.xxbeer
                                       cD.xxpover#cD.xxpover
                                       cD.xxpover#cD.xxafdc15
                                       cD.xxpover#cD.xxgunlaw
                                       cD.xxpover#cD.xxbeer
                                       cD.xxafdc15#cD.xxafdc15
                                       cD.xxafdc15#cD.xxgunlaw
                                       cD.xxafdc15#cD.xxbeer
                                       cD.xxgunlaw#cD.xxgunlaw
                                       cD.xxgunlaw#cD.xxbeer
                                       cD.xxbeer#cD.xxbeer L.xxprison
                                       cL.xxprison#cL.xxprison L.xxpolice
                                       cL.xxpolice#cL.xxpolice L.xxunemp
                                       cL.xxunemp#cL.xxunemp L.xxincome
                                       cL.xxincome#cL.xxincome L.xxpover
                                       cL.xxpover#cL.xxpover L.xxafdc15
                                       cL.xxafdc15#cL.xxafdc15 L.xxgunlaw
                                       cL.xxgunlaw#cL.xxgunlaw L.xxbeer
                                       cL.xxbeer#cL.xxbeer Mxxprison
                                       c.Mxxprison#c.Mxxprison Mxxpolice
                                       c.Mxxpolice#c.Mxxpolice Mxxunemp
                                       c.Mxxunemp#c.Mxxunemp Mxxincome
                                       c.Mxxincome#c.Mxxincome Mxxpover
                                       c.Mxxpover#c.Mxxpover Mxxafdc15
                                       c.Mxxafdc15#c.Mxxafdc15 Mxxgunlaw
                                       c.Mxxgunlaw#c.Mxxgunlaw Mxxbeer
                                       c.Mxxbeer#c.Mxxbeer xxprison0
                                       c.xxprison0#c.xxprison0 xxpolice0
                                       c.xxpolice0#c.xxpolice0 xxunemp0
                                       c.xxunemp0#c.xxunemp0 xxincome0
                                       c.xxincome0#c.xxincome0 xxpover0
                                       c.xxpover0#c.xxpover0 xxafdc150
                                       c.xxafdc150#c.xxafdc150 xxgunlaw0
                                       c.xxgunlaw0#c.xxgunlaw0 xxbeer0
                                       c.xxbeer0#c.xxbeer0 Dxxprison0
                                       c.Dxxprison0#c.Dxxprison0 Dxxpolice0
                                       c.Dxxpolice0#c.Dxxpolice0 Dxxunemp0
                                       c.Dxxunemp0#c.Dxxunemp0 Dxxincome0
                                       c.Dxxincome0#c.Dxxincome0 Dxxpover0
                                       c.Dxxpover0#c.Dxxpover0 Dxxafdc150
                                       c.Dxxafdc150#c.Dxxafdc150 Dxxgunlaw0
                                       c.Dxxgunlaw0#c.Dxxgunlaw0 Dxxbeer0
                                       c.Dxxbeer0#c.Dxxbeer0 c.prop0#c.trend
                                       c.prop0#c.trend#c.trend
                                       c.prop0#c.prop0#c.trend
                                       c.prop0#c.prop0#c.trend#c.trend
                                       c.Dprop0#c.trend
                                       c.Dprop0#c.trend#c.trend
                                       c.Dprop0#c.Dprop0#c.trend
                                       c.Dprop0#c.Dprop0#c.trend#c.trend
                                       cD.xxprison#c.trend
                                       cD.xxprison#c.trend#c.trend
                                       cD.xxpolice#c.trend
                                       cD.xxpolice#c.trend#c.trend
                                       cD.xxunemp#c.trend
                                       cD.xxunemp#c.trend#c.trend
                                       cD.xxincome#c.trend
                                       cD.xxincome#c.trend#c.trend
                                       cD.xxpover#c.trend
                                       cD.xxpover#c.trend#c.trend
                                       cD.xxafdc15#c.trend
                                       cD.xxafdc15#c.trend#c.trend
                                       cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#c.trend#c.trend
                                       cD.xxbeer#c.trend
                                       cD.xxbeer#c.trend#c.trend
                                       cD.xxprison#cD.xxprison#c.trend
                                       cD.xxprison#cD.xxprison#c.trend#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend#c.trend
                                       cD.xxprison#cD.xxincome#c.trend
                                       cD.xxprison#cD.xxincome#c.trend#c.trend
                                       cD.xxprison#cD.xxpover#c.trend
                                       cD.xxprison#cD.xxpover#c.trend#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend#c.trend
                                       cD.xxincome#cD.xxincome#c.trend
                                       cD.xxincome#cD.xxincome#c.trend#c.trend
                                       cD.xxincome#cD.xxpover#c.trend
                                       cD.xxincome#cD.xxpover#c.trend#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend#c.trend
                                       cD.xxpover#cD.xxpover#c.trend
                                       cD.xxpover#cD.xxpover#c.trend#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend#c.trend
                                       cL.xxprison#c.trend
                                       cL.xxprison#c.trend#c.trend
                                       cL.xxprison#cL.xxprison#c.trend
                                       cL.xxprison#cL.xxprison#c.trend#c.trend
                                       cL.xxpolice#c.trend
                                       cL.xxpolice#c.trend#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend#c.trend
                                       cL.xxunemp#c.trend
                                       cL.xxunemp#c.trend#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend#c.trend
                                       cL.xxincome#c.trend
                                       cL.xxincome#c.trend#c.trend
                                       cL.xxincome#cL.xxincome#c.trend
                                       cL.xxincome#cL.xxincome#c.trend#c.trend
                                       cL.xxpover#c.trend
                                       cL.xxpover#c.trend#c.trend
                                       cL.xxpover#cL.xxpover#c.trend
                                       cL.xxpover#cL.xxpover#c.trend#c.trend
                                       cL.xxafdc15#c.trend
                                       cL.xxafdc15#c.trend#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend#c.trend
                                       cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#c.trend#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend#c.trend
                                       cL.xxbeer#c.trend
                                       cL.xxbeer#c.trend#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend#c.trend
                                       c.Mxxprison#c.trend
                                       c.Mxxprison#c.trend#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend#c.trend
                                       c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.trend#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend#c.trend
                                       c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.trend#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend#c.trend
                                       c.Mxxincome#c.trend
                                       c.Mxxincome#c.trend#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend#c.trend
                                       c.Mxxpover#c.trend
                                       c.Mxxpover#c.trend#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend#c.trend
                                       c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.trend#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend#c.trend
                                       c.xxprison0#c.trend
                                       c.xxprison0#c.trend#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.xxprison0#c.xxprison0#c.trend#c.trend
                                       c.xxpolice0#c.trend
                                       c.xxpolice0#c.trend#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend#c.trend
                                       c.xxunemp0#c.trend
                                       c.xxunemp0#c.trend#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend#c.trend
                                       c.xxincome0#c.trend
                                       c.xxincome0#c.trend#c.trend
                                       c.xxincome0#c.xxincome0#c.trend
                                       c.xxincome0#c.xxincome0#c.trend#c.trend
                                       c.xxpover0#c.trend
                                       c.xxpover0#c.trend#c.trend
                                       c.xxpover0#c.xxpover0#c.trend
                                       c.xxpover0#c.xxpover0#c.trend#c.trend
                                       c.xxafdc150#c.trend
                                       c.xxafdc150#c.trend#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend#c.trend
                                       c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.trend#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend#c.trend
                                       c.xxbeer0#c.trend
                                       c.xxbeer0#c.trend#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend#c.trend
                                       c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.trend#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend#c.trend
                                       c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.trend#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend#c.trend
                                       c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.trend#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend#c.trend
                                       c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.trend#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend#c.trend
Selected controls (32):                prop0 cL.xxpolice#cL.xxpolice xxpover0
                                       c.xxpover0#c.xxpover0 Dxxincome0
                                       Dxxpover0 Dxxbeer0
                                       c.Dprop0#c.Dprop0#c.trend#c.trend
                                       cL.xxincome#c.trend#c.trend
                                       cL.xxincome#cL.xxincome#c.trend#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend#c.trend
                                       c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.xxpover0#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxincome0#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxbeer0#c.trend 86b.year 87.year
                                       88.year 89.year 90.year 91.year 92.year
                                       93.year 94.year 95.year 96.year 97.year
Unpenalized controls (12):             86b.year 87.year 88.year 89.year
                                       90.year 91.year 92.year 93.year 94.year
                                       95.year 96.year 97.year

Structural equation:

OLS using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.1129452    .0471613     -2.39    0.017     -.2053797    -.0205107
-------------+----------------------------------------------------------------

OLS using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.1243104    .0561115     -2.22    0.027     -.2342869    -.0143339
-------------+----------------------------------------------------------------

OLS with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.1249273    .0537028     -2.33    0.020     -.2301828    -.0196718
             |
       prop0 |    .0792361    .0437197      1.81    0.070      -.006453     .1649251
             |
 cL.xxpolice#|
 cL.xxpolice |   -.0043274    .0119129     -0.36    0.716     -.0276763     .0190214
             |
    xxpover0 |    .0789171    .3117382      0.25    0.800     -.5320785     .6899127
             |
  c.xxpover0#|
  c.xxpover0 |    .3729211    .9758498      0.38    0.702     -1.539709     2.285552
             |
  Dxxincome0 |    34.99602    18.23882      1.92    0.055     -.7514051     70.74345
   Dxxpover0 |    .0143833    .1089095      0.13    0.895     -.1990754      .227842
    Dxxbeer0 |    .2692004    .6794504      0.40    0.692     -1.062498     1.600899
             |
    c.Dprop0#|
    c.Dprop0#|
     c.trend#|
     c.trend |   -.9080259    .3727286     -2.44    0.015      -1.63856    -.1774913
             |
 cL.xxincome#|
     c.trend#|
     c.trend |    41.52011    84.98057      0.49    0.625     -125.0387      208.079
             |
 cL.xxincome#|
 cL.xxincome#|
     c.trend#|
     c.trend |    200.7512    427.7834      0.47    0.639      -637.689     1039.191
             |
   cL.xxbeer#|
   cL.xxbeer#|
     c.trend#|
     c.trend |    .0770561    .2640172      0.29    0.770      -.440408     .5945202
             |
 c.Mxxpolice#|
     c.trend |    .0287607    .1942463      0.15    0.882     -.3519551     .4094765
             |
 c.Mxxpolice#|
 c.Mxxpolice#|
     c.trend |   -.0106548    .0986216     -0.11    0.914     -.2039495     .1826399
             |
 c.Mxxincome#|
 c.Mxxincome#|
     c.trend#|
     c.trend |    -428.356    96.97366     -4.42    0.000     -618.4209    -238.2911
             |
 c.xxprison0#|
 c.xxprison0#|
     c.trend |     .030852    .0101745      3.03    0.002      .0109104     .0507937
             |
  c.xxpover0#|
     c.trend |   -.2958701    .2304414     -1.28    0.199     -.7475269     .1557867
             |
 c.Dxxunemp0#|
 c.Dxxunemp0#|
     c.trend#|
     c.trend |   -65.24584    59.34795     -1.10    0.272     -181.5657     51.07401
             |
          c. |
  Dxxincome0#|
     c.trend |   -41.23409    34.61589     -1.19    0.234       -109.08      26.6118
             |
          c. |
  Dxxafdc150#|
          c. |
  Dxxafdc150#|
     c.trend#|
     c.trend |   -.2834092     .644429     -0.44    0.660     -1.546467     .9796484
             |
  c.Dxxbeer0#|
     c.trend |   -1.099811     1.17389     -0.94    0.349     -3.400593     1.200971
             |
        year |
         87  |   -.0512272    .0913204     -0.56    0.575     -.2302119     .1277576
         88  |   -.1289526    .2392057     -0.54    0.590     -.5977871     .3398819
         89  |   -.2005595    .4462036     -0.45    0.653     -1.075103     .6739836
         90  |   -.3109494    .7122762     -0.44    0.662     -1.706985     1.085086
         91  |   -.4462902    1.037459     -0.43    0.667     -2.479673     1.587092
         92  |   -.6627095    1.421645     -0.47    0.641     -3.449083     2.123664
         93  |   -.8505574    1.864888     -0.46    0.648     -4.505671     2.804556
         94  |   -1.044099    2.367257     -0.44    0.659     -5.683837      3.59564
         95  |   -1.295079    2.928717     -0.44    0.658      -7.03526     4.445101
         96  |   -1.641102    3.549381     -0.46    0.644     -8.597762     5.315557
         97  |   -1.955717    4.228819     -0.46    0.644     -10.24405     6.332617
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    D.efaprop
------------------------------------------------------------------------------
Options: pnotpen(i.year) robust
1.  (PDS/CHS) Selecting HD controls for dep var D.lpc_prop...
Selected:  xxafdc150 c.prop0#c.trend#c.trend c.Mxxincome#c.trend#c.trend
          c.Mxxincome#c.Mxxincome#c.trend#c.trend c.xxincome0#c.trend#c.trend
          c.xxincome0#c.xxincome0#c.trend#c.trend
Also inc:  86b.year 87.year 88.year 89.year 90.year 91.year 92.year 93.year
          94.year 95.year 96.year 97.year
2.  (PDS/CHS) Selecting HD controls for exog regressor D.efaprop...
Selected:  prop0 L.xxprison L.xxpolice L.xxincome Mxxincome Dxxincome0
          c.xxprison0#c.xxprison0#c.trend#c.trend
          c.xxbeer0#c.xxbeer0#c.trend#c.trend c.Dxxincome0#c.trend
          c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend c.Dxxbeer0#c.trend
Also inc:  86b.year 87.year 88.year 89.year 90.year 91.year 92.year 93.year
          94.year 95.year 96.year 97.year


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      heteroskedastic
Number of observations:                600
Exogenous (1):                         D.efaprop
High-dim controls (336):               prop0 c.prop0#c.prop0 Dprop0
                                       c.Dprop0#c.Dprop0 D.xxprison D.xxpolice
                                       D.xxunemp D.xxincome D.xxpover
                                       D.xxafdc15 D.xxgunlaw D.xxbeer
                                       cD.xxprison#cD.xxprison
                                       cD.xxprison#cD.xxpolice
                                       cD.xxprison#cD.xxunemp
                                       cD.xxprison#cD.xxincome
                                       cD.xxprison#cD.xxpover
                                       cD.xxprison#cD.xxafdc15
                                       cD.xxprison#cD.xxgunlaw
                                       cD.xxprison#cD.xxbeer
                                       cD.xxpolice#cD.xxpolice
                                       cD.xxpolice#cD.xxunemp
                                       cD.xxpolice#cD.xxincome
                                       cD.xxpolice#cD.xxpover
                                       cD.xxpolice#cD.xxafdc15
                                       cD.xxpolice#cD.xxgunlaw
                                       cD.xxpolice#cD.xxbeer
                                       cD.xxunemp#cD.xxunemp
                                       cD.xxunemp#cD.xxincome
                                       cD.xxunemp#cD.xxpover
                                       cD.xxunemp#cD.xxafdc15
                                       cD.xxunemp#cD.xxgunlaw
                                       cD.xxunemp#cD.xxbeer
                                       cD.xxincome#cD.xxincome
                                       cD.xxincome#cD.xxpover
                                       cD.xxincome#cD.xxafdc15
                                       cD.xxincome#cD.xxgunlaw
                                       cD.xxincome#cD.xxbeer
                                       cD.xxpover#cD.xxpover
                                       cD.xxpover#cD.xxafdc15
                                       cD.xxpover#cD.xxgunlaw
                                       cD.xxpover#cD.xxbeer
                                       cD.xxafdc15#cD.xxafdc15
                                       cD.xxafdc15#cD.xxgunlaw
                                       cD.xxafdc15#cD.xxbeer
                                       cD.xxgunlaw#cD.xxgunlaw
                                       cD.xxgunlaw#cD.xxbeer
                                       cD.xxbeer#cD.xxbeer L.xxprison
                                       cL.xxprison#cL.xxprison L.xxpolice
                                       cL.xxpolice#cL.xxpolice L.xxunemp
                                       cL.xxunemp#cL.xxunemp L.xxincome
                                       cL.xxincome#cL.xxincome L.xxpover
                                       cL.xxpover#cL.xxpover L.xxafdc15
                                       cL.xxafdc15#cL.xxafdc15 L.xxgunlaw
                                       cL.xxgunlaw#cL.xxgunlaw L.xxbeer
                                       cL.xxbeer#cL.xxbeer Mxxprison
                                       c.Mxxprison#c.Mxxprison Mxxpolice
                                       c.Mxxpolice#c.Mxxpolice Mxxunemp
                                       c.Mxxunemp#c.Mxxunemp Mxxincome
                                       c.Mxxincome#c.Mxxincome Mxxpover
                                       c.Mxxpover#c.Mxxpover Mxxafdc15
                                       c.Mxxafdc15#c.Mxxafdc15 Mxxgunlaw
                                       c.Mxxgunlaw#c.Mxxgunlaw Mxxbeer
                                       c.Mxxbeer#c.Mxxbeer xxprison0
                                       c.xxprison0#c.xxprison0 xxpolice0
                                       c.xxpolice0#c.xxpolice0 xxunemp0
                                       c.xxunemp0#c.xxunemp0 xxincome0
                                       c.xxincome0#c.xxincome0 xxpover0
                                       c.xxpover0#c.xxpover0 xxafdc150
                                       c.xxafdc150#c.xxafdc150 xxgunlaw0
                                       c.xxgunlaw0#c.xxgunlaw0 xxbeer0
                                       c.xxbeer0#c.xxbeer0 Dxxprison0
                                       c.Dxxprison0#c.Dxxprison0 Dxxpolice0
                                       c.Dxxpolice0#c.Dxxpolice0 Dxxunemp0
                                       c.Dxxunemp0#c.Dxxunemp0 Dxxincome0
                                       c.Dxxincome0#c.Dxxincome0 Dxxpover0
                                       c.Dxxpover0#c.Dxxpover0 Dxxafdc150
                                       c.Dxxafdc150#c.Dxxafdc150 Dxxgunlaw0
                                       c.Dxxgunlaw0#c.Dxxgunlaw0 Dxxbeer0
                                       c.Dxxbeer0#c.Dxxbeer0 c.prop0#c.trend
                                       c.prop0#c.trend#c.trend
                                       c.prop0#c.prop0#c.trend
                                       c.prop0#c.prop0#c.trend#c.trend
                                       c.Dprop0#c.trend
                                       c.Dprop0#c.trend#c.trend
                                       c.Dprop0#c.Dprop0#c.trend
                                       c.Dprop0#c.Dprop0#c.trend#c.trend
                                       cD.xxprison#c.trend
                                       cD.xxprison#c.trend#c.trend
                                       cD.xxpolice#c.trend
                                       cD.xxpolice#c.trend#c.trend
                                       cD.xxunemp#c.trend
                                       cD.xxunemp#c.trend#c.trend
                                       cD.xxincome#c.trend
                                       cD.xxincome#c.trend#c.trend
                                       cD.xxpover#c.trend
                                       cD.xxpover#c.trend#c.trend
                                       cD.xxafdc15#c.trend
                                       cD.xxafdc15#c.trend#c.trend
                                       cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#c.trend#c.trend
                                       cD.xxbeer#c.trend
                                       cD.xxbeer#c.trend#c.trend
                                       cD.xxprison#cD.xxprison#c.trend
                                       cD.xxprison#cD.xxprison#c.trend#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend#c.trend
                                       cD.xxprison#cD.xxincome#c.trend
                                       cD.xxprison#cD.xxincome#c.trend#c.trend
                                       cD.xxprison#cD.xxpover#c.trend
                                       cD.xxprison#cD.xxpover#c.trend#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend#c.trend
                                       cD.xxincome#cD.xxincome#c.trend
                                       cD.xxincome#cD.xxincome#c.trend#c.trend
                                       cD.xxincome#cD.xxpover#c.trend
                                       cD.xxincome#cD.xxpover#c.trend#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend#c.trend
                                       cD.xxpover#cD.xxpover#c.trend
                                       cD.xxpover#cD.xxpover#c.trend#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend#c.trend
                                       cL.xxprison#c.trend
                                       cL.xxprison#c.trend#c.trend
                                       cL.xxprison#cL.xxprison#c.trend
                                       cL.xxprison#cL.xxprison#c.trend#c.trend
                                       cL.xxpolice#c.trend
                                       cL.xxpolice#c.trend#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend#c.trend
                                       cL.xxunemp#c.trend
                                       cL.xxunemp#c.trend#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend#c.trend
                                       cL.xxincome#c.trend
                                       cL.xxincome#c.trend#c.trend
                                       cL.xxincome#cL.xxincome#c.trend
                                       cL.xxincome#cL.xxincome#c.trend#c.trend
                                       cL.xxpover#c.trend
                                       cL.xxpover#c.trend#c.trend
                                       cL.xxpover#cL.xxpover#c.trend
                                       cL.xxpover#cL.xxpover#c.trend#c.trend
                                       cL.xxafdc15#c.trend
                                       cL.xxafdc15#c.trend#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend#c.trend
                                       cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#c.trend#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend#c.trend
                                       cL.xxbeer#c.trend
                                       cL.xxbeer#c.trend#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend#c.trend
                                       c.Mxxprison#c.trend
                                       c.Mxxprison#c.trend#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend#c.trend
                                       c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.trend#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend#c.trend
                                       c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.trend#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend#c.trend
                                       c.Mxxincome#c.trend
                                       c.Mxxincome#c.trend#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend#c.trend
                                       c.Mxxpover#c.trend
                                       c.Mxxpover#c.trend#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend#c.trend
                                       c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.trend#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend#c.trend
                                       c.xxprison0#c.trend
                                       c.xxprison0#c.trend#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.xxprison0#c.xxprison0#c.trend#c.trend
                                       c.xxpolice0#c.trend
                                       c.xxpolice0#c.trend#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend#c.trend
                                       c.xxunemp0#c.trend
                                       c.xxunemp0#c.trend#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend#c.trend
                                       c.xxincome0#c.trend
                                       c.xxincome0#c.trend#c.trend
                                       c.xxincome0#c.xxincome0#c.trend
                                       c.xxincome0#c.xxincome0#c.trend#c.trend
                                       c.xxpover0#c.trend
                                       c.xxpover0#c.trend#c.trend
                                       c.xxpover0#c.xxpover0#c.trend
                                       c.xxpover0#c.xxpover0#c.trend#c.trend
                                       c.xxafdc150#c.trend
                                       c.xxafdc150#c.trend#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend#c.trend
                                       c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.trend#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend#c.trend
                                       c.xxbeer0#c.trend
                                       c.xxbeer0#c.trend#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend#c.trend
                                       c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.trend#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend#c.trend
                                       c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.trend#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend#c.trend
                                       c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.trend#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend#c.trend
                                       c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.trend#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend#c.trend
Selected controls (29):                prop0 L.xxprison L.xxpolice L.xxincome
                                       Mxxincome xxafdc150 Dxxincome0
                                       c.prop0#c.trend#c.trend
                                       c.Mxxincome#c.trend#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend#c.trend
                                       c.xxprison0#c.xxprison0#c.trend#c.trend
                                       c.xxincome0#c.trend#c.trend
                                       c.xxincome0#c.xxincome0#c.trend#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend#c.trend
                                       c.Dxxincome0#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxbeer0#c.trend 86b.year 87.year
                                       88.year 89.year 90.year 91.year 92.year
                                       93.year 94.year 95.year 96.year 97.year
Unpenalized controls (13):             86b.year 87.year 88.year 89.year
                                       90.year 91.year 92.year 93.year 94.year
                                       95.year 96.year 97.year _cons

Structural equation:

OLS using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.0901707    .0371218     -2.43    0.015     -.1629281    -.0174132
-------------+----------------------------------------------------------------

OLS using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.0815171    .0412596     -1.98    0.048     -.1623844    -.0006497
-------------+----------------------------------------------------------------

OLS with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.1043327    .0550339     -1.90    0.058     -.2121972     .0035319
             |
       prop0 |    .0603249    .0388486      1.55    0.120      -.015817     .1364668
             |
    xxprison |
         L1. |    .0080054    .0061558      1.30    0.193     -.0040597     .0200704
             |
    xxpolice |
         L1. |   -.0138804    .0144047     -0.96    0.335     -.0421132     .0143523
             |
    xxincome |
         L1. |    35.43162    8.915832      3.97    0.000      17.95691     52.90633
             |
   Mxxincome |   -37.17162    10.07015     -3.69    0.000     -56.90876    -17.43448
   xxafdc150 |     -.00849    .0135324     -0.63    0.530      -.035013     .0180329
  Dxxincome0 |    45.78121    24.60904      1.86    0.063     -2.451623     94.01405
             |
     c.prop0#|
     c.trend#|
     c.trend |   -.1564537    .0592307     -2.64    0.008     -.2725438    -.0403635
             |
 c.Mxxincome#|
     c.trend#|
     c.trend |    751.2119     1110.86      0.68    0.499     -1426.034     2928.458
             |
 c.Mxxincome#|
 c.Mxxincome#|
     c.trend#|
     c.trend |   -3713.925    5490.676     -0.68    0.499     -14475.45     7047.601
             |
 c.xxprison0#|
 c.xxprison0#|
     c.trend#|
     c.trend |    .0216117     .011734      1.84    0.066     -.0013864     .0446099
             |
 c.xxincome0#|
     c.trend#|
     c.trend |   -501.7564    1018.661     -0.49    0.622     -2498.294     1494.782
             |
 c.xxincome0#|
 c.xxincome0#|
     c.trend#|
     c.trend |    2502.293    5090.656      0.49    0.623      -7475.21      12479.8
             |
   c.xxbeer0#|
   c.xxbeer0#|
     c.trend#|
     c.trend |   -.1130256    .2303059     -0.49    0.624     -.5644169     .3383656
             |
          c. |
  Dxxincome0#|
     c.trend |   -48.36178    46.98322     -1.03    0.303     -140.4472     43.72363
             |
          c. |
  Dxxafdc150#|
          c. |
  Dxxafdc150#|
     c.trend#|
     c.trend |    .3091996    .5478801      0.56    0.573     -.7646257     1.383025
             |
  c.Dxxbeer0#|
     c.trend |   -.8144925    .6588336     -1.24    0.216     -2.105783     .4767976
             |
        year |
         87  |   -.2933012    .3692027     -0.79    0.427     -1.016925     .4303228
         88  |   -.7574075    .9839872     -0.77    0.441     -2.685987     1.171172
         89  |   -1.369933     1.84491     -0.74    0.458      -4.98589     2.246025
         90  |    -2.17282     2.95188     -0.74    0.462     -7.958398     3.612758
         91  |   -3.148265    4.305268     -0.73    0.465     -11.58643     5.289905
         92  |   -4.354988    5.904155     -0.74    0.461     -15.92692     7.216943
         93  |   -5.686088    7.748045     -0.73    0.463     -20.87198     9.499802
         94  |   -7.172672    9.838669     -0.73    0.466     -26.45611     12.11076
         95  |   -8.862582    12.17699     -0.73    0.467     -32.72905     15.00388
         96  |   -10.79021    14.75864     -0.73    0.465     -39.71662     18.13621
         97  |   -12.83471    17.58625     -0.73    0.466     -47.30313      21.6337
             |
       _cons |    .1592432    .3405101      0.47    0.640     -.5081442     .8266307
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    D.efaprop
------------------------------------------------------------------------------
Options: pnotpen(i.year) robust fe
Fixed effects transformation...
1.  (PDS/CHS) Selecting HD controls for dep var D.lpc_prop...
Selected:  L.xxunemp
Also inc:  86b.year 87.year 88.year 89.year 90.year 91.year 92.year 93.year
          94.year 95.year 96.year 97.year
2.  (PDS/CHS) Selecting HD controls for exog regressor D.efaprop...
Selected:  D.xxincome L.xxunemp c.prop0#c.trend#c.trend
          c.Mxxbeer#c.Mxxbeer#c.trend c.xxprison0#c.xxprison0#c.trend
          c.Dxxunemp0#c.Dxxunemp0#c.trend#c.trend c.Dxxincome0#c.trend
          c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
Also inc:  86b.year 87.year 88.year 89.year 90.year 91.year 92.year 93.year
          94.year 95.year 96.year 97.year


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      heteroskedastic
Number of observations:                600
Number of fixed effects:                50
Exogenous (1):                         D.efaprop
High-dim controls (336):               prop0 c.prop0#c.prop0 Dprop0
                                       c.Dprop0#c.Dprop0 D.xxprison D.xxpolice
                                       D.xxunemp D.xxincome D.xxpover
                                       D.xxafdc15 D.xxgunlaw D.xxbeer
                                       cD.xxprison#cD.xxprison
                                       cD.xxprison#cD.xxpolice
                                       cD.xxprison#cD.xxunemp
                                       cD.xxprison#cD.xxincome
                                       cD.xxprison#cD.xxpover
                                       cD.xxprison#cD.xxafdc15
                                       cD.xxprison#cD.xxgunlaw
                                       cD.xxprison#cD.xxbeer
                                       cD.xxpolice#cD.xxpolice
                                       cD.xxpolice#cD.xxunemp
                                       cD.xxpolice#cD.xxincome
                                       cD.xxpolice#cD.xxpover
                                       cD.xxpolice#cD.xxafdc15
                                       cD.xxpolice#cD.xxgunlaw
                                       cD.xxpolice#cD.xxbeer
                                       cD.xxunemp#cD.xxunemp
                                       cD.xxunemp#cD.xxincome
                                       cD.xxunemp#cD.xxpover
                                       cD.xxunemp#cD.xxafdc15
                                       cD.xxunemp#cD.xxgunlaw
                                       cD.xxunemp#cD.xxbeer
                                       cD.xxincome#cD.xxincome
                                       cD.xxincome#cD.xxpover
                                       cD.xxincome#cD.xxafdc15
                                       cD.xxincome#cD.xxgunlaw
                                       cD.xxincome#cD.xxbeer
                                       cD.xxpover#cD.xxpover
                                       cD.xxpover#cD.xxafdc15
                                       cD.xxpover#cD.xxgunlaw
                                       cD.xxpover#cD.xxbeer
                                       cD.xxafdc15#cD.xxafdc15
                                       cD.xxafdc15#cD.xxgunlaw
                                       cD.xxafdc15#cD.xxbeer
                                       cD.xxgunlaw#cD.xxgunlaw
                                       cD.xxgunlaw#cD.xxbeer
                                       cD.xxbeer#cD.xxbeer L.xxprison
                                       cL.xxprison#cL.xxprison L.xxpolice
                                       cL.xxpolice#cL.xxpolice L.xxunemp
                                       cL.xxunemp#cL.xxunemp L.xxincome
                                       cL.xxincome#cL.xxincome L.xxpover
                                       cL.xxpover#cL.xxpover L.xxafdc15
                                       cL.xxafdc15#cL.xxafdc15 L.xxgunlaw
                                       cL.xxgunlaw#cL.xxgunlaw L.xxbeer
                                       cL.xxbeer#cL.xxbeer Mxxprison
                                       c.Mxxprison#c.Mxxprison Mxxpolice
                                       c.Mxxpolice#c.Mxxpolice Mxxunemp
                                       c.Mxxunemp#c.Mxxunemp Mxxincome
                                       c.Mxxincome#c.Mxxincome Mxxpover
                                       c.Mxxpover#c.Mxxpover Mxxafdc15
                                       c.Mxxafdc15#c.Mxxafdc15 Mxxgunlaw
                                       c.Mxxgunlaw#c.Mxxgunlaw Mxxbeer
                                       c.Mxxbeer#c.Mxxbeer xxprison0
                                       c.xxprison0#c.xxprison0 xxpolice0
                                       c.xxpolice0#c.xxpolice0 xxunemp0
                                       c.xxunemp0#c.xxunemp0 xxincome0
                                       c.xxincome0#c.xxincome0 xxpover0
                                       c.xxpover0#c.xxpover0 xxafdc150
                                       c.xxafdc150#c.xxafdc150 xxgunlaw0
                                       c.xxgunlaw0#c.xxgunlaw0 xxbeer0
                                       c.xxbeer0#c.xxbeer0 Dxxprison0
                                       c.Dxxprison0#c.Dxxprison0 Dxxpolice0
                                       c.Dxxpolice0#c.Dxxpolice0 Dxxunemp0
                                       c.Dxxunemp0#c.Dxxunemp0 Dxxincome0
                                       c.Dxxincome0#c.Dxxincome0 Dxxpover0
                                       c.Dxxpover0#c.Dxxpover0 Dxxafdc150
                                       c.Dxxafdc150#c.Dxxafdc150 Dxxgunlaw0
                                       c.Dxxgunlaw0#c.Dxxgunlaw0 Dxxbeer0
                                       c.Dxxbeer0#c.Dxxbeer0 c.prop0#c.trend
                                       c.prop0#c.trend#c.trend
                                       c.prop0#c.prop0#c.trend
                                       c.prop0#c.prop0#c.trend#c.trend
                                       c.Dprop0#c.trend
                                       c.Dprop0#c.trend#c.trend
                                       c.Dprop0#c.Dprop0#c.trend
                                       c.Dprop0#c.Dprop0#c.trend#c.trend
                                       cD.xxprison#c.trend
                                       cD.xxprison#c.trend#c.trend
                                       cD.xxpolice#c.trend
                                       cD.xxpolice#c.trend#c.trend
                                       cD.xxunemp#c.trend
                                       cD.xxunemp#c.trend#c.trend
                                       cD.xxincome#c.trend
                                       cD.xxincome#c.trend#c.trend
                                       cD.xxpover#c.trend
                                       cD.xxpover#c.trend#c.trend
                                       cD.xxafdc15#c.trend
                                       cD.xxafdc15#c.trend#c.trend
                                       cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#c.trend#c.trend
                                       cD.xxbeer#c.trend
                                       cD.xxbeer#c.trend#c.trend
                                       cD.xxprison#cD.xxprison#c.trend
                                       cD.xxprison#cD.xxprison#c.trend#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend#c.trend
                                       cD.xxprison#cD.xxincome#c.trend
                                       cD.xxprison#cD.xxincome#c.trend#c.trend
                                       cD.xxprison#cD.xxpover#c.trend
                                       cD.xxprison#cD.xxpover#c.trend#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend#c.trend
                                       cD.xxincome#cD.xxincome#c.trend
                                       cD.xxincome#cD.xxincome#c.trend#c.trend
                                       cD.xxincome#cD.xxpover#c.trend
                                       cD.xxincome#cD.xxpover#c.trend#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend#c.trend
                                       cD.xxpover#cD.xxpover#c.trend
                                       cD.xxpover#cD.xxpover#c.trend#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend#c.trend
                                       cL.xxprison#c.trend
                                       cL.xxprison#c.trend#c.trend
                                       cL.xxprison#cL.xxprison#c.trend
                                       cL.xxprison#cL.xxprison#c.trend#c.trend
                                       cL.xxpolice#c.trend
                                       cL.xxpolice#c.trend#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend#c.trend
                                       cL.xxunemp#c.trend
                                       cL.xxunemp#c.trend#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend#c.trend
                                       cL.xxincome#c.trend
                                       cL.xxincome#c.trend#c.trend
                                       cL.xxincome#cL.xxincome#c.trend
                                       cL.xxincome#cL.xxincome#c.trend#c.trend
                                       cL.xxpover#c.trend
                                       cL.xxpover#c.trend#c.trend
                                       cL.xxpover#cL.xxpover#c.trend
                                       cL.xxpover#cL.xxpover#c.trend#c.trend
                                       cL.xxafdc15#c.trend
                                       cL.xxafdc15#c.trend#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend#c.trend
                                       cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#c.trend#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend#c.trend
                                       cL.xxbeer#c.trend
                                       cL.xxbeer#c.trend#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend#c.trend
                                       c.Mxxprison#c.trend
                                       c.Mxxprison#c.trend#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend#c.trend
                                       c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.trend#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend#c.trend
                                       c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.trend#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend#c.trend
                                       c.Mxxincome#c.trend
                                       c.Mxxincome#c.trend#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend#c.trend
                                       c.Mxxpover#c.trend
                                       c.Mxxpover#c.trend#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend#c.trend
                                       c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.trend#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend#c.trend
                                       c.xxprison0#c.trend
                                       c.xxprison0#c.trend#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.xxprison0#c.xxprison0#c.trend#c.trend
                                       c.xxpolice0#c.trend
                                       c.xxpolice0#c.trend#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend#c.trend
                                       c.xxunemp0#c.trend
                                       c.xxunemp0#c.trend#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend#c.trend
                                       c.xxincome0#c.trend
                                       c.xxincome0#c.trend#c.trend
                                       c.xxincome0#c.xxincome0#c.trend
                                       c.xxincome0#c.xxincome0#c.trend#c.trend
                                       c.xxpover0#c.trend
                                       c.xxpover0#c.trend#c.trend
                                       c.xxpover0#c.xxpover0#c.trend
                                       c.xxpover0#c.xxpover0#c.trend#c.trend
                                       c.xxafdc150#c.trend
                                       c.xxafdc150#c.trend#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend#c.trend
                                       c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.trend#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend#c.trend
                                       c.xxbeer0#c.trend
                                       c.xxbeer0#c.trend#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend#c.trend
                                       c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.trend#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend#c.trend
                                       c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.trend#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend#c.trend
                                       c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.trend#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend#c.trend
                                       c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.trend#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend#c.trend
Selected controls (20):                D.xxincome L.xxunemp
                                       c.prop0#c.trend#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxincome0#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       86b.year 87.year 88.year 89.year 90.year
                                       91.year 92.year 93.year 94.year 95.year
                                       96.year 97.year
Unpenalized controls (12):             86b.year 87.year 88.year 89.year
                                       90.year 91.year 92.year 93.year 94.year
                                       95.year 96.year 97.year

Structural equation (fixed effects, #groups=50):

OLS using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.0545445    .0613174     -0.89    0.374     -.1747244     .0656355
-------------+----------------------------------------------------------------

OLS using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.0708728     .066728     -1.06    0.288     -.2016574     .0599117
-------------+----------------------------------------------------------------

OLS with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.0708728    .0655627     -1.08    0.280     -.1993734     .0576277
             |
    xxincome |
         D1. |   -27.59272    13.83443     -1.99    0.046     -54.70771    -.4777299
             |
     xxunemp |
         L1. |   -.8351233     .215151     -3.88    0.000     -1.256811    -.4134351
             |
     c.prop0#|
     c.trend#|
     c.trend |   -.0947974    .0576251     -1.65    0.100     -.2077406     .0181457
             |
   c.Mxxbeer#|
   c.Mxxbeer#|
     c.trend |    .6889324    .3605034      1.91    0.056     -.0176413     1.395506
             |
 c.xxprison0#|
 c.xxprison0#|
     c.trend |   -.0046991    .0166347     -0.28    0.778     -.0373025     .0279044
             |
 c.Dxxunemp0#|
 c.Dxxunemp0#|
     c.trend#|
     c.trend |   -78.31638    72.66661     -1.08    0.281     -220.7403     64.10756
             |
          c. |
  Dxxincome0#|
     c.trend |   -28.25837    39.22787     -0.72    0.471     -105.1436     48.62685
             |
          c. |
  Dxxafdc150#|
          c. |
  Dxxafdc150#|
     c.trend#|
     c.trend |   -.5932685    .8528173     -0.70    0.487      -2.26476     1.078223
             |
        year |
         87  |   -.0266762    .0087537     -3.05    0.002     -.0438332    -.0095193
         88  |   -.0499206    .0099531     -5.02    0.000     -.0694283     -.030413
         89  |   -.0428834    .0131407     -3.26    0.001     -.0686387    -.0171281
         90  |   -.0478202    .0161614     -2.96    0.003      -.079496    -.0161445
         91  |   -.0462237     .018521     -2.50    0.013     -.0825242    -.0099232
         92  |   -.0842623    .0183434     -4.59    0.000     -.1202147      -.04831
         93  |   -.0752757    .0185256     -4.06    0.000     -.1115851    -.0389663
         94  |   -.0457316     .019393     -2.36    0.018     -.0837411     -.007722
         95  |   -.0378468    .0220703     -1.71    0.086     -.0811037     .0054102
         96  |   -.0906559    .0224875     -4.03    0.000     -.1347307    -.0465811
         97  |   -.0875697    .0248299     -3.53    0.000     -.1362354    -.0389039
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    D.efaprop
------------------------------------------------------------------------------
Options: pnotpen(i.year) robust nocons
1.  (PDS/CHS) Selecting HD controls for dep var D.lpc_prop...
Selected:  L.xxincome xxpover0 c.prop0#c.trend#c.trend
Also inc:  86b.year 87.year 88.year 89.year 90.year 91.year 92.year 93.year
          94.year 95.year 96.year 97.year
2.  (PDS/CHS) Selecting HD controls for exog regressor D.efaprop...
Selected:  prop0 L.xxprison cL.xxpolice#cL.xxpolice xxpover0
          c.xxpover0#c.xxpover0 Dxxincome0 Dxxpover0
          cL.xxincome#c.trend#c.trend cL.xxincome#cL.xxincome#c.trend
          c.Mxxincome#c.Mxxincome#c.trend
          c.xxprison0#c.xxprison0#c.trend#c.trend c.xxbeer0#c.trend#c.trend
          c.Dxxincome0#c.trend c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
          c.Dxxbeer0#c.trend
Also inc:  86b.year 87.year 88.year 89.year 90.year 91.year 92.year 93.year
          94.year 95.year 96.year 97.year


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      heteroskedastic
Number of observations:                600
Exogenous (1):                         D.efaprop
High-dim controls (336):               prop0 c.prop0#c.prop0 Dprop0
                                       c.Dprop0#c.Dprop0 D.xxprison D.xxpolice
                                       D.xxunemp D.xxincome D.xxpover
                                       D.xxafdc15 D.xxgunlaw D.xxbeer
                                       cD.xxprison#cD.xxprison
                                       cD.xxprison#cD.xxpolice
                                       cD.xxprison#cD.xxunemp
                                       cD.xxprison#cD.xxincome
                                       cD.xxprison#cD.xxpover
                                       cD.xxprison#cD.xxafdc15
                                       cD.xxprison#cD.xxgunlaw
                                       cD.xxprison#cD.xxbeer
                                       cD.xxpolice#cD.xxpolice
                                       cD.xxpolice#cD.xxunemp
                                       cD.xxpolice#cD.xxincome
                                       cD.xxpolice#cD.xxpover
                                       cD.xxpolice#cD.xxafdc15
                                       cD.xxpolice#cD.xxgunlaw
                                       cD.xxpolice#cD.xxbeer
                                       cD.xxunemp#cD.xxunemp
                                       cD.xxunemp#cD.xxincome
                                       cD.xxunemp#cD.xxpover
                                       cD.xxunemp#cD.xxafdc15
                                       cD.xxunemp#cD.xxgunlaw
                                       cD.xxunemp#cD.xxbeer
                                       cD.xxincome#cD.xxincome
                                       cD.xxincome#cD.xxpover
                                       cD.xxincome#cD.xxafdc15
                                       cD.xxincome#cD.xxgunlaw
                                       cD.xxincome#cD.xxbeer
                                       cD.xxpover#cD.xxpover
                                       cD.xxpover#cD.xxafdc15
                                       cD.xxpover#cD.xxgunlaw
                                       cD.xxpover#cD.xxbeer
                                       cD.xxafdc15#cD.xxafdc15
                                       cD.xxafdc15#cD.xxgunlaw
                                       cD.xxafdc15#cD.xxbeer
                                       cD.xxgunlaw#cD.xxgunlaw
                                       cD.xxgunlaw#cD.xxbeer
                                       cD.xxbeer#cD.xxbeer L.xxprison
                                       cL.xxprison#cL.xxprison L.xxpolice
                                       cL.xxpolice#cL.xxpolice L.xxunemp
                                       cL.xxunemp#cL.xxunemp L.xxincome
                                       cL.xxincome#cL.xxincome L.xxpover
                                       cL.xxpover#cL.xxpover L.xxafdc15
                                       cL.xxafdc15#cL.xxafdc15 L.xxgunlaw
                                       cL.xxgunlaw#cL.xxgunlaw L.xxbeer
                                       cL.xxbeer#cL.xxbeer Mxxprison
                                       c.Mxxprison#c.Mxxprison Mxxpolice
                                       c.Mxxpolice#c.Mxxpolice Mxxunemp
                                       c.Mxxunemp#c.Mxxunemp Mxxincome
                                       c.Mxxincome#c.Mxxincome Mxxpover
                                       c.Mxxpover#c.Mxxpover Mxxafdc15
                                       c.Mxxafdc15#c.Mxxafdc15 Mxxgunlaw
                                       c.Mxxgunlaw#c.Mxxgunlaw Mxxbeer
                                       c.Mxxbeer#c.Mxxbeer xxprison0
                                       c.xxprison0#c.xxprison0 xxpolice0
                                       c.xxpolice0#c.xxpolice0 xxunemp0
                                       c.xxunemp0#c.xxunemp0 xxincome0
                                       c.xxincome0#c.xxincome0 xxpover0
                                       c.xxpover0#c.xxpover0 xxafdc150
                                       c.xxafdc150#c.xxafdc150 xxgunlaw0
                                       c.xxgunlaw0#c.xxgunlaw0 xxbeer0
                                       c.xxbeer0#c.xxbeer0 Dxxprison0
                                       c.Dxxprison0#c.Dxxprison0 Dxxpolice0
                                       c.Dxxpolice0#c.Dxxpolice0 Dxxunemp0
                                       c.Dxxunemp0#c.Dxxunemp0 Dxxincome0
                                       c.Dxxincome0#c.Dxxincome0 Dxxpover0
                                       c.Dxxpover0#c.Dxxpover0 Dxxafdc150
                                       c.Dxxafdc150#c.Dxxafdc150 Dxxgunlaw0
                                       c.Dxxgunlaw0#c.Dxxgunlaw0 Dxxbeer0
                                       c.Dxxbeer0#c.Dxxbeer0 c.prop0#c.trend
                                       c.prop0#c.trend#c.trend
                                       c.prop0#c.prop0#c.trend
                                       c.prop0#c.prop0#c.trend#c.trend
                                       c.Dprop0#c.trend
                                       c.Dprop0#c.trend#c.trend
                                       c.Dprop0#c.Dprop0#c.trend
                                       c.Dprop0#c.Dprop0#c.trend#c.trend
                                       cD.xxprison#c.trend
                                       cD.xxprison#c.trend#c.trend
                                       cD.xxpolice#c.trend
                                       cD.xxpolice#c.trend#c.trend
                                       cD.xxunemp#c.trend
                                       cD.xxunemp#c.trend#c.trend
                                       cD.xxincome#c.trend
                                       cD.xxincome#c.trend#c.trend
                                       cD.xxpover#c.trend
                                       cD.xxpover#c.trend#c.trend
                                       cD.xxafdc15#c.trend
                                       cD.xxafdc15#c.trend#c.trend
                                       cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#c.trend#c.trend
                                       cD.xxbeer#c.trend
                                       cD.xxbeer#c.trend#c.trend
                                       cD.xxprison#cD.xxprison#c.trend
                                       cD.xxprison#cD.xxprison#c.trend#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend#c.trend
                                       cD.xxprison#cD.xxincome#c.trend
                                       cD.xxprison#cD.xxincome#c.trend#c.trend
                                       cD.xxprison#cD.xxpover#c.trend
                                       cD.xxprison#cD.xxpover#c.trend#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend#c.trend
                                       cD.xxincome#cD.xxincome#c.trend
                                       cD.xxincome#cD.xxincome#c.trend#c.trend
                                       cD.xxincome#cD.xxpover#c.trend
                                       cD.xxincome#cD.xxpover#c.trend#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend#c.trend
                                       cD.xxpover#cD.xxpover#c.trend
                                       cD.xxpover#cD.xxpover#c.trend#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend#c.trend
                                       cL.xxprison#c.trend
                                       cL.xxprison#c.trend#c.trend
                                       cL.xxprison#cL.xxprison#c.trend
                                       cL.xxprison#cL.xxprison#c.trend#c.trend
                                       cL.xxpolice#c.trend
                                       cL.xxpolice#c.trend#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend#c.trend
                                       cL.xxunemp#c.trend
                                       cL.xxunemp#c.trend#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend#c.trend
                                       cL.xxincome#c.trend
                                       cL.xxincome#c.trend#c.trend
                                       cL.xxincome#cL.xxincome#c.trend
                                       cL.xxincome#cL.xxincome#c.trend#c.trend
                                       cL.xxpover#c.trend
                                       cL.xxpover#c.trend#c.trend
                                       cL.xxpover#cL.xxpover#c.trend
                                       cL.xxpover#cL.xxpover#c.trend#c.trend
                                       cL.xxafdc15#c.trend
                                       cL.xxafdc15#c.trend#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend#c.trend
                                       cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#c.trend#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend#c.trend
                                       cL.xxbeer#c.trend
                                       cL.xxbeer#c.trend#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend#c.trend
                                       c.Mxxprison#c.trend
                                       c.Mxxprison#c.trend#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend#c.trend
                                       c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.trend#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend#c.trend
                                       c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.trend#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend#c.trend
                                       c.Mxxincome#c.trend
                                       c.Mxxincome#c.trend#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend#c.trend
                                       c.Mxxpover#c.trend
                                       c.Mxxpover#c.trend#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend#c.trend
                                       c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.trend#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend#c.trend
                                       c.xxprison0#c.trend
                                       c.xxprison0#c.trend#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.xxprison0#c.xxprison0#c.trend#c.trend
                                       c.xxpolice0#c.trend
                                       c.xxpolice0#c.trend#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend#c.trend
                                       c.xxunemp0#c.trend
                                       c.xxunemp0#c.trend#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend#c.trend
                                       c.xxincome0#c.trend
                                       c.xxincome0#c.trend#c.trend
                                       c.xxincome0#c.xxincome0#c.trend
                                       c.xxincome0#c.xxincome0#c.trend#c.trend
                                       c.xxpover0#c.trend
                                       c.xxpover0#c.trend#c.trend
                                       c.xxpover0#c.xxpover0#c.trend
                                       c.xxpover0#c.xxpover0#c.trend#c.trend
                                       c.xxafdc150#c.trend
                                       c.xxafdc150#c.trend#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend#c.trend
                                       c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.trend#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend#c.trend
                                       c.xxbeer0#c.trend
                                       c.xxbeer0#c.trend#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend#c.trend
                                       c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.trend#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend#c.trend
                                       c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.trend#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend#c.trend
                                       c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.trend#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend#c.trend
                                       c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.trend#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend#c.trend
Selected controls (29):                prop0 L.xxprison
                                       cL.xxpolice#cL.xxpolice L.xxincome
                                       xxpover0 c.xxpover0#c.xxpover0
                                       Dxxincome0 Dxxpover0
                                       c.prop0#c.trend#c.trend
                                       cL.xxincome#c.trend#c.trend
                                       cL.xxincome#cL.xxincome#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend
                                       c.xxprison0#c.xxprison0#c.trend#c.trend
                                       c.xxbeer0#c.trend#c.trend
                                       c.Dxxincome0#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxbeer0#c.trend 86b.year 87.year
                                       88.year 89.year 90.year 91.year 92.year
                                       93.year 94.year 95.year 96.year 97.year
Unpenalized controls (12):             86b.year 87.year 88.year 89.year
                                       90.year 91.year 92.year 93.year 94.year
                                       95.year 96.year 97.year

Structural equation:

OLS using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.1009135    .0350913     -2.88    0.004     -.1696911    -.0321359
-------------+----------------------------------------------------------------

OLS using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.1088839    .0408103     -2.67    0.008     -.1888706    -.0288972
-------------+----------------------------------------------------------------

OLS with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.1339299    .0512802     -2.61    0.009     -.2344373    -.0334225
             |
       prop0 |    .0539498     .035069      1.54    0.124     -.0147842     .1226838
             |
    xxprison |
         L1. |    .0093131    .0050627      1.84    0.066     -.0006097     .0192359
             |
 cL.xxpolice#|
 cL.xxpolice |   -.0114589    .0060985     -1.88    0.060     -.0234117     .0004939
             |
    xxincome |
         L1. |   -.6608146    .6529444     -1.01    0.312     -1.940562      .618933
             |
    xxpover0 |    .3293696    .3233231      1.02    0.308      -.304332     .9630711
             |
  c.xxpover0#|
  c.xxpover0 |   -.6773576    .9752944     -0.69    0.487     -2.588899     1.234184
             |
  Dxxincome0 |    33.79308    24.50941      1.38    0.168     -14.24449     81.83064
   Dxxpover0 |    .0975484    .1032517      0.94    0.345     -.1048212      .299918
             |
     c.prop0#|
     c.trend#|
     c.trend |   -.1519796     .058393     -2.60    0.009     -.2664277    -.0375315
             |
 cL.xxincome#|
     c.trend#|
     c.trend |   -20.63245    13.61609     -1.52    0.130      -47.3195     6.054596
             |
 cL.xxincome#|
 cL.xxincome#|
     c.trend |    395.0867    90.50894      4.37    0.000      217.6924     572.4809
             |
 c.Mxxincome#|
 c.Mxxincome#|
     c.trend |   -287.1712    78.43577     -3.66    0.000     -440.9025    -133.4399
             |
 c.xxprison0#|
 c.xxprison0#|
     c.trend#|
     c.trend |    .0266001    .0109948      2.42    0.016      .0050506     .0481496
             |
   c.xxbeer0#|
     c.trend#|
     c.trend |    .0353476    .1045891      0.34    0.735     -.1696434     .2403386
             |
          c. |
  Dxxincome0#|
     c.trend |   -24.86264    35.15336     -0.71    0.479     -93.76196     44.03668
             |
          c. |
  Dxxafdc150#|
          c. |
  Dxxafdc150#|
     c.trend#|
     c.trend |    .2976352    .5254807      0.57    0.571      -.732288     1.327558
             |
  c.Dxxbeer0#|
     c.trend |   -.7549021    .5904931     -1.28    0.201     -1.912247     .4024432
             |
        year |
         87  |   -.0594176    .0320022     -1.86    0.063     -.1221407     .0033056
         88  |    -.091387    .0480021     -1.90    0.057     -.1854694     .0026954
         89  |   -.0648725    .0555227     -1.17    0.243      -.173695     .0439501
         90  |   -.0242576     .066651     -0.36    0.716     -.1548911      .106376
         91  |    .0475868    .0988141      0.48    0.630     -.1460852     .2412588
         92  |    .0941692    .1564882      0.60    0.547      -.212542     .4008804
         93  |    .2214649    .2368594      0.94    0.350      -.242771     .6857007
         94  |     .399495    .3383642      1.18    0.238     -.2636867     1.062677
         95  |    .5769229    .4605564      1.25    0.210     -.3257512     1.479597
         96  |    .7187798    .6032798      1.19    0.233     -.4636268     1.901186
         97  |    .9517546    .7642384      1.25    0.213     -.5461253     2.449634
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    D.efaprop
------------------------------------------------------------------------------
Options: pnotpen(i.year) cluster(statenum)
1.  (PDS/CHS) Selecting HD controls for dep var D.lpc_prop...
Selected:  xxafdc150 c.Mxxincome#c.trend c.Mxxincome#c.Mxxincome#c.trend
Also inc:  86b.year 87.year 88.year 89.year 90.year 91.year 92.year 93.year
          94.year 95.year 96.year 97.year
2.  (PDS/CHS) Selecting HD controls for exog regressor D.efaprop...
Selected:  prop0 cD.xxprison#cD.xxbeer L.xxincome
Also inc:  86b.year 87.year 88.year 89.year 90.year 91.year 92.year 93.year
          94.year 95.year 96.year 97.year


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      cluster-lasso
Number of observations:                600
Number of clusters:                     50
Exogenous (1):                         D.efaprop
High-dim controls (336):               prop0 c.prop0#c.prop0 Dprop0
                                       c.Dprop0#c.Dprop0 D.xxprison D.xxpolice
                                       D.xxunemp D.xxincome D.xxpover
                                       D.xxafdc15 D.xxgunlaw D.xxbeer
                                       cD.xxprison#cD.xxprison
                                       cD.xxprison#cD.xxpolice
                                       cD.xxprison#cD.xxunemp
                                       cD.xxprison#cD.xxincome
                                       cD.xxprison#cD.xxpover
                                       cD.xxprison#cD.xxafdc15
                                       cD.xxprison#cD.xxgunlaw
                                       cD.xxprison#cD.xxbeer
                                       cD.xxpolice#cD.xxpolice
                                       cD.xxpolice#cD.xxunemp
                                       cD.xxpolice#cD.xxincome
                                       cD.xxpolice#cD.xxpover
                                       cD.xxpolice#cD.xxafdc15
                                       cD.xxpolice#cD.xxgunlaw
                                       cD.xxpolice#cD.xxbeer
                                       cD.xxunemp#cD.xxunemp
                                       cD.xxunemp#cD.xxincome
                                       cD.xxunemp#cD.xxpover
                                       cD.xxunemp#cD.xxafdc15
                                       cD.xxunemp#cD.xxgunlaw
                                       cD.xxunemp#cD.xxbeer
                                       cD.xxincome#cD.xxincome
                                       cD.xxincome#cD.xxpover
                                       cD.xxincome#cD.xxafdc15
                                       cD.xxincome#cD.xxgunlaw
                                       cD.xxincome#cD.xxbeer
                                       cD.xxpover#cD.xxpover
                                       cD.xxpover#cD.xxafdc15
                                       cD.xxpover#cD.xxgunlaw
                                       cD.xxpover#cD.xxbeer
                                       cD.xxafdc15#cD.xxafdc15
                                       cD.xxafdc15#cD.xxgunlaw
                                       cD.xxafdc15#cD.xxbeer
                                       cD.xxgunlaw#cD.xxgunlaw
                                       cD.xxgunlaw#cD.xxbeer
                                       cD.xxbeer#cD.xxbeer L.xxprison
                                       cL.xxprison#cL.xxprison L.xxpolice
                                       cL.xxpolice#cL.xxpolice L.xxunemp
                                       cL.xxunemp#cL.xxunemp L.xxincome
                                       cL.xxincome#cL.xxincome L.xxpover
                                       cL.xxpover#cL.xxpover L.xxafdc15
                                       cL.xxafdc15#cL.xxafdc15 L.xxgunlaw
                                       cL.xxgunlaw#cL.xxgunlaw L.xxbeer
                                       cL.xxbeer#cL.xxbeer Mxxprison
                                       c.Mxxprison#c.Mxxprison Mxxpolice
                                       c.Mxxpolice#c.Mxxpolice Mxxunemp
                                       c.Mxxunemp#c.Mxxunemp Mxxincome
                                       c.Mxxincome#c.Mxxincome Mxxpover
                                       c.Mxxpover#c.Mxxpover Mxxafdc15
                                       c.Mxxafdc15#c.Mxxafdc15 Mxxgunlaw
                                       c.Mxxgunlaw#c.Mxxgunlaw Mxxbeer
                                       c.Mxxbeer#c.Mxxbeer xxprison0
                                       c.xxprison0#c.xxprison0 xxpolice0
                                       c.xxpolice0#c.xxpolice0 xxunemp0
                                       c.xxunemp0#c.xxunemp0 xxincome0
                                       c.xxincome0#c.xxincome0 xxpover0
                                       c.xxpover0#c.xxpover0 xxafdc150
                                       c.xxafdc150#c.xxafdc150 xxgunlaw0
                                       c.xxgunlaw0#c.xxgunlaw0 xxbeer0
                                       c.xxbeer0#c.xxbeer0 Dxxprison0
                                       c.Dxxprison0#c.Dxxprison0 Dxxpolice0
                                       c.Dxxpolice0#c.Dxxpolice0 Dxxunemp0
                                       c.Dxxunemp0#c.Dxxunemp0 Dxxincome0
                                       c.Dxxincome0#c.Dxxincome0 Dxxpover0
                                       c.Dxxpover0#c.Dxxpover0 Dxxafdc150
                                       c.Dxxafdc150#c.Dxxafdc150 Dxxgunlaw0
                                       c.Dxxgunlaw0#c.Dxxgunlaw0 Dxxbeer0
                                       c.Dxxbeer0#c.Dxxbeer0 c.prop0#c.trend
                                       c.prop0#c.trend#c.trend
                                       c.prop0#c.prop0#c.trend
                                       c.prop0#c.prop0#c.trend#c.trend
                                       c.Dprop0#c.trend
                                       c.Dprop0#c.trend#c.trend
                                       c.Dprop0#c.Dprop0#c.trend
                                       c.Dprop0#c.Dprop0#c.trend#c.trend
                                       cD.xxprison#c.trend
                                       cD.xxprison#c.trend#c.trend
                                       cD.xxpolice#c.trend
                                       cD.xxpolice#c.trend#c.trend
                                       cD.xxunemp#c.trend
                                       cD.xxunemp#c.trend#c.trend
                                       cD.xxincome#c.trend
                                       cD.xxincome#c.trend#c.trend
                                       cD.xxpover#c.trend
                                       cD.xxpover#c.trend#c.trend
                                       cD.xxafdc15#c.trend
                                       cD.xxafdc15#c.trend#c.trend
                                       cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#c.trend#c.trend
                                       cD.xxbeer#c.trend
                                       cD.xxbeer#c.trend#c.trend
                                       cD.xxprison#cD.xxprison#c.trend
                                       cD.xxprison#cD.xxprison#c.trend#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend#c.trend
                                       cD.xxprison#cD.xxincome#c.trend
                                       cD.xxprison#cD.xxincome#c.trend#c.trend
                                       cD.xxprison#cD.xxpover#c.trend
                                       cD.xxprison#cD.xxpover#c.trend#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend#c.trend
                                       cD.xxincome#cD.xxincome#c.trend
                                       cD.xxincome#cD.xxincome#c.trend#c.trend
                                       cD.xxincome#cD.xxpover#c.trend
                                       cD.xxincome#cD.xxpover#c.trend#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend#c.trend
                                       cD.xxpover#cD.xxpover#c.trend
                                       cD.xxpover#cD.xxpover#c.trend#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend#c.trend
                                       cL.xxprison#c.trend
                                       cL.xxprison#c.trend#c.trend
                                       cL.xxprison#cL.xxprison#c.trend
                                       cL.xxprison#cL.xxprison#c.trend#c.trend
                                       cL.xxpolice#c.trend
                                       cL.xxpolice#c.trend#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend#c.trend
                                       cL.xxunemp#c.trend
                                       cL.xxunemp#c.trend#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend#c.trend
                                       cL.xxincome#c.trend
                                       cL.xxincome#c.trend#c.trend
                                       cL.xxincome#cL.xxincome#c.trend
                                       cL.xxincome#cL.xxincome#c.trend#c.trend
                                       cL.xxpover#c.trend
                                       cL.xxpover#c.trend#c.trend
                                       cL.xxpover#cL.xxpover#c.trend
                                       cL.xxpover#cL.xxpover#c.trend#c.trend
                                       cL.xxafdc15#c.trend
                                       cL.xxafdc15#c.trend#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend#c.trend
                                       cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#c.trend#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend#c.trend
                                       cL.xxbeer#c.trend
                                       cL.xxbeer#c.trend#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend#c.trend
                                       c.Mxxprison#c.trend
                                       c.Mxxprison#c.trend#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend#c.trend
                                       c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.trend#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend#c.trend
                                       c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.trend#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend#c.trend
                                       c.Mxxincome#c.trend
                                       c.Mxxincome#c.trend#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend#c.trend
                                       c.Mxxpover#c.trend
                                       c.Mxxpover#c.trend#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend#c.trend
                                       c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.trend#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend#c.trend
                                       c.xxprison0#c.trend
                                       c.xxprison0#c.trend#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.xxprison0#c.xxprison0#c.trend#c.trend
                                       c.xxpolice0#c.trend
                                       c.xxpolice0#c.trend#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend#c.trend
                                       c.xxunemp0#c.trend
                                       c.xxunemp0#c.trend#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend#c.trend
                                       c.xxincome0#c.trend
                                       c.xxincome0#c.trend#c.trend
                                       c.xxincome0#c.xxincome0#c.trend
                                       c.xxincome0#c.xxincome0#c.trend#c.trend
                                       c.xxpover0#c.trend
                                       c.xxpover0#c.trend#c.trend
                                       c.xxpover0#c.xxpover0#c.trend
                                       c.xxpover0#c.xxpover0#c.trend#c.trend
                                       c.xxafdc150#c.trend
                                       c.xxafdc150#c.trend#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend#c.trend
                                       c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.trend#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend#c.trend
                                       c.xxbeer0#c.trend
                                       c.xxbeer0#c.trend#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend#c.trend
                                       c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.trend#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend#c.trend
                                       c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.trend#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend#c.trend
                                       c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.trend#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend#c.trend
                                       c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.trend#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend#c.trend
Selected controls (18):                prop0 cD.xxprison#cD.xxbeer L.xxincome
                                       xxafdc150 c.Mxxincome#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend 86b.year
                                       87.year 88.year 89.year 90.year 91.year
                                       92.year 93.year 94.year 95.year 96.year
                                       97.year
Unpenalized controls (13):             86b.year 87.year 88.year 89.year
                                       90.year 91.year 92.year 93.year 94.year
                                       95.year 96.year 97.year _cons

Structural equation:

OLS using CHS lasso-orthogonalized vars
(Std. Err. adjusted for 50 clusters in statenum)
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.0645436    .0441481     -1.46    0.144     -.1510722     .0219851
-------------+----------------------------------------------------------------

OLS using CHS post-lasso-orthogonalized vars
(Std. Err. adjusted for 50 clusters in statenum)
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.0618678     .047495     -1.30    0.193     -.1549563     .0312208
-------------+----------------------------------------------------------------

OLS with PDS-selected variables and full regressor set
(Std. Err. adjusted for 50 clusters in statenum)
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.0668603    .0452538     -1.48    0.140      -.155556     .0218355
             |
       prop0 |   -.0011269    .0206507     -0.05    0.956     -.0416015     .0393478
             |
 cD.xxprison#|
   cD.xxbeer |   -.3755804    2.540546     -0.15    0.882     -5.354958     4.603798
             |
    xxincome |
         L1. |    7.393157    2.450447      3.02    0.003      2.590368     12.19595
             |
   xxafdc150 |   -.0246563    .0075289     -3.27    0.001     -.0394126       -.0099
             |
 c.Mxxincome#|
     c.trend |   -40.96234    115.2377     -0.36    0.722     -266.8241     184.8994
             |
 c.Mxxincome#|
 c.Mxxincome#|
     c.trend |    138.1464    577.4327      0.24    0.811      -993.601     1269.894
             |
        year |
         87  |    .2058697    .4802558      0.43    0.668     -.7354144     1.147154
         88  |    .4132732    .9598575      0.43    0.667     -1.468013     2.294559
         89  |    .6519585    1.438858      0.45    0.650     -2.168151     3.472068
         90  |    .8804196    1.918883      0.46    0.646     -2.880523     4.641362
         91  |    1.109581     2.39777      0.46    0.644     -3.589962     5.809124
         92  |    1.283064    2.877954      0.45    0.656     -4.357623     6.923751
         93  |    1.517959    3.358704      0.45    0.651      -5.06498     8.100899
         94  |    1.771554    3.835287      0.46    0.644      -5.74547     9.288579
         95  |    2.005793    4.317482      0.46    0.642     -6.456317      10.4679
         96  |    2.184353    4.795731      0.46    0.649     -7.215107     11.58381
         97  |    2.418729    5.273521      0.46    0.646     -7.917183     12.75464
             |
       _cons |   -.4435721    .4956124     -0.89    0.371     -1.414955     .5278103
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    D.efaprop
------------------------------------------------------------------------------
Options: pnotpen(i.year) cluster(statenum) fe
Fixed effects transformation...
1.  (PDS/CHS) Selecting HD controls for dep var D.lpc_prop...
Selected:  L.xxunemp
Also inc:  86b.year 87.year 88.year 89.year 90.year 91.year 92.year 93.year
          94.year 95.year 96.year 97.year
2.  (PDS/CHS) Selecting HD controls for exog regressor D.efaprop...
Selected:  D.xxincome L.xxunemp c.prop0#c.prop0#c.trend
          c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
Also inc:  86b.year 87.year 88.year 89.year 90.year 91.year 92.year 93.year
          94.year 95.year 96.year 97.year


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      cluster-lasso
Number of observations:                600
Number of clusters:                     50
Number of fixed effects:                50
Exogenous (1):                         D.efaprop
High-dim controls (336):               prop0 c.prop0#c.prop0 Dprop0
                                       c.Dprop0#c.Dprop0 D.xxprison D.xxpolice
                                       D.xxunemp D.xxincome D.xxpover
                                       D.xxafdc15 D.xxgunlaw D.xxbeer
                                       cD.xxprison#cD.xxprison
                                       cD.xxprison#cD.xxpolice
                                       cD.xxprison#cD.xxunemp
                                       cD.xxprison#cD.xxincome
                                       cD.xxprison#cD.xxpover
                                       cD.xxprison#cD.xxafdc15
                                       cD.xxprison#cD.xxgunlaw
                                       cD.xxprison#cD.xxbeer
                                       cD.xxpolice#cD.xxpolice
                                       cD.xxpolice#cD.xxunemp
                                       cD.xxpolice#cD.xxincome
                                       cD.xxpolice#cD.xxpover
                                       cD.xxpolice#cD.xxafdc15
                                       cD.xxpolice#cD.xxgunlaw
                                       cD.xxpolice#cD.xxbeer
                                       cD.xxunemp#cD.xxunemp
                                       cD.xxunemp#cD.xxincome
                                       cD.xxunemp#cD.xxpover
                                       cD.xxunemp#cD.xxafdc15
                                       cD.xxunemp#cD.xxgunlaw
                                       cD.xxunemp#cD.xxbeer
                                       cD.xxincome#cD.xxincome
                                       cD.xxincome#cD.xxpover
                                       cD.xxincome#cD.xxafdc15
                                       cD.xxincome#cD.xxgunlaw
                                       cD.xxincome#cD.xxbeer
                                       cD.xxpover#cD.xxpover
                                       cD.xxpover#cD.xxafdc15
                                       cD.xxpover#cD.xxgunlaw
                                       cD.xxpover#cD.xxbeer
                                       cD.xxafdc15#cD.xxafdc15
                                       cD.xxafdc15#cD.xxgunlaw
                                       cD.xxafdc15#cD.xxbeer
                                       cD.xxgunlaw#cD.xxgunlaw
                                       cD.xxgunlaw#cD.xxbeer
                                       cD.xxbeer#cD.xxbeer L.xxprison
                                       cL.xxprison#cL.xxprison L.xxpolice
                                       cL.xxpolice#cL.xxpolice L.xxunemp
                                       cL.xxunemp#cL.xxunemp L.xxincome
                                       cL.xxincome#cL.xxincome L.xxpover
                                       cL.xxpover#cL.xxpover L.xxafdc15
                                       cL.xxafdc15#cL.xxafdc15 L.xxgunlaw
                                       cL.xxgunlaw#cL.xxgunlaw L.xxbeer
                                       cL.xxbeer#cL.xxbeer Mxxprison
                                       c.Mxxprison#c.Mxxprison Mxxpolice
                                       c.Mxxpolice#c.Mxxpolice Mxxunemp
                                       c.Mxxunemp#c.Mxxunemp Mxxincome
                                       c.Mxxincome#c.Mxxincome Mxxpover
                                       c.Mxxpover#c.Mxxpover Mxxafdc15
                                       c.Mxxafdc15#c.Mxxafdc15 Mxxgunlaw
                                       c.Mxxgunlaw#c.Mxxgunlaw Mxxbeer
                                       c.Mxxbeer#c.Mxxbeer xxprison0
                                       c.xxprison0#c.xxprison0 xxpolice0
                                       c.xxpolice0#c.xxpolice0 xxunemp0
                                       c.xxunemp0#c.xxunemp0 xxincome0
                                       c.xxincome0#c.xxincome0 xxpover0
                                       c.xxpover0#c.xxpover0 xxafdc150
                                       c.xxafdc150#c.xxafdc150 xxgunlaw0
                                       c.xxgunlaw0#c.xxgunlaw0 xxbeer0
                                       c.xxbeer0#c.xxbeer0 Dxxprison0
                                       c.Dxxprison0#c.Dxxprison0 Dxxpolice0
                                       c.Dxxpolice0#c.Dxxpolice0 Dxxunemp0
                                       c.Dxxunemp0#c.Dxxunemp0 Dxxincome0
                                       c.Dxxincome0#c.Dxxincome0 Dxxpover0
                                       c.Dxxpover0#c.Dxxpover0 Dxxafdc150
                                       c.Dxxafdc150#c.Dxxafdc150 Dxxgunlaw0
                                       c.Dxxgunlaw0#c.Dxxgunlaw0 Dxxbeer0
                                       c.Dxxbeer0#c.Dxxbeer0 c.prop0#c.trend
                                       c.prop0#c.trend#c.trend
                                       c.prop0#c.prop0#c.trend
                                       c.prop0#c.prop0#c.trend#c.trend
                                       c.Dprop0#c.trend
                                       c.Dprop0#c.trend#c.trend
                                       c.Dprop0#c.Dprop0#c.trend
                                       c.Dprop0#c.Dprop0#c.trend#c.trend
                                       cD.xxprison#c.trend
                                       cD.xxprison#c.trend#c.trend
                                       cD.xxpolice#c.trend
                                       cD.xxpolice#c.trend#c.trend
                                       cD.xxunemp#c.trend
                                       cD.xxunemp#c.trend#c.trend
                                       cD.xxincome#c.trend
                                       cD.xxincome#c.trend#c.trend
                                       cD.xxpover#c.trend
                                       cD.xxpover#c.trend#c.trend
                                       cD.xxafdc15#c.trend
                                       cD.xxafdc15#c.trend#c.trend
                                       cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#c.trend#c.trend
                                       cD.xxbeer#c.trend
                                       cD.xxbeer#c.trend#c.trend
                                       cD.xxprison#cD.xxprison#c.trend
                                       cD.xxprison#cD.xxprison#c.trend#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend#c.trend
                                       cD.xxprison#cD.xxincome#c.trend
                                       cD.xxprison#cD.xxincome#c.trend#c.trend
                                       cD.xxprison#cD.xxpover#c.trend
                                       cD.xxprison#cD.xxpover#c.trend#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend#c.trend
                                       cD.xxincome#cD.xxincome#c.trend
                                       cD.xxincome#cD.xxincome#c.trend#c.trend
                                       cD.xxincome#cD.xxpover#c.trend
                                       cD.xxincome#cD.xxpover#c.trend#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend#c.trend
                                       cD.xxpover#cD.xxpover#c.trend
                                       cD.xxpover#cD.xxpover#c.trend#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend#c.trend
                                       cL.xxprison#c.trend
                                       cL.xxprison#c.trend#c.trend
                                       cL.xxprison#cL.xxprison#c.trend
                                       cL.xxprison#cL.xxprison#c.trend#c.trend
                                       cL.xxpolice#c.trend
                                       cL.xxpolice#c.trend#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend#c.trend
                                       cL.xxunemp#c.trend
                                       cL.xxunemp#c.trend#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend#c.trend
                                       cL.xxincome#c.trend
                                       cL.xxincome#c.trend#c.trend
                                       cL.xxincome#cL.xxincome#c.trend
                                       cL.xxincome#cL.xxincome#c.trend#c.trend
                                       cL.xxpover#c.trend
                                       cL.xxpover#c.trend#c.trend
                                       cL.xxpover#cL.xxpover#c.trend
                                       cL.xxpover#cL.xxpover#c.trend#c.trend
                                       cL.xxafdc15#c.trend
                                       cL.xxafdc15#c.trend#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend#c.trend
                                       cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#c.trend#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend#c.trend
                                       cL.xxbeer#c.trend
                                       cL.xxbeer#c.trend#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend#c.trend
                                       c.Mxxprison#c.trend
                                       c.Mxxprison#c.trend#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend#c.trend
                                       c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.trend#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend#c.trend
                                       c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.trend#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend#c.trend
                                       c.Mxxincome#c.trend
                                       c.Mxxincome#c.trend#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend#c.trend
                                       c.Mxxpover#c.trend
                                       c.Mxxpover#c.trend#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend#c.trend
                                       c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.trend#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend#c.trend
                                       c.xxprison0#c.trend
                                       c.xxprison0#c.trend#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.xxprison0#c.xxprison0#c.trend#c.trend
                                       c.xxpolice0#c.trend
                                       c.xxpolice0#c.trend#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend#c.trend
                                       c.xxunemp0#c.trend
                                       c.xxunemp0#c.trend#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend#c.trend
                                       c.xxincome0#c.trend
                                       c.xxincome0#c.trend#c.trend
                                       c.xxincome0#c.xxincome0#c.trend
                                       c.xxincome0#c.xxincome0#c.trend#c.trend
                                       c.xxpover0#c.trend
                                       c.xxpover0#c.trend#c.trend
                                       c.xxpover0#c.xxpover0#c.trend
                                       c.xxpover0#c.xxpover0#c.trend#c.trend
                                       c.xxafdc150#c.trend
                                       c.xxafdc150#c.trend#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend#c.trend
                                       c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.trend#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend#c.trend
                                       c.xxbeer0#c.trend
                                       c.xxbeer0#c.trend#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend#c.trend
                                       c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.trend#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend#c.trend
                                       c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.trend#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend#c.trend
                                       c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.trend#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend#c.trend
                                       c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.trend#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend#c.trend
Selected controls (16):                D.xxincome L.xxunemp
                                       c.prop0#c.prop0#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       86b.year 87.year 88.year 89.year 90.year
                                       91.year 92.year 93.year 94.year 95.year
                                       96.year 97.year
Unpenalized controls (12):             86b.year 87.year 88.year 89.year
                                       90.year 91.year 92.year 93.year 94.year
                                       95.year 96.year 97.year

Structural equation (fixed effects, #groups=50):

OLS using CHS lasso-orthogonalized vars
(Std. Err. adjusted for 50 clusters in statenum)
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.0932012    .0668382     -1.39    0.163     -.2242017     .0377993
-------------+----------------------------------------------------------------

OLS using CHS post-lasso-orthogonalized vars
(Std. Err. adjusted for 50 clusters in statenum)
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.0829405    .0748093     -1.11    0.268      -.229564      .063683
-------------+----------------------------------------------------------------

OLS with PDS-selected variables and full regressor set
(Std. Err. adjusted for 50 clusters in statenum)
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.0829405    .0721085     -1.15    0.250     -.2242706     .0583896
             |
    xxincome |
         D1. |   -27.37665    15.67586     -1.75    0.081     -58.10078     3.347475
             |
     xxunemp |
         L1. |   -.8423193    .2004038     -4.20    0.000     -1.235104     -.449535
             |
     c.prop0#|
     c.prop0#|
     c.trend |    -.229436    .0804544     -2.85    0.004     -.3871238    -.0717483
             |
          c. |
  Dxxafdc150#|
          c. |
  Dxxafdc150#|
     c.trend#|
     c.trend |   -.6779636    .7268227     -0.93    0.351      -2.10251     .7465828
             |
        year |
         87  |    -.023664    .0088252     -2.68    0.007     -.0409612    -.0063669
         88  |   -.0444541    .0090865     -4.89    0.000     -.0622634    -.0266449
         89  |   -.0349657    .0102283     -3.42    0.001     -.0550128    -.0149186
         90  |   -.0377691    .0133733     -2.82    0.005     -.0639803    -.0115579
         91  |   -.0342581    .0143935     -2.38    0.017     -.0624689    -.0060472
         92  |   -.0708148    .0151894     -4.66    0.000     -.1005854    -.0410443
         93  |   -.0605907    .0144438     -4.19    0.000     -.0889001    -.0322813
         94  |   -.0302278    .0142542     -2.12    0.034     -.0581655    -.0022901
         95  |   -.0217481     .015333     -1.42    0.156     -.0518002     .0083039
         96  |   -.0741265    .0139363     -5.32    0.000     -.1014413    -.0468118
         97  |   -.0707745    .0147365     -4.80    0.000     -.0996576    -.0418914
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    D.efaprop
------------------------------------------------------------------------------
Options: pnotpen(i.year) cluster(statenum) nocons
1.  (PDS/CHS) Selecting HD controls for dep var D.lpc_prop...
Selected:  Mxxpover xxpover0 c.Mxxincome#c.Mxxincome#c.trend#c.trend
Also inc:  86b.year 87.year 88.year 89.year 90.year 91.year 92.year 93.year
          94.year 95.year 96.year 97.year
2.  (PDS/CHS) Selecting HD controls for exog regressor D.efaprop...
Selected:  prop0 D.xxbeer cL.xxpolice#cL.xxpolice c.xxunemp0#c.xxunemp0
          c.xxpover0#c.xxpover0 cL.xxincome#cL.xxincome#c.trend
          c.Mxxincome#c.Mxxincome#c.trend
Also inc:  86b.year 87.year 88.year 89.year 90.year 91.year 92.year 93.year
          94.year 95.year 96.year 97.year


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      cluster-lasso
Number of observations:                600
Number of clusters:                     50
Exogenous (1):                         D.efaprop
High-dim controls (336):               prop0 c.prop0#c.prop0 Dprop0
                                       c.Dprop0#c.Dprop0 D.xxprison D.xxpolice
                                       D.xxunemp D.xxincome D.xxpover
                                       D.xxafdc15 D.xxgunlaw D.xxbeer
                                       cD.xxprison#cD.xxprison
                                       cD.xxprison#cD.xxpolice
                                       cD.xxprison#cD.xxunemp
                                       cD.xxprison#cD.xxincome
                                       cD.xxprison#cD.xxpover
                                       cD.xxprison#cD.xxafdc15
                                       cD.xxprison#cD.xxgunlaw
                                       cD.xxprison#cD.xxbeer
                                       cD.xxpolice#cD.xxpolice
                                       cD.xxpolice#cD.xxunemp
                                       cD.xxpolice#cD.xxincome
                                       cD.xxpolice#cD.xxpover
                                       cD.xxpolice#cD.xxafdc15
                                       cD.xxpolice#cD.xxgunlaw
                                       cD.xxpolice#cD.xxbeer
                                       cD.xxunemp#cD.xxunemp
                                       cD.xxunemp#cD.xxincome
                                       cD.xxunemp#cD.xxpover
                                       cD.xxunemp#cD.xxafdc15
                                       cD.xxunemp#cD.xxgunlaw
                                       cD.xxunemp#cD.xxbeer
                                       cD.xxincome#cD.xxincome
                                       cD.xxincome#cD.xxpover
                                       cD.xxincome#cD.xxafdc15
                                       cD.xxincome#cD.xxgunlaw
                                       cD.xxincome#cD.xxbeer
                                       cD.xxpover#cD.xxpover
                                       cD.xxpover#cD.xxafdc15
                                       cD.xxpover#cD.xxgunlaw
                                       cD.xxpover#cD.xxbeer
                                       cD.xxafdc15#cD.xxafdc15
                                       cD.xxafdc15#cD.xxgunlaw
                                       cD.xxafdc15#cD.xxbeer
                                       cD.xxgunlaw#cD.xxgunlaw
                                       cD.xxgunlaw#cD.xxbeer
                                       cD.xxbeer#cD.xxbeer L.xxprison
                                       cL.xxprison#cL.xxprison L.xxpolice
                                       cL.xxpolice#cL.xxpolice L.xxunemp
                                       cL.xxunemp#cL.xxunemp L.xxincome
                                       cL.xxincome#cL.xxincome L.xxpover
                                       cL.xxpover#cL.xxpover L.xxafdc15
                                       cL.xxafdc15#cL.xxafdc15 L.xxgunlaw
                                       cL.xxgunlaw#cL.xxgunlaw L.xxbeer
                                       cL.xxbeer#cL.xxbeer Mxxprison
                                       c.Mxxprison#c.Mxxprison Mxxpolice
                                       c.Mxxpolice#c.Mxxpolice Mxxunemp
                                       c.Mxxunemp#c.Mxxunemp Mxxincome
                                       c.Mxxincome#c.Mxxincome Mxxpover
                                       c.Mxxpover#c.Mxxpover Mxxafdc15
                                       c.Mxxafdc15#c.Mxxafdc15 Mxxgunlaw
                                       c.Mxxgunlaw#c.Mxxgunlaw Mxxbeer
                                       c.Mxxbeer#c.Mxxbeer xxprison0
                                       c.xxprison0#c.xxprison0 xxpolice0
                                       c.xxpolice0#c.xxpolice0 xxunemp0
                                       c.xxunemp0#c.xxunemp0 xxincome0
                                       c.xxincome0#c.xxincome0 xxpover0
                                       c.xxpover0#c.xxpover0 xxafdc150
                                       c.xxafdc150#c.xxafdc150 xxgunlaw0
                                       c.xxgunlaw0#c.xxgunlaw0 xxbeer0
                                       c.xxbeer0#c.xxbeer0 Dxxprison0
                                       c.Dxxprison0#c.Dxxprison0 Dxxpolice0
                                       c.Dxxpolice0#c.Dxxpolice0 Dxxunemp0
                                       c.Dxxunemp0#c.Dxxunemp0 Dxxincome0
                                       c.Dxxincome0#c.Dxxincome0 Dxxpover0
                                       c.Dxxpover0#c.Dxxpover0 Dxxafdc150
                                       c.Dxxafdc150#c.Dxxafdc150 Dxxgunlaw0
                                       c.Dxxgunlaw0#c.Dxxgunlaw0 Dxxbeer0
                                       c.Dxxbeer0#c.Dxxbeer0 c.prop0#c.trend
                                       c.prop0#c.trend#c.trend
                                       c.prop0#c.prop0#c.trend
                                       c.prop0#c.prop0#c.trend#c.trend
                                       c.Dprop0#c.trend
                                       c.Dprop0#c.trend#c.trend
                                       c.Dprop0#c.Dprop0#c.trend
                                       c.Dprop0#c.Dprop0#c.trend#c.trend
                                       cD.xxprison#c.trend
                                       cD.xxprison#c.trend#c.trend
                                       cD.xxpolice#c.trend
                                       cD.xxpolice#c.trend#c.trend
                                       cD.xxunemp#c.trend
                                       cD.xxunemp#c.trend#c.trend
                                       cD.xxincome#c.trend
                                       cD.xxincome#c.trend#c.trend
                                       cD.xxpover#c.trend
                                       cD.xxpover#c.trend#c.trend
                                       cD.xxafdc15#c.trend
                                       cD.xxafdc15#c.trend#c.trend
                                       cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#c.trend#c.trend
                                       cD.xxbeer#c.trend
                                       cD.xxbeer#c.trend#c.trend
                                       cD.xxprison#cD.xxprison#c.trend
                                       cD.xxprison#cD.xxprison#c.trend#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend#c.trend
                                       cD.xxprison#cD.xxincome#c.trend
                                       cD.xxprison#cD.xxincome#c.trend#c.trend
                                       cD.xxprison#cD.xxpover#c.trend
                                       cD.xxprison#cD.xxpover#c.trend#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend#c.trend
                                       cD.xxincome#cD.xxincome#c.trend
                                       cD.xxincome#cD.xxincome#c.trend#c.trend
                                       cD.xxincome#cD.xxpover#c.trend
                                       cD.xxincome#cD.xxpover#c.trend#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend#c.trend
                                       cD.xxpover#cD.xxpover#c.trend
                                       cD.xxpover#cD.xxpover#c.trend#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend#c.trend
                                       cL.xxprison#c.trend
                                       cL.xxprison#c.trend#c.trend
                                       cL.xxprison#cL.xxprison#c.trend
                                       cL.xxprison#cL.xxprison#c.trend#c.trend
                                       cL.xxpolice#c.trend
                                       cL.xxpolice#c.trend#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend#c.trend
                                       cL.xxunemp#c.trend
                                       cL.xxunemp#c.trend#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend#c.trend
                                       cL.xxincome#c.trend
                                       cL.xxincome#c.trend#c.trend
                                       cL.xxincome#cL.xxincome#c.trend
                                       cL.xxincome#cL.xxincome#c.trend#c.trend
                                       cL.xxpover#c.trend
                                       cL.xxpover#c.trend#c.trend
                                       cL.xxpover#cL.xxpover#c.trend
                                       cL.xxpover#cL.xxpover#c.trend#c.trend
                                       cL.xxafdc15#c.trend
                                       cL.xxafdc15#c.trend#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend#c.trend
                                       cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#c.trend#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend#c.trend
                                       cL.xxbeer#c.trend
                                       cL.xxbeer#c.trend#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend#c.trend
                                       c.Mxxprison#c.trend
                                       c.Mxxprison#c.trend#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend#c.trend
                                       c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.trend#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend#c.trend
                                       c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.trend#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend#c.trend
                                       c.Mxxincome#c.trend
                                       c.Mxxincome#c.trend#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend#c.trend
                                       c.Mxxpover#c.trend
                                       c.Mxxpover#c.trend#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend#c.trend
                                       c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.trend#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend#c.trend
                                       c.xxprison0#c.trend
                                       c.xxprison0#c.trend#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.xxprison0#c.xxprison0#c.trend#c.trend
                                       c.xxpolice0#c.trend
                                       c.xxpolice0#c.trend#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend#c.trend
                                       c.xxunemp0#c.trend
                                       c.xxunemp0#c.trend#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend#c.trend
                                       c.xxincome0#c.trend
                                       c.xxincome0#c.trend#c.trend
                                       c.xxincome0#c.xxincome0#c.trend
                                       c.xxincome0#c.xxincome0#c.trend#c.trend
                                       c.xxpover0#c.trend
                                       c.xxpover0#c.trend#c.trend
                                       c.xxpover0#c.xxpover0#c.trend
                                       c.xxpover0#c.xxpover0#c.trend#c.trend
                                       c.xxafdc150#c.trend
                                       c.xxafdc150#c.trend#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend#c.trend
                                       c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.trend#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend#c.trend
                                       c.xxbeer0#c.trend
                                       c.xxbeer0#c.trend#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend#c.trend
                                       c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.trend#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend#c.trend
                                       c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.trend#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend#c.trend
                                       c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.trend#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend#c.trend
                                       c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.trend#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend#c.trend
Selected controls (22):                prop0 D.xxbeer cL.xxpolice#cL.xxpolice
                                       Mxxpover c.xxunemp0#c.xxunemp0 xxpover0
                                       c.xxpover0#c.xxpover0
                                       cL.xxincome#cL.xxincome#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend#c.trend
                                       86b.year 87.year 88.year 89.year 90.year
                                       91.year 92.year 93.year 94.year 95.year
                                       96.year 97.year
Unpenalized controls (12):             86b.year 87.year 88.year 89.year
                                       90.year 91.year 92.year 93.year 94.year
                                       95.year 96.year 97.year

Structural equation:

OLS using CHS lasso-orthogonalized vars
(Std. Err. adjusted for 50 clusters in statenum)
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.0785114    .0326212     -2.41    0.016     -.1424479    -.0145749
-------------+----------------------------------------------------------------

OLS using CHS post-lasso-orthogonalized vars
(Std. Err. adjusted for 50 clusters in statenum)
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.0487425    .0490138     -0.99    0.320     -.1448078     .0473228
-------------+----------------------------------------------------------------

OLS with PDS-selected variables and full regressor set
(Std. Err. adjusted for 50 clusters in statenum)
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.0480633    .0483025     -1.00    0.320     -.1427346     .0466079
             |
       prop0 |   -.0216161    .0229181     -0.94    0.346     -.0665347     .0233025
             |
      xxbeer |
         D1. |   -.0190673    .1584906     -0.12    0.904     -.3297031     .2915685
             |
 cL.xxpolice#|
 cL.xxpolice |   -.0045112    .0039517     -1.14    0.254     -.0122563     .0032339
             |
    Mxxpover |    .0864593    .0758033      1.14    0.254     -.0621124     .2350311
             |
  c.xxunemp0#|
  c.xxunemp0 |   -.8178715    .5656383     -1.45    0.148     -1.926502     .2907592
             |
    xxpover0 |    .0505307    .1524452      0.33    0.740     -.2482564     .3493178
             |
  c.xxpover0#|
  c.xxpover0 |    .0612709    .4625592      0.13    0.895     -.8453284     .9678702
             |
 cL.xxincome#|
 cL.xxincome#|
     c.trend |    310.9421    83.98215      3.70    0.000      146.3401     475.5441
             |
 c.Mxxincome#|
 c.Mxxincome#|
     c.trend |    -261.158    86.39862     -3.02    0.003     -430.4962    -91.81984
             |
 c.Mxxincome#|
 c.Mxxincome#|
     c.trend#|
     c.trend |   -73.25176    27.47001     -2.67    0.008      -127.092    -19.41153
             |
        year |
         87  |   -.0434432     .015779     -2.75    0.006     -.0743694    -.0125171
         88  |   -.0757982    .0229667     -3.30    0.001     -.1208121    -.0307843
         89  |   -.0690883    .0298552     -2.31    0.021     -.1276035    -.0105731
         90  |    -.064755     .037721     -1.72    0.086     -.1386868     .0091769
         91  |   -.0475468    .0462427     -1.03    0.304     -.1381809     .0430873
         92  |   -.0728763    .0597782     -1.22    0.223     -.1900394     .0442868
         93  |   -.0349877    .0770671     -0.45    0.650     -.1860364      .116061
         94  |    .0353652    .0985258      0.36    0.720     -.1577418     .2284722
         95  |    .0863492    .1251715      0.69    0.490     -.1589824     .3316808
         96  |    .0834945    .1561019      0.53    0.593     -.2224596     .3894485
         97  |     .151532    .1909583      0.79    0.427     -.2227394     .5258035
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    D.efaprop
------------------------------------------------------------------------------
Options: aset(i.year)
1.  (PDS/CHS) Selecting HD controls for dep var D.lpc_prop...
Selected:  cL.xxunemp#c.trend c.xxafdc150#c.trend 92.year
Also inc:  86b.year 87.year 88.year 89.year 90.year 91.year 93.year 94.year
          95.year 96.year 97.year
2.  (PDS/CHS) Selecting HD controls for exog regressor D.efaprop...
Selected:  prop0 cD.xxprison#cD.xxunemp cD.xxincome#cD.xxincome L.xxpolice
          L.xxincome Mxxincome c.Dprop0#c.Dprop0#c.trend#c.trend
          cD.xxunemp#cD.xxunemp#c.trend cL.xxunemp#c.trend
          cL.xxbeer#cL.xxbeer#c.trend c.Mxxpolice#c.Mxxpolice#c.trend
          c.xxprison0#c.xxprison0#c.trend c.Dxxincome0#c.trend
          c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend c.Dxxbeer0#c.trend 89.year
          90.year 91.year 92.year 93.year 96.year 97.year
Also inc:  86b.year 87.year 88.year 94.year 95.year


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      homoskedastic
Number of observations:                600
Exogenous (1):                         D.efaprop
High-dim controls (348):               prop0 c.prop0#c.prop0 Dprop0
                                       c.Dprop0#c.Dprop0 D.xxprison D.xxpolice
                                       D.xxunemp D.xxincome D.xxpover
                                       D.xxafdc15 D.xxgunlaw D.xxbeer
                                       cD.xxprison#cD.xxprison
                                       cD.xxprison#cD.xxpolice
                                       cD.xxprison#cD.xxunemp
                                       cD.xxprison#cD.xxincome
                                       cD.xxprison#cD.xxpover
                                       cD.xxprison#cD.xxafdc15
                                       cD.xxprison#cD.xxgunlaw
                                       cD.xxprison#cD.xxbeer
                                       cD.xxpolice#cD.xxpolice
                                       cD.xxpolice#cD.xxunemp
                                       cD.xxpolice#cD.xxincome
                                       cD.xxpolice#cD.xxpover
                                       cD.xxpolice#cD.xxafdc15
                                       cD.xxpolice#cD.xxgunlaw
                                       cD.xxpolice#cD.xxbeer
                                       cD.xxunemp#cD.xxunemp
                                       cD.xxunemp#cD.xxincome
                                       cD.xxunemp#cD.xxpover
                                       cD.xxunemp#cD.xxafdc15
                                       cD.xxunemp#cD.xxgunlaw
                                       cD.xxunemp#cD.xxbeer
                                       cD.xxincome#cD.xxincome
                                       cD.xxincome#cD.xxpover
                                       cD.xxincome#cD.xxafdc15
                                       cD.xxincome#cD.xxgunlaw
                                       cD.xxincome#cD.xxbeer
                                       cD.xxpover#cD.xxpover
                                       cD.xxpover#cD.xxafdc15
                                       cD.xxpover#cD.xxgunlaw
                                       cD.xxpover#cD.xxbeer
                                       cD.xxafdc15#cD.xxafdc15
                                       cD.xxafdc15#cD.xxgunlaw
                                       cD.xxafdc15#cD.xxbeer
                                       cD.xxgunlaw#cD.xxgunlaw
                                       cD.xxgunlaw#cD.xxbeer
                                       cD.xxbeer#cD.xxbeer L.xxprison
                                       cL.xxprison#cL.xxprison L.xxpolice
                                       cL.xxpolice#cL.xxpolice L.xxunemp
                                       cL.xxunemp#cL.xxunemp L.xxincome
                                       cL.xxincome#cL.xxincome L.xxpover
                                       cL.xxpover#cL.xxpover L.xxafdc15
                                       cL.xxafdc15#cL.xxafdc15 L.xxgunlaw
                                       cL.xxgunlaw#cL.xxgunlaw L.xxbeer
                                       cL.xxbeer#cL.xxbeer Mxxprison
                                       c.Mxxprison#c.Mxxprison Mxxpolice
                                       c.Mxxpolice#c.Mxxpolice Mxxunemp
                                       c.Mxxunemp#c.Mxxunemp Mxxincome
                                       c.Mxxincome#c.Mxxincome Mxxpover
                                       c.Mxxpover#c.Mxxpover Mxxafdc15
                                       c.Mxxafdc15#c.Mxxafdc15 Mxxgunlaw
                                       c.Mxxgunlaw#c.Mxxgunlaw Mxxbeer
                                       c.Mxxbeer#c.Mxxbeer xxprison0
                                       c.xxprison0#c.xxprison0 xxpolice0
                                       c.xxpolice0#c.xxpolice0 xxunemp0
                                       c.xxunemp0#c.xxunemp0 xxincome0
                                       c.xxincome0#c.xxincome0 xxpover0
                                       c.xxpover0#c.xxpover0 xxafdc150
                                       c.xxafdc150#c.xxafdc150 xxgunlaw0
                                       c.xxgunlaw0#c.xxgunlaw0 xxbeer0
                                       c.xxbeer0#c.xxbeer0 Dxxprison0
                                       c.Dxxprison0#c.Dxxprison0 Dxxpolice0
                                       c.Dxxpolice0#c.Dxxpolice0 Dxxunemp0
                                       c.Dxxunemp0#c.Dxxunemp0 Dxxincome0
                                       c.Dxxincome0#c.Dxxincome0 Dxxpover0
                                       c.Dxxpover0#c.Dxxpover0 Dxxafdc150
                                       c.Dxxafdc150#c.Dxxafdc150 Dxxgunlaw0
                                       c.Dxxgunlaw0#c.Dxxgunlaw0 Dxxbeer0
                                       c.Dxxbeer0#c.Dxxbeer0 c.prop0#c.trend
                                       c.prop0#c.trend#c.trend
                                       c.prop0#c.prop0#c.trend
                                       c.prop0#c.prop0#c.trend#c.trend
                                       c.Dprop0#c.trend
                                       c.Dprop0#c.trend#c.trend
                                       c.Dprop0#c.Dprop0#c.trend
                                       c.Dprop0#c.Dprop0#c.trend#c.trend
                                       cD.xxprison#c.trend
                                       cD.xxprison#c.trend#c.trend
                                       cD.xxpolice#c.trend
                                       cD.xxpolice#c.trend#c.trend
                                       cD.xxunemp#c.trend
                                       cD.xxunemp#c.trend#c.trend
                                       cD.xxincome#c.trend
                                       cD.xxincome#c.trend#c.trend
                                       cD.xxpover#c.trend
                                       cD.xxpover#c.trend#c.trend
                                       cD.xxafdc15#c.trend
                                       cD.xxafdc15#c.trend#c.trend
                                       cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#c.trend#c.trend
                                       cD.xxbeer#c.trend
                                       cD.xxbeer#c.trend#c.trend
                                       cD.xxprison#cD.xxprison#c.trend
                                       cD.xxprison#cD.xxprison#c.trend#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend#c.trend
                                       cD.xxprison#cD.xxincome#c.trend
                                       cD.xxprison#cD.xxincome#c.trend#c.trend
                                       cD.xxprison#cD.xxpover#c.trend
                                       cD.xxprison#cD.xxpover#c.trend#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend#c.trend
                                       cD.xxincome#cD.xxincome#c.trend
                                       cD.xxincome#cD.xxincome#c.trend#c.trend
                                       cD.xxincome#cD.xxpover#c.trend
                                       cD.xxincome#cD.xxpover#c.trend#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend#c.trend
                                       cD.xxpover#cD.xxpover#c.trend
                                       cD.xxpover#cD.xxpover#c.trend#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend#c.trend
                                       cL.xxprison#c.trend
                                       cL.xxprison#c.trend#c.trend
                                       cL.xxprison#cL.xxprison#c.trend
                                       cL.xxprison#cL.xxprison#c.trend#c.trend
                                       cL.xxpolice#c.trend
                                       cL.xxpolice#c.trend#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend#c.trend
                                       cL.xxunemp#c.trend
                                       cL.xxunemp#c.trend#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend#c.trend
                                       cL.xxincome#c.trend
                                       cL.xxincome#c.trend#c.trend
                                       cL.xxincome#cL.xxincome#c.trend
                                       cL.xxincome#cL.xxincome#c.trend#c.trend
                                       cL.xxpover#c.trend
                                       cL.xxpover#c.trend#c.trend
                                       cL.xxpover#cL.xxpover#c.trend
                                       cL.xxpover#cL.xxpover#c.trend#c.trend
                                       cL.xxafdc15#c.trend
                                       cL.xxafdc15#c.trend#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend#c.trend
                                       cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#c.trend#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend#c.trend
                                       cL.xxbeer#c.trend
                                       cL.xxbeer#c.trend#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend#c.trend
                                       c.Mxxprison#c.trend
                                       c.Mxxprison#c.trend#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend#c.trend
                                       c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.trend#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend#c.trend
                                       c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.trend#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend#c.trend
                                       c.Mxxincome#c.trend
                                       c.Mxxincome#c.trend#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend#c.trend
                                       c.Mxxpover#c.trend
                                       c.Mxxpover#c.trend#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend#c.trend
                                       c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.trend#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend#c.trend
                                       c.xxprison0#c.trend
                                       c.xxprison0#c.trend#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.xxprison0#c.xxprison0#c.trend#c.trend
                                       c.xxpolice0#c.trend
                                       c.xxpolice0#c.trend#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend#c.trend
                                       c.xxunemp0#c.trend
                                       c.xxunemp0#c.trend#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend#c.trend
                                       c.xxincome0#c.trend
                                       c.xxincome0#c.trend#c.trend
                                       c.xxincome0#c.xxincome0#c.trend
                                       c.xxincome0#c.xxincome0#c.trend#c.trend
                                       c.xxpover0#c.trend
                                       c.xxpover0#c.trend#c.trend
                                       c.xxpover0#c.xxpover0#c.trend
                                       c.xxpover0#c.xxpover0#c.trend#c.trend
                                       c.xxafdc150#c.trend
                                       c.xxafdc150#c.trend#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend#c.trend
                                       c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.trend#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend#c.trend
                                       c.xxbeer0#c.trend
                                       c.xxbeer0#c.trend#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend#c.trend
                                       c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.trend#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend#c.trend
                                       c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.trend#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend#c.trend
                                       c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.trend#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend#c.trend
                                       c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.trend#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend#c.trend
                                       86b.year 87.year 88.year 89.year 90.year
                                       91.year 92.year 93.year 94.year 95.year
                                       96.year 97.year
Selected controls (28):                prop0 cD.xxprison#cD.xxunemp
                                       cD.xxincome#cD.xxincome L.xxpolice
                                       L.xxincome Mxxincome
                                       c.Dprop0#c.Dprop0#c.trend#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend
                                       cL.xxunemp#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.xxafdc150#c.trend c.Dxxincome0#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxbeer0#c.trend 86b.year 87.year
                                       88.year 89.year 90.year 91.year 92.year
                                       93.year 94.year 95.year 96.year 97.year
  of which, amelioration set (12):     86b.year 87.year 88.year 89.year
                                       90.year 91.year 92.year 93.year 94.year
                                       95.year 96.year 97.year
Unpenalized controls (1):              _cons

Structural equation:

OLS using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.1341758    .0428122     -3.13    0.002     -.2180862    -.0502654
-------------+----------------------------------------------------------------

OLS using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.1349711    .0548869     -2.46    0.014     -.2425475    -.0273947
-------------+----------------------------------------------------------------

OLS with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.1485241    .0536284     -2.77    0.006     -.2536338    -.0434144
             |
       prop0 |    .1005553    .0415773      2.42    0.016      .0190653     .1820454
             |
 cD.xxprison#|
  cD.xxunemp |    1.950646    2.986743      0.65    0.514     -3.903262     7.804555
             |
 cD.xxincome#|
 cD.xxincome |   -35185.59     19222.7     -1.83    0.067     -72861.39     2490.199
             |
    xxpolice |
         L1. |   -.0220305     .021499     -1.02    0.305     -.0641678     .0201068
             |
    xxincome |
         L1. |     25.1241    8.777503      2.86    0.004      7.920508     42.32769
             |
   Mxxincome |   -26.98396    9.100124     -2.97    0.003     -44.81987    -9.148043
             |
    c.Dprop0#|
    c.Dprop0#|
     c.trend#|
     c.trend |   -1.022042    .3721408     -2.75    0.006     -1.751424     -.292659
             |
  cD.xxunemp#|
  cD.xxunemp#|
     c.trend |    74.65977    34.77825      2.15    0.032      6.495658     142.8239
             |
  cL.xxunemp#|
     c.trend |   -.6389254    .2718466     -2.35    0.019     -1.171735    -.1061158
             |
   cL.xxbeer#|
   cL.xxbeer#|
     c.trend |   -.1349534    .1851515     -0.73    0.466     -.4978438      .227937
             |
 c.Mxxpolice#|
 c.Mxxpolice#|
     c.trend |    .0102739      .01945      0.53    0.597     -.0278475     .0483952
             |
 c.xxprison0#|
 c.xxprison0#|
     c.trend |    .0300844    .0123033      2.45    0.014      .0059704     .0541984
             |
 c.xxafdc150#|
     c.trend |   -.0091631    .0219461     -0.42    0.676     -.0521768     .0338505
             |
          c. |
  Dxxincome0#|
     c.trend |    16.86016    16.23492      1.04    0.299      -14.9597     48.68003
             |
          c. |
  Dxxafdc150#|
          c. |
  Dxxafdc150#|
     c.trend#|
     c.trend |   -.4115828    .6699445     -0.61    0.539      -1.72465     .9014844
             |
  c.Dxxbeer0#|
     c.trend |   -.5261811    .6092698     -0.86    0.388     -1.720328     .6679658
             |
        year |
         87  |   -.0230703    .0100228     -2.30    0.021     -.0427147    -.0034259
         88  |   -.0385895    .0112178     -3.44    0.001      -.060576     -.016603
         89  |   -.0243877    .0132325     -1.84    0.065     -.0503229     .0015474
         90  |   -.0253038     .015513     -1.63    0.103     -.0557088     .0051011
         91  |   -.0217395     .017528     -1.24    0.215     -.0560937     .0126147
         92  |   -.0618375    .0197789     -3.13    0.002     -.1006034    -.0230715
         93  |   -.0531705     .022941     -2.32    0.020      -.098134     -.008207
         94  |   -.0243029    .0250331     -0.97    0.332      -.073367     .0247611
         95  |   -.0148198    .0284912     -0.52    0.603     -.0706616      .041022
         96  |    -.075567    .0314538     -2.40    0.016     -.1372153    -.0139186
         97  |   -.0714443    .0345653     -2.07    0.039     -.1391911    -.0036976
             |
       _cons |    .2734788    .2333251      1.17    0.241     -.1838301     .7307876
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    D.efaprop
------------------------------------------------------------------------------
Options: aset(i.year)   fe
Fixed effects transformation...
1.  (PDS/CHS) Selecting HD controls for dep var D.lpc_prop...
Selected:  cL.xxafdc15#cL.xxafdc15 cL.xxunemp#c.trend
          cL.xxunemp#cL.xxunemp#c.trend 92.year
Also inc:  86b.year 87.year 88.year 89.year 90.year 91.year 93.year 94.year
          95.year 96.year 97.year
2.  (PDS/CHS) Selecting HD controls for exog regressor D.efaprop...
Selected:  D.xxincome cD.xxprison#cD.xxunemp c.prop0#c.trend#c.trend
          c.prop0#c.prop0#c.trend#c.trend cL.xxunemp#cL.xxunemp#c.trend
          cL.xxafdc15#cL.xxafdc15#c.trend cL.xxbeer#cL.xxbeer#c.trend
          c.xxprison0#c.xxprison0#c.trend c.Dxxunemp0#c.Dxxunemp0#c.trend
          c.Dxxincome0#c.trend c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
          89.year 90.year 91.year 92.year 93.year 96.year 97.year
Also inc:  86b.year 87.year 88.year 94.year 95.year


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      homoskedastic
Number of observations:                600
Number of fixed effects:                50
Exogenous (1):                         D.efaprop
High-dim controls (348):               prop0 c.prop0#c.prop0 Dprop0
                                       c.Dprop0#c.Dprop0 D.xxprison D.xxpolice
                                       D.xxunemp D.xxincome D.xxpover
                                       D.xxafdc15 D.xxgunlaw D.xxbeer
                                       cD.xxprison#cD.xxprison
                                       cD.xxprison#cD.xxpolice
                                       cD.xxprison#cD.xxunemp
                                       cD.xxprison#cD.xxincome
                                       cD.xxprison#cD.xxpover
                                       cD.xxprison#cD.xxafdc15
                                       cD.xxprison#cD.xxgunlaw
                                       cD.xxprison#cD.xxbeer
                                       cD.xxpolice#cD.xxpolice
                                       cD.xxpolice#cD.xxunemp
                                       cD.xxpolice#cD.xxincome
                                       cD.xxpolice#cD.xxpover
                                       cD.xxpolice#cD.xxafdc15
                                       cD.xxpolice#cD.xxgunlaw
                                       cD.xxpolice#cD.xxbeer
                                       cD.xxunemp#cD.xxunemp
                                       cD.xxunemp#cD.xxincome
                                       cD.xxunemp#cD.xxpover
                                       cD.xxunemp#cD.xxafdc15
                                       cD.xxunemp#cD.xxgunlaw
                                       cD.xxunemp#cD.xxbeer
                                       cD.xxincome#cD.xxincome
                                       cD.xxincome#cD.xxpover
                                       cD.xxincome#cD.xxafdc15
                                       cD.xxincome#cD.xxgunlaw
                                       cD.xxincome#cD.xxbeer
                                       cD.xxpover#cD.xxpover
                                       cD.xxpover#cD.xxafdc15
                                       cD.xxpover#cD.xxgunlaw
                                       cD.xxpover#cD.xxbeer
                                       cD.xxafdc15#cD.xxafdc15
                                       cD.xxafdc15#cD.xxgunlaw
                                       cD.xxafdc15#cD.xxbeer
                                       cD.xxgunlaw#cD.xxgunlaw
                                       cD.xxgunlaw#cD.xxbeer
                                       cD.xxbeer#cD.xxbeer L.xxprison
                                       cL.xxprison#cL.xxprison L.xxpolice
                                       cL.xxpolice#cL.xxpolice L.xxunemp
                                       cL.xxunemp#cL.xxunemp L.xxincome
                                       cL.xxincome#cL.xxincome L.xxpover
                                       cL.xxpover#cL.xxpover L.xxafdc15
                                       cL.xxafdc15#cL.xxafdc15 L.xxgunlaw
                                       cL.xxgunlaw#cL.xxgunlaw L.xxbeer
                                       cL.xxbeer#cL.xxbeer Mxxprison
                                       c.Mxxprison#c.Mxxprison Mxxpolice
                                       c.Mxxpolice#c.Mxxpolice Mxxunemp
                                       c.Mxxunemp#c.Mxxunemp Mxxincome
                                       c.Mxxincome#c.Mxxincome Mxxpover
                                       c.Mxxpover#c.Mxxpover Mxxafdc15
                                       c.Mxxafdc15#c.Mxxafdc15 Mxxgunlaw
                                       c.Mxxgunlaw#c.Mxxgunlaw Mxxbeer
                                       c.Mxxbeer#c.Mxxbeer xxprison0
                                       c.xxprison0#c.xxprison0 xxpolice0
                                       c.xxpolice0#c.xxpolice0 xxunemp0
                                       c.xxunemp0#c.xxunemp0 xxincome0
                                       c.xxincome0#c.xxincome0 xxpover0
                                       c.xxpover0#c.xxpover0 xxafdc150
                                       c.xxafdc150#c.xxafdc150 xxgunlaw0
                                       c.xxgunlaw0#c.xxgunlaw0 xxbeer0
                                       c.xxbeer0#c.xxbeer0 Dxxprison0
                                       c.Dxxprison0#c.Dxxprison0 Dxxpolice0
                                       c.Dxxpolice0#c.Dxxpolice0 Dxxunemp0
                                       c.Dxxunemp0#c.Dxxunemp0 Dxxincome0
                                       c.Dxxincome0#c.Dxxincome0 Dxxpover0
                                       c.Dxxpover0#c.Dxxpover0 Dxxafdc150
                                       c.Dxxafdc150#c.Dxxafdc150 Dxxgunlaw0
                                       c.Dxxgunlaw0#c.Dxxgunlaw0 Dxxbeer0
                                       c.Dxxbeer0#c.Dxxbeer0 c.prop0#c.trend
                                       c.prop0#c.trend#c.trend
                                       c.prop0#c.prop0#c.trend
                                       c.prop0#c.prop0#c.trend#c.trend
                                       c.Dprop0#c.trend
                                       c.Dprop0#c.trend#c.trend
                                       c.Dprop0#c.Dprop0#c.trend
                                       c.Dprop0#c.Dprop0#c.trend#c.trend
                                       cD.xxprison#c.trend
                                       cD.xxprison#c.trend#c.trend
                                       cD.xxpolice#c.trend
                                       cD.xxpolice#c.trend#c.trend
                                       cD.xxunemp#c.trend
                                       cD.xxunemp#c.trend#c.trend
                                       cD.xxincome#c.trend
                                       cD.xxincome#c.trend#c.trend
                                       cD.xxpover#c.trend
                                       cD.xxpover#c.trend#c.trend
                                       cD.xxafdc15#c.trend
                                       cD.xxafdc15#c.trend#c.trend
                                       cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#c.trend#c.trend
                                       cD.xxbeer#c.trend
                                       cD.xxbeer#c.trend#c.trend
                                       cD.xxprison#cD.xxprison#c.trend
                                       cD.xxprison#cD.xxprison#c.trend#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend#c.trend
                                       cD.xxprison#cD.xxincome#c.trend
                                       cD.xxprison#cD.xxincome#c.trend#c.trend
                                       cD.xxprison#cD.xxpover#c.trend
                                       cD.xxprison#cD.xxpover#c.trend#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend#c.trend
                                       cD.xxincome#cD.xxincome#c.trend
                                       cD.xxincome#cD.xxincome#c.trend#c.trend
                                       cD.xxincome#cD.xxpover#c.trend
                                       cD.xxincome#cD.xxpover#c.trend#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend#c.trend
                                       cD.xxpover#cD.xxpover#c.trend
                                       cD.xxpover#cD.xxpover#c.trend#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend#c.trend
                                       cL.xxprison#c.trend
                                       cL.xxprison#c.trend#c.trend
                                       cL.xxprison#cL.xxprison#c.trend
                                       cL.xxprison#cL.xxprison#c.trend#c.trend
                                       cL.xxpolice#c.trend
                                       cL.xxpolice#c.trend#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend#c.trend
                                       cL.xxunemp#c.trend
                                       cL.xxunemp#c.trend#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend#c.trend
                                       cL.xxincome#c.trend
                                       cL.xxincome#c.trend#c.trend
                                       cL.xxincome#cL.xxincome#c.trend
                                       cL.xxincome#cL.xxincome#c.trend#c.trend
                                       cL.xxpover#c.trend
                                       cL.xxpover#c.trend#c.trend
                                       cL.xxpover#cL.xxpover#c.trend
                                       cL.xxpover#cL.xxpover#c.trend#c.trend
                                       cL.xxafdc15#c.trend
                                       cL.xxafdc15#c.trend#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend#c.trend
                                       cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#c.trend#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend#c.trend
                                       cL.xxbeer#c.trend
                                       cL.xxbeer#c.trend#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend#c.trend
                                       c.Mxxprison#c.trend
                                       c.Mxxprison#c.trend#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend#c.trend
                                       c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.trend#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend#c.trend
                                       c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.trend#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend#c.trend
                                       c.Mxxincome#c.trend
                                       c.Mxxincome#c.trend#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend#c.trend
                                       c.Mxxpover#c.trend
                                       c.Mxxpover#c.trend#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend#c.trend
                                       c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.trend#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend#c.trend
                                       c.xxprison0#c.trend
                                       c.xxprison0#c.trend#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.xxprison0#c.xxprison0#c.trend#c.trend
                                       c.xxpolice0#c.trend
                                       c.xxpolice0#c.trend#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend#c.trend
                                       c.xxunemp0#c.trend
                                       c.xxunemp0#c.trend#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend#c.trend
                                       c.xxincome0#c.trend
                                       c.xxincome0#c.trend#c.trend
                                       c.xxincome0#c.xxincome0#c.trend
                                       c.xxincome0#c.xxincome0#c.trend#c.trend
                                       c.xxpover0#c.trend
                                       c.xxpover0#c.trend#c.trend
                                       c.xxpover0#c.xxpover0#c.trend
                                       c.xxpover0#c.xxpover0#c.trend#c.trend
                                       c.xxafdc150#c.trend
                                       c.xxafdc150#c.trend#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend#c.trend
                                       c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.trend#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend#c.trend
                                       c.xxbeer0#c.trend
                                       c.xxbeer0#c.trend#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend#c.trend
                                       c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.trend#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend#c.trend
                                       c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.trend#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend#c.trend
                                       c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.trend#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend#c.trend
                                       c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.trend#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend#c.trend
                                       86b.year 87.year 88.year 89.year 90.year
                                       91.year 92.year 93.year 94.year 95.year
                                       96.year 97.year
Selected controls (25):                D.xxincome cD.xxprison#cD.xxunemp
                                       cL.xxafdc15#cL.xxafdc15
                                       c.prop0#c.trend#c.trend
                                       c.prop0#c.prop0#c.trend#c.trend
                                       cL.xxunemp#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend
                                       c.Dxxincome0#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       86b.year 87.year 88.year 89.year 90.year
                                       91.year 92.year 93.year 94.year 95.year
                                       96.year 97.year
  of which, amelioration set (12):     86b.year 87.year 88.year 89.year
                                       90.year 91.year 92.year 93.year 94.year
                                       95.year 96.year 97.year

Structural equation (fixed effects, #groups=50):

OLS using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.1564198    .0617164     -2.53    0.011     -.2773818    -.0354578
-------------+----------------------------------------------------------------

OLS using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.1159503    .0744602     -1.56    0.119     -.2618895     .0299889
-------------+----------------------------------------------------------------

OLS with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.1423221    .0768098     -1.85    0.064     -.2928665     .0082222
             |
    xxincome |
         D1. |    -20.7571    11.94772     -1.74    0.082      -44.1742     2.660008
             |
 cD.xxprison#|
  cD.xxunemp |    3.244904    3.294209      0.99    0.325     -3.211627     9.701435
             |
 cL.xxafdc15#|
 cL.xxafdc15 |    .0164504    .0185292      0.89    0.375     -.0198661      .052767
             |
     c.prop0#|
     c.trend#|
     c.trend |   -.0366712     .186204     -0.20    0.844     -.4016244     .3282821
             |
     c.prop0#|
     c.prop0#|
     c.trend#|
     c.trend |   -.1856112    .2644449     -0.70    0.483     -.7039137     .3326913
             |
  cL.xxunemp#|
     c.trend |   -.3063864    1.598774     -0.19    0.848     -3.439927     2.827154
             |
  cL.xxunemp#|
  cL.xxunemp#|
     c.trend |   -2.264714    13.00293     -0.17    0.862     -27.74999     23.22056
             |
 cL.xxafdc15#|
 cL.xxafdc15#|
     c.trend |    .0292364    .0324325      0.90    0.367     -.0343302      .092803
             |
   cL.xxbeer#|
   cL.xxbeer#|
     c.trend |    .7868493    .4470647      1.76    0.078     -.0893814      1.66308
             |
 c.xxprison0#|
 c.xxprison0#|
     c.trend |   -.0053881    .0221776     -0.24    0.808     -.0488555     .0380792
             |
 c.Dxxunemp0#|
 c.Dxxunemp0#|
     c.trend |   -26.12572    96.78954     -0.27    0.787     -215.8297     163.5783
             |
          c. |
  Dxxincome0#|
     c.trend |   -26.51375    36.84814     -0.72    0.472     -98.73478     45.70728
             |
          c. |
  Dxxafdc150#|
          c. |
  Dxxafdc150#|
     c.trend#|
     c.trend |   -1.075694    1.028686     -1.05    0.296     -3.091881     .9404931
             |
        year |
         87  |   -.0197771    .0107485     -1.84    0.066     -.0408438     .0012896
         88  |   -.0366312    .0137259     -2.67    0.008     -.0635335    -.0097288
         89  |   -.0212625    .0176878     -1.20    0.229     -.0559299      .013405
         90  |   -.0227085    .0221466     -1.03    0.305     -.0661151     .0206981
         91  |   -.0203081    .0270982     -0.75    0.454     -.0734196     .0328035
         92  |   -.0617881    .0315184     -1.96    0.050      -.123563    -.0000132
         93  |   -.0509831    .0356276     -1.43    0.152     -.1208118     .0188457
         94  |   -.0198776    .0402092     -0.49    0.621     -.0986861     .0589309
         95  |   -.0072022    .0440011     -0.16    0.870     -.0934427     .0790383
         96  |   -.0568048    .0471014     -1.21    0.228     -.1491219     .0355123
         97  |   -.0501697    .0511117     -0.98    0.326     -.1503468     .0500074
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    D.efaprop
------------------------------------------------------------------------------
Options: aset(i.year)   nocons
1.  (PDS/CHS) Selecting HD controls for dep var D.lpc_prop...
Selected:  Mxxincome cL.xxunemp#c.trend c.xxafdc150#c.trend 92.year
Also inc:  86b.year 87.year 88.year 89.year 90.year 91.year 93.year 94.year
          95.year 96.year 97.year
2.  (PDS/CHS) Selecting HD controls for exog regressor D.efaprop...
Selected:  prop0 cD.xxprison#cD.xxunemp L.xxprison cL.xxpolice#cL.xxpolice
          cL.xxincome#cL.xxincome xxpover0 c.Dprop0#c.Dprop0#c.trend#c.trend
          cD.xxunemp#cD.xxunemp#c.trend cL.xxafdc15#cL.xxafdc15#c.trend
          cL.xxbeer#cL.xxbeer#c.trend c.Mxxpolice#c.Mxxpolice#c.trend
          c.xxprison0#c.xxprison0#c.trend c.Dxxincome0#c.trend
          c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend c.Dxxbeer0#c.trend 90.year
          91.year 92.year 93.year 97.year
Also inc:  86b.year 87.year 88.year 89.year 94.year 95.year 96.year


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      homoskedastic
Number of observations:                600
Exogenous (1):                         D.efaprop
High-dim controls (348):               prop0 c.prop0#c.prop0 Dprop0
                                       c.Dprop0#c.Dprop0 D.xxprison D.xxpolice
                                       D.xxunemp D.xxincome D.xxpover
                                       D.xxafdc15 D.xxgunlaw D.xxbeer
                                       cD.xxprison#cD.xxprison
                                       cD.xxprison#cD.xxpolice
                                       cD.xxprison#cD.xxunemp
                                       cD.xxprison#cD.xxincome
                                       cD.xxprison#cD.xxpover
                                       cD.xxprison#cD.xxafdc15
                                       cD.xxprison#cD.xxgunlaw
                                       cD.xxprison#cD.xxbeer
                                       cD.xxpolice#cD.xxpolice
                                       cD.xxpolice#cD.xxunemp
                                       cD.xxpolice#cD.xxincome
                                       cD.xxpolice#cD.xxpover
                                       cD.xxpolice#cD.xxafdc15
                                       cD.xxpolice#cD.xxgunlaw
                                       cD.xxpolice#cD.xxbeer
                                       cD.xxunemp#cD.xxunemp
                                       cD.xxunemp#cD.xxincome
                                       cD.xxunemp#cD.xxpover
                                       cD.xxunemp#cD.xxafdc15
                                       cD.xxunemp#cD.xxgunlaw
                                       cD.xxunemp#cD.xxbeer
                                       cD.xxincome#cD.xxincome
                                       cD.xxincome#cD.xxpover
                                       cD.xxincome#cD.xxafdc15
                                       cD.xxincome#cD.xxgunlaw
                                       cD.xxincome#cD.xxbeer
                                       cD.xxpover#cD.xxpover
                                       cD.xxpover#cD.xxafdc15
                                       cD.xxpover#cD.xxgunlaw
                                       cD.xxpover#cD.xxbeer
                                       cD.xxafdc15#cD.xxafdc15
                                       cD.xxafdc15#cD.xxgunlaw
                                       cD.xxafdc15#cD.xxbeer
                                       cD.xxgunlaw#cD.xxgunlaw
                                       cD.xxgunlaw#cD.xxbeer
                                       cD.xxbeer#cD.xxbeer L.xxprison
                                       cL.xxprison#cL.xxprison L.xxpolice
                                       cL.xxpolice#cL.xxpolice L.xxunemp
                                       cL.xxunemp#cL.xxunemp L.xxincome
                                       cL.xxincome#cL.xxincome L.xxpover
                                       cL.xxpover#cL.xxpover L.xxafdc15
                                       cL.xxafdc15#cL.xxafdc15 L.xxgunlaw
                                       cL.xxgunlaw#cL.xxgunlaw L.xxbeer
                                       cL.xxbeer#cL.xxbeer Mxxprison
                                       c.Mxxprison#c.Mxxprison Mxxpolice
                                       c.Mxxpolice#c.Mxxpolice Mxxunemp
                                       c.Mxxunemp#c.Mxxunemp Mxxincome
                                       c.Mxxincome#c.Mxxincome Mxxpover
                                       c.Mxxpover#c.Mxxpover Mxxafdc15
                                       c.Mxxafdc15#c.Mxxafdc15 Mxxgunlaw
                                       c.Mxxgunlaw#c.Mxxgunlaw Mxxbeer
                                       c.Mxxbeer#c.Mxxbeer xxprison0
                                       c.xxprison0#c.xxprison0 xxpolice0
                                       c.xxpolice0#c.xxpolice0 xxunemp0
                                       c.xxunemp0#c.xxunemp0 xxincome0
                                       c.xxincome0#c.xxincome0 xxpover0
                                       c.xxpover0#c.xxpover0 xxafdc150
                                       c.xxafdc150#c.xxafdc150 xxgunlaw0
                                       c.xxgunlaw0#c.xxgunlaw0 xxbeer0
                                       c.xxbeer0#c.xxbeer0 Dxxprison0
                                       c.Dxxprison0#c.Dxxprison0 Dxxpolice0
                                       c.Dxxpolice0#c.Dxxpolice0 Dxxunemp0
                                       c.Dxxunemp0#c.Dxxunemp0 Dxxincome0
                                       c.Dxxincome0#c.Dxxincome0 Dxxpover0
                                       c.Dxxpover0#c.Dxxpover0 Dxxafdc150
                                       c.Dxxafdc150#c.Dxxafdc150 Dxxgunlaw0
                                       c.Dxxgunlaw0#c.Dxxgunlaw0 Dxxbeer0
                                       c.Dxxbeer0#c.Dxxbeer0 c.prop0#c.trend
                                       c.prop0#c.trend#c.trend
                                       c.prop0#c.prop0#c.trend
                                       c.prop0#c.prop0#c.trend#c.trend
                                       c.Dprop0#c.trend
                                       c.Dprop0#c.trend#c.trend
                                       c.Dprop0#c.Dprop0#c.trend
                                       c.Dprop0#c.Dprop0#c.trend#c.trend
                                       cD.xxprison#c.trend
                                       cD.xxprison#c.trend#c.trend
                                       cD.xxpolice#c.trend
                                       cD.xxpolice#c.trend#c.trend
                                       cD.xxunemp#c.trend
                                       cD.xxunemp#c.trend#c.trend
                                       cD.xxincome#c.trend
                                       cD.xxincome#c.trend#c.trend
                                       cD.xxpover#c.trend
                                       cD.xxpover#c.trend#c.trend
                                       cD.xxafdc15#c.trend
                                       cD.xxafdc15#c.trend#c.trend
                                       cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#c.trend#c.trend
                                       cD.xxbeer#c.trend
                                       cD.xxbeer#c.trend#c.trend
                                       cD.xxprison#cD.xxprison#c.trend
                                       cD.xxprison#cD.xxprison#c.trend#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend#c.trend
                                       cD.xxprison#cD.xxincome#c.trend
                                       cD.xxprison#cD.xxincome#c.trend#c.trend
                                       cD.xxprison#cD.xxpover#c.trend
                                       cD.xxprison#cD.xxpover#c.trend#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend#c.trend
                                       cD.xxincome#cD.xxincome#c.trend
                                       cD.xxincome#cD.xxincome#c.trend#c.trend
                                       cD.xxincome#cD.xxpover#c.trend
                                       cD.xxincome#cD.xxpover#c.trend#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend#c.trend
                                       cD.xxpover#cD.xxpover#c.trend
                                       cD.xxpover#cD.xxpover#c.trend#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend#c.trend
                                       cL.xxprison#c.trend
                                       cL.xxprison#c.trend#c.trend
                                       cL.xxprison#cL.xxprison#c.trend
                                       cL.xxprison#cL.xxprison#c.trend#c.trend
                                       cL.xxpolice#c.trend
                                       cL.xxpolice#c.trend#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend#c.trend
                                       cL.xxunemp#c.trend
                                       cL.xxunemp#c.trend#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend#c.trend
                                       cL.xxincome#c.trend
                                       cL.xxincome#c.trend#c.trend
                                       cL.xxincome#cL.xxincome#c.trend
                                       cL.xxincome#cL.xxincome#c.trend#c.trend
                                       cL.xxpover#c.trend
                                       cL.xxpover#c.trend#c.trend
                                       cL.xxpover#cL.xxpover#c.trend
                                       cL.xxpover#cL.xxpover#c.trend#c.trend
                                       cL.xxafdc15#c.trend
                                       cL.xxafdc15#c.trend#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend#c.trend
                                       cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#c.trend#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend#c.trend
                                       cL.xxbeer#c.trend
                                       cL.xxbeer#c.trend#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend#c.trend
                                       c.Mxxprison#c.trend
                                       c.Mxxprison#c.trend#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend#c.trend
                                       c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.trend#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend#c.trend
                                       c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.trend#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend#c.trend
                                       c.Mxxincome#c.trend
                                       c.Mxxincome#c.trend#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend#c.trend
                                       c.Mxxpover#c.trend
                                       c.Mxxpover#c.trend#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend#c.trend
                                       c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.trend#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend#c.trend
                                       c.xxprison0#c.trend
                                       c.xxprison0#c.trend#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.xxprison0#c.xxprison0#c.trend#c.trend
                                       c.xxpolice0#c.trend
                                       c.xxpolice0#c.trend#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend#c.trend
                                       c.xxunemp0#c.trend
                                       c.xxunemp0#c.trend#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend#c.trend
                                       c.xxincome0#c.trend
                                       c.xxincome0#c.trend#c.trend
                                       c.xxincome0#c.xxincome0#c.trend
                                       c.xxincome0#c.xxincome0#c.trend#c.trend
                                       c.xxpover0#c.trend
                                       c.xxpover0#c.trend#c.trend
                                       c.xxpover0#c.xxpover0#c.trend
                                       c.xxpover0#c.xxpover0#c.trend#c.trend
                                       c.xxafdc150#c.trend
                                       c.xxafdc150#c.trend#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend#c.trend
                                       c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.trend#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend#c.trend
                                       c.xxbeer0#c.trend
                                       c.xxbeer0#c.trend#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend#c.trend
                                       c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.trend#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend#c.trend
                                       c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.trend#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend#c.trend
                                       c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.trend#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend#c.trend
                                       c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.trend#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend#c.trend
                                       86b.year 87.year 88.year 89.year 90.year
                                       91.year 92.year 93.year 94.year 95.year
                                       96.year 97.year
Selected controls (30):                prop0 cD.xxprison#cD.xxunemp L.xxprison
                                       cL.xxpolice#cL.xxpolice
                                       cL.xxincome#cL.xxincome Mxxincome
                                       xxpover0
                                       c.Dprop0#c.Dprop0#c.trend#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend
                                       cL.xxunemp#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.xxafdc150#c.trend c.Dxxincome0#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxbeer0#c.trend 86b.year 87.year
                                       88.year 89.year 90.year 91.year 92.year
                                       93.year 94.year 95.year 96.year 97.year
  of which, amelioration set (12):     86b.year 87.year 88.year 89.year
                                       90.year 91.year 92.year 93.year 94.year
                                       95.year 96.year 97.year

Structural equation:

OLS using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.1319714    .0405315     -3.26    0.001     -.2114117    -.0525311
-------------+----------------------------------------------------------------

OLS using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.1119962    .0534389     -2.10    0.036     -.2167345     -.007258
-------------+----------------------------------------------------------------

OLS with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.1465701    .0542644     -2.70    0.007     -.2529263    -.0402139
             |
       prop0 |     .064569    .0447033      1.44    0.149     -.0230478     .1521858
             |
 cD.xxprison#|
  cD.xxunemp |    3.531632    2.959608      1.19    0.233     -2.269092     9.332356
             |
    xxprison |
         L1. |    .0059791    .0057549      1.04    0.299     -.0053003     .0172585
             |
 cL.xxpolice#|
 cL.xxpolice |   -.0112989    .0111256     -1.02    0.310     -.0331047      .010507
             |
 cL.xxincome#|
 cL.xxincome |    47.77429    23.95047      1.99    0.046      .8322224     94.71635
             |
   Mxxincome |   -4.479014    2.370704     -1.89    0.059     -9.125508     .1674793
    xxpover0 |    .2197357    .0727999      3.02    0.003      .0770505     .3624209
             |
    c.Dprop0#|
    c.Dprop0#|
     c.trend#|
     c.trend |   -.9447458    .3745185     -2.52    0.012     -1.678789    -.2107029
             |
  cD.xxunemp#|
  cD.xxunemp#|
     c.trend |    84.48327    35.14222      2.40    0.016      15.60578     153.3608
             |
  cL.xxunemp#|
     c.trend |   -.7788384    .2710882     -2.87    0.004     -1.310162    -.2475153
             |
 cL.xxafdc15#|
 cL.xxafdc15#|
     c.trend |    .0151696    .0220948      0.69    0.492     -.0281355     .0584747
             |
   cL.xxbeer#|
   cL.xxbeer#|
     c.trend |   -.0723643    .1896288     -0.38    0.703     -.4440299     .2993013
             |
 c.Mxxpolice#|
 c.Mxxpolice#|
     c.trend |    .0019398    .0202427      0.10    0.924     -.0377352     .0416148
             |
 c.xxprison0#|
 c.xxprison0#|
     c.trend |    .0218312    .0126454      1.73    0.084     -.0029533     .0466156
             |
 c.xxafdc150#|
     c.trend |   -.0288675    .0272606     -1.06    0.290     -.0822973     .0245623
             |
          c. |
  Dxxincome0#|
     c.trend |    14.91864    16.75896      0.89    0.373     -17.92833      47.7656
             |
          c. |
  Dxxafdc150#|
          c. |
  Dxxafdc150#|
     c.trend#|
     c.trend |   -.0349553    .6746046     -0.05    0.959     -1.357156     1.287245
             |
  c.Dxxbeer0#|
     c.trend |   -.9306563    .6375938     -1.46    0.144     -2.180317     .3190045
             |
        year |
         87  |    -.012276    .0093972     -1.31    0.191      -.030694     .0061421
         88  |   -.0264298    .0101347     -2.61    0.009     -.0462934    -.0065662
         89  |   -.0085126    .0112714     -0.76    0.450     -.0306042      .013579
         90  |   -.0042123    .0126438     -0.33    0.739     -.0289936     .0205691
         91  |    .0013159    .0144316      0.09    0.927     -.0269695     .0296013
         92  |   -.0374117     .016466     -2.27    0.023     -.0696845     -.005139
         93  |   -.0212175    .0184929     -1.15    0.251     -.0574629      .015028
         94  |    .0067549    .0201414      0.34    0.737     -.0327215     .0462313
         95  |    .0196308     .021834      0.90    0.369      -.023163     .0624246
         96  |   -.0296983     .024006     -1.24    0.216     -.0767493     .0173527
         97  |   -.0175915    .0264585     -0.66    0.506     -.0694492     .0342662
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    D.efaprop
------------------------------------------------------------------------------
Options: aset(i.year) robust
1.  (PDS/CHS) Selecting HD controls for dep var D.lpc_prop...
Selected:  c.prop0#c.trend cL.xxunemp#c.trend cL.xxunemp#cL.xxunemp#c.trend
          c.Mxxpolice#c.Mxxpolice#c.trend c.xxafdc150#c.trend
          c.xxafdc150#c.xxafdc150#c.trend 92.year
Also inc:  86b.year 87.year 88.year 89.year 90.year 91.year 93.year 94.year
          95.year 96.year 97.year
2.  (PDS/CHS) Selecting HD controls for exog regressor D.efaprop...
Selected:  prop0 D.xxbeer cD.xxincome#cD.xxincome L.xxprison L.xxpolice
          L.xxincome Mxxincome cD.xxunemp#cD.xxunemp#c.trend cL.xxunemp#c.trend
          cL.xxafdc15#cL.xxafdc15#c.trend cL.xxbeer#cL.xxbeer#c.trend
          c.xxprison0#c.xxprison0#c.trend c.Dxxincome0#c.trend
          c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend c.Dxxbeer0#c.trend 87.year
          90.year 91.year 92.year 93.year 97.year
Also inc:  86b.year 88.year 89.year 94.year 95.year 96.year


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      heteroskedastic
Number of observations:                600
Exogenous (1):                         D.efaprop
High-dim controls (348):               prop0 c.prop0#c.prop0 Dprop0
                                       c.Dprop0#c.Dprop0 D.xxprison D.xxpolice
                                       D.xxunemp D.xxincome D.xxpover
                                       D.xxafdc15 D.xxgunlaw D.xxbeer
                                       cD.xxprison#cD.xxprison
                                       cD.xxprison#cD.xxpolice
                                       cD.xxprison#cD.xxunemp
                                       cD.xxprison#cD.xxincome
                                       cD.xxprison#cD.xxpover
                                       cD.xxprison#cD.xxafdc15
                                       cD.xxprison#cD.xxgunlaw
                                       cD.xxprison#cD.xxbeer
                                       cD.xxpolice#cD.xxpolice
                                       cD.xxpolice#cD.xxunemp
                                       cD.xxpolice#cD.xxincome
                                       cD.xxpolice#cD.xxpover
                                       cD.xxpolice#cD.xxafdc15
                                       cD.xxpolice#cD.xxgunlaw
                                       cD.xxpolice#cD.xxbeer
                                       cD.xxunemp#cD.xxunemp
                                       cD.xxunemp#cD.xxincome
                                       cD.xxunemp#cD.xxpover
                                       cD.xxunemp#cD.xxafdc15
                                       cD.xxunemp#cD.xxgunlaw
                                       cD.xxunemp#cD.xxbeer
                                       cD.xxincome#cD.xxincome
                                       cD.xxincome#cD.xxpover
                                       cD.xxincome#cD.xxafdc15
                                       cD.xxincome#cD.xxgunlaw
                                       cD.xxincome#cD.xxbeer
                                       cD.xxpover#cD.xxpover
                                       cD.xxpover#cD.xxafdc15
                                       cD.xxpover#cD.xxgunlaw
                                       cD.xxpover#cD.xxbeer
                                       cD.xxafdc15#cD.xxafdc15
                                       cD.xxafdc15#cD.xxgunlaw
                                       cD.xxafdc15#cD.xxbeer
                                       cD.xxgunlaw#cD.xxgunlaw
                                       cD.xxgunlaw#cD.xxbeer
                                       cD.xxbeer#cD.xxbeer L.xxprison
                                       cL.xxprison#cL.xxprison L.xxpolice
                                       cL.xxpolice#cL.xxpolice L.xxunemp
                                       cL.xxunemp#cL.xxunemp L.xxincome
                                       cL.xxincome#cL.xxincome L.xxpover
                                       cL.xxpover#cL.xxpover L.xxafdc15
                                       cL.xxafdc15#cL.xxafdc15 L.xxgunlaw
                                       cL.xxgunlaw#cL.xxgunlaw L.xxbeer
                                       cL.xxbeer#cL.xxbeer Mxxprison
                                       c.Mxxprison#c.Mxxprison Mxxpolice
                                       c.Mxxpolice#c.Mxxpolice Mxxunemp
                                       c.Mxxunemp#c.Mxxunemp Mxxincome
                                       c.Mxxincome#c.Mxxincome Mxxpover
                                       c.Mxxpover#c.Mxxpover Mxxafdc15
                                       c.Mxxafdc15#c.Mxxafdc15 Mxxgunlaw
                                       c.Mxxgunlaw#c.Mxxgunlaw Mxxbeer
                                       c.Mxxbeer#c.Mxxbeer xxprison0
                                       c.xxprison0#c.xxprison0 xxpolice0
                                       c.xxpolice0#c.xxpolice0 xxunemp0
                                       c.xxunemp0#c.xxunemp0 xxincome0
                                       c.xxincome0#c.xxincome0 xxpover0
                                       c.xxpover0#c.xxpover0 xxafdc150
                                       c.xxafdc150#c.xxafdc150 xxgunlaw0
                                       c.xxgunlaw0#c.xxgunlaw0 xxbeer0
                                       c.xxbeer0#c.xxbeer0 Dxxprison0
                                       c.Dxxprison0#c.Dxxprison0 Dxxpolice0
                                       c.Dxxpolice0#c.Dxxpolice0 Dxxunemp0
                                       c.Dxxunemp0#c.Dxxunemp0 Dxxincome0
                                       c.Dxxincome0#c.Dxxincome0 Dxxpover0
                                       c.Dxxpover0#c.Dxxpover0 Dxxafdc150
                                       c.Dxxafdc150#c.Dxxafdc150 Dxxgunlaw0
                                       c.Dxxgunlaw0#c.Dxxgunlaw0 Dxxbeer0
                                       c.Dxxbeer0#c.Dxxbeer0 c.prop0#c.trend
                                       c.prop0#c.trend#c.trend
                                       c.prop0#c.prop0#c.trend
                                       c.prop0#c.prop0#c.trend#c.trend
                                       c.Dprop0#c.trend
                                       c.Dprop0#c.trend#c.trend
                                       c.Dprop0#c.Dprop0#c.trend
                                       c.Dprop0#c.Dprop0#c.trend#c.trend
                                       cD.xxprison#c.trend
                                       cD.xxprison#c.trend#c.trend
                                       cD.xxpolice#c.trend
                                       cD.xxpolice#c.trend#c.trend
                                       cD.xxunemp#c.trend
                                       cD.xxunemp#c.trend#c.trend
                                       cD.xxincome#c.trend
                                       cD.xxincome#c.trend#c.trend
                                       cD.xxpover#c.trend
                                       cD.xxpover#c.trend#c.trend
                                       cD.xxafdc15#c.trend
                                       cD.xxafdc15#c.trend#c.trend
                                       cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#c.trend#c.trend
                                       cD.xxbeer#c.trend
                                       cD.xxbeer#c.trend#c.trend
                                       cD.xxprison#cD.xxprison#c.trend
                                       cD.xxprison#cD.xxprison#c.trend#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend#c.trend
                                       cD.xxprison#cD.xxincome#c.trend
                                       cD.xxprison#cD.xxincome#c.trend#c.trend
                                       cD.xxprison#cD.xxpover#c.trend
                                       cD.xxprison#cD.xxpover#c.trend#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend#c.trend
                                       cD.xxincome#cD.xxincome#c.trend
                                       cD.xxincome#cD.xxincome#c.trend#c.trend
                                       cD.xxincome#cD.xxpover#c.trend
                                       cD.xxincome#cD.xxpover#c.trend#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend#c.trend
                                       cD.xxpover#cD.xxpover#c.trend
                                       cD.xxpover#cD.xxpover#c.trend#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend#c.trend
                                       cL.xxprison#c.trend
                                       cL.xxprison#c.trend#c.trend
                                       cL.xxprison#cL.xxprison#c.trend
                                       cL.xxprison#cL.xxprison#c.trend#c.trend
                                       cL.xxpolice#c.trend
                                       cL.xxpolice#c.trend#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend#c.trend
                                       cL.xxunemp#c.trend
                                       cL.xxunemp#c.trend#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend#c.trend
                                       cL.xxincome#c.trend
                                       cL.xxincome#c.trend#c.trend
                                       cL.xxincome#cL.xxincome#c.trend
                                       cL.xxincome#cL.xxincome#c.trend#c.trend
                                       cL.xxpover#c.trend
                                       cL.xxpover#c.trend#c.trend
                                       cL.xxpover#cL.xxpover#c.trend
                                       cL.xxpover#cL.xxpover#c.trend#c.trend
                                       cL.xxafdc15#c.trend
                                       cL.xxafdc15#c.trend#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend#c.trend
                                       cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#c.trend#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend#c.trend
                                       cL.xxbeer#c.trend
                                       cL.xxbeer#c.trend#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend#c.trend
                                       c.Mxxprison#c.trend
                                       c.Mxxprison#c.trend#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend#c.trend
                                       c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.trend#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend#c.trend
                                       c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.trend#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend#c.trend
                                       c.Mxxincome#c.trend
                                       c.Mxxincome#c.trend#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend#c.trend
                                       c.Mxxpover#c.trend
                                       c.Mxxpover#c.trend#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend#c.trend
                                       c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.trend#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend#c.trend
                                       c.xxprison0#c.trend
                                       c.xxprison0#c.trend#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.xxprison0#c.xxprison0#c.trend#c.trend
                                       c.xxpolice0#c.trend
                                       c.xxpolice0#c.trend#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend#c.trend
                                       c.xxunemp0#c.trend
                                       c.xxunemp0#c.trend#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend#c.trend
                                       c.xxincome0#c.trend
                                       c.xxincome0#c.trend#c.trend
                                       c.xxincome0#c.xxincome0#c.trend
                                       c.xxincome0#c.xxincome0#c.trend#c.trend
                                       c.xxpover0#c.trend
                                       c.xxpover0#c.trend#c.trend
                                       c.xxpover0#c.xxpover0#c.trend
                                       c.xxpover0#c.xxpover0#c.trend#c.trend
                                       c.xxafdc150#c.trend
                                       c.xxafdc150#c.trend#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend#c.trend
                                       c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.trend#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend#c.trend
                                       c.xxbeer0#c.trend
                                       c.xxbeer0#c.trend#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend#c.trend
                                       c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.trend#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend#c.trend
                                       c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.trend#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend#c.trend
                                       c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.trend#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend#c.trend
                                       c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.trend#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend#c.trend
                                       86b.year 87.year 88.year 89.year 90.year
                                       91.year 92.year 93.year 94.year 95.year
                                       96.year 97.year
Selected controls (32):                prop0 D.xxbeer cD.xxincome#cD.xxincome
                                       L.xxprison L.xxpolice L.xxincome
                                       Mxxincome c.prop0#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend
                                       cL.xxunemp#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.xxafdc150#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend
                                       c.Dxxincome0#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxbeer0#c.trend 86b.year 87.year
                                       88.year 89.year 90.year 91.year 92.year
                                       93.year 94.year 95.year 96.year 97.year
  of which, amelioration set (12):     86b.year 87.year 88.year 89.year
                                       90.year 91.year 92.year 93.year 94.year
                                       95.year 96.year 97.year
Unpenalized controls (1):              _cons

Structural equation:

OLS using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.1104749    .0356529     -3.10    0.002     -.1803533    -.0405964
-------------+----------------------------------------------------------------

OLS using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.0639536    .0422654     -1.51    0.130     -.1467922      .018885
-------------+----------------------------------------------------------------

OLS with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.1166432    .0487138     -2.39    0.017     -.2121205    -.0211658
             |
       prop0 |    .1054876    .0467974      2.25    0.024      .0137664     .1972088
             |
      xxbeer |
         D1. |   -.0445589    .1734192     -0.26    0.797     -.3844542     .2953364
             |
 cD.xxincome#|
 cD.xxincome |   -34400.35    24408.56     -1.41    0.159     -82240.24     13439.54
             |
    xxprison |
         L1. |    .0083199     .005751      1.45    0.148     -.0029519     .0195918
             |
    xxpolice |
         L1. |    -.028516    .0195923     -1.46    0.146     -.0669161     .0098842
             |
    xxincome |
         L1. |     24.1492    10.56046      2.29    0.022      3.451081     44.84732
             |
   Mxxincome |   -25.58997    10.71358     -2.39    0.017      -46.5882    -4.591738
             |
     c.prop0#|
     c.trend |   -.1827571    .0651417     -2.81    0.005     -.3104325    -.0550817
             |
  cD.xxunemp#|
  cD.xxunemp#|
     c.trend |    81.87588    29.16931      2.81    0.005      24.70509     139.0467
             |
  cL.xxunemp#|
     c.trend |   -.8455916    1.179407     -0.72    0.473     -3.157186     1.466003
             |
  cL.xxunemp#|
  cL.xxunemp#|
     c.trend |    .9437267     9.00835      0.10    0.917     -16.71231     18.59977
             |
 cL.xxafdc15#|
 cL.xxafdc15#|
     c.trend |    .0193365    .0202758      0.95    0.340     -.0204033     .0590762
             |
   cL.xxbeer#|
   cL.xxbeer#|
     c.trend |   -.1245115    .2028864     -0.61    0.539     -.5221614     .2731385
             |
 c.Mxxpolice#|
 c.Mxxpolice#|
     c.trend |    .0079866    .0177713      0.45    0.653     -.0268446     .0428178
             |
 c.xxprison0#|
 c.xxprison0#|
     c.trend |    .0246992    .0110037      2.24    0.025      .0031324      .046266
             |
 c.xxafdc150#|
     c.trend |    -.048125    .0844125     -0.57    0.569     -.2135704     .1173204
             |
 c.xxafdc150#|
 c.xxafdc150#|
     c.trend |    .0179526    .0491688      0.37    0.715     -.0784165     .1143216
             |
          c. |
  Dxxincome0#|
     c.trend |    15.99601    18.26438      0.88    0.381     -19.80152     51.79355
             |
          c. |
  Dxxafdc150#|
          c. |
  Dxxafdc150#|
     c.trend#|
     c.trend |   -.0502672    .5914762     -0.08    0.932     -1.209539     1.109005
             |
  c.Dxxbeer0#|
     c.trend |   -.6973754    .6249357     -1.12    0.264     -1.922227      .527476
             |
        year |
         87  |   -.0223654    .0099623     -2.25    0.025     -.0418912    -.0028396
         88  |   -.0363608    .0147041     -2.47    0.013     -.0651804    -.0075412
         89  |   -.0207315    .0191967     -1.08    0.280     -.0583564     .0168934
         90  |   -.0184723    .0253599     -0.73    0.466     -.0681768     .0312321
         91  |    -.013228    .0299304     -0.44    0.659     -.0718906     .0454345
         92  |   -.0512921     .034611     -1.48    0.138     -.1191285     .0165443
         93  |   -.0406503    .0415233     -0.98    0.328     -.1220344     .0407339
         94  |   -.0090963    .0476467     -0.19    0.849     -.1024822     .0842895
         95  |    .0031053    .0560891      0.06    0.956     -.1068274      .113038
         96  |   -.0536849    .0599914     -0.89    0.371     -.1712658      .063896
         97  |   -.0467221     .066264     -0.71    0.481     -.1765971     .0831529
             |
       _cons |    .2335838    .2050736      1.14    0.255     -.1683531     .6355206
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    D.efaprop
------------------------------------------------------------------------------
Options: aset(i.year) robust fe
Fixed effects transformation...
1.  (PDS/CHS) Selecting HD controls for dep var D.lpc_prop...
Selected:  L.xxprison cL.xxafdc15#cL.xxafdc15 c.prop0#c.trend
          cL.xxunemp#c.trend cL.xxunemp#cL.xxunemp#c.trend
          c.Mxxpolice#c.Mxxpolice#c.trend 92.year
Also inc:  86b.year 87.year 88.year 89.year 90.year 91.year 93.year 94.year
          95.year 96.year 97.year
2.  (PDS/CHS) Selecting HD controls for exog regressor D.efaprop...
Selected:  D.xxincome cD.xxincome#cD.xxincome c.prop0#c.trend#c.trend
          c.prop0#c.prop0#c.trend#c.trend cL.xxunemp#cL.xxunemp#c.trend
          cL.xxafdc15#cL.xxafdc15#c.trend cL.xxbeer#cL.xxbeer#c.trend
          c.xxprison0#c.xxprison0#c.trend c.Dxxunemp0#c.Dxxunemp0#c.trend
          c.Dxxincome0#c.trend 89.year 90.year 91.year 92.year 93.year 94.year
          96.year 97.year
Also inc:  86b.year 87.year 88.year 95.year


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      heteroskedastic
Number of observations:                600
Number of fixed effects:                50
Exogenous (1):                         D.efaprop
High-dim controls (348):               prop0 c.prop0#c.prop0 Dprop0
                                       c.Dprop0#c.Dprop0 D.xxprison D.xxpolice
                                       D.xxunemp D.xxincome D.xxpover
                                       D.xxafdc15 D.xxgunlaw D.xxbeer
                                       cD.xxprison#cD.xxprison
                                       cD.xxprison#cD.xxpolice
                                       cD.xxprison#cD.xxunemp
                                       cD.xxprison#cD.xxincome
                                       cD.xxprison#cD.xxpover
                                       cD.xxprison#cD.xxafdc15
                                       cD.xxprison#cD.xxgunlaw
                                       cD.xxprison#cD.xxbeer
                                       cD.xxpolice#cD.xxpolice
                                       cD.xxpolice#cD.xxunemp
                                       cD.xxpolice#cD.xxincome
                                       cD.xxpolice#cD.xxpover
                                       cD.xxpolice#cD.xxafdc15
                                       cD.xxpolice#cD.xxgunlaw
                                       cD.xxpolice#cD.xxbeer
                                       cD.xxunemp#cD.xxunemp
                                       cD.xxunemp#cD.xxincome
                                       cD.xxunemp#cD.xxpover
                                       cD.xxunemp#cD.xxafdc15
                                       cD.xxunemp#cD.xxgunlaw
                                       cD.xxunemp#cD.xxbeer
                                       cD.xxincome#cD.xxincome
                                       cD.xxincome#cD.xxpover
                                       cD.xxincome#cD.xxafdc15
                                       cD.xxincome#cD.xxgunlaw
                                       cD.xxincome#cD.xxbeer
                                       cD.xxpover#cD.xxpover
                                       cD.xxpover#cD.xxafdc15
                                       cD.xxpover#cD.xxgunlaw
                                       cD.xxpover#cD.xxbeer
                                       cD.xxafdc15#cD.xxafdc15
                                       cD.xxafdc15#cD.xxgunlaw
                                       cD.xxafdc15#cD.xxbeer
                                       cD.xxgunlaw#cD.xxgunlaw
                                       cD.xxgunlaw#cD.xxbeer
                                       cD.xxbeer#cD.xxbeer L.xxprison
                                       cL.xxprison#cL.xxprison L.xxpolice
                                       cL.xxpolice#cL.xxpolice L.xxunemp
                                       cL.xxunemp#cL.xxunemp L.xxincome
                                       cL.xxincome#cL.xxincome L.xxpover
                                       cL.xxpover#cL.xxpover L.xxafdc15
                                       cL.xxafdc15#cL.xxafdc15 L.xxgunlaw
                                       cL.xxgunlaw#cL.xxgunlaw L.xxbeer
                                       cL.xxbeer#cL.xxbeer Mxxprison
                                       c.Mxxprison#c.Mxxprison Mxxpolice
                                       c.Mxxpolice#c.Mxxpolice Mxxunemp
                                       c.Mxxunemp#c.Mxxunemp Mxxincome
                                       c.Mxxincome#c.Mxxincome Mxxpover
                                       c.Mxxpover#c.Mxxpover Mxxafdc15
                                       c.Mxxafdc15#c.Mxxafdc15 Mxxgunlaw
                                       c.Mxxgunlaw#c.Mxxgunlaw Mxxbeer
                                       c.Mxxbeer#c.Mxxbeer xxprison0
                                       c.xxprison0#c.xxprison0 xxpolice0
                                       c.xxpolice0#c.xxpolice0 xxunemp0
                                       c.xxunemp0#c.xxunemp0 xxincome0
                                       c.xxincome0#c.xxincome0 xxpover0
                                       c.xxpover0#c.xxpover0 xxafdc150
                                       c.xxafdc150#c.xxafdc150 xxgunlaw0
                                       c.xxgunlaw0#c.xxgunlaw0 xxbeer0
                                       c.xxbeer0#c.xxbeer0 Dxxprison0
                                       c.Dxxprison0#c.Dxxprison0 Dxxpolice0
                                       c.Dxxpolice0#c.Dxxpolice0 Dxxunemp0
                                       c.Dxxunemp0#c.Dxxunemp0 Dxxincome0
                                       c.Dxxincome0#c.Dxxincome0 Dxxpover0
                                       c.Dxxpover0#c.Dxxpover0 Dxxafdc150
                                       c.Dxxafdc150#c.Dxxafdc150 Dxxgunlaw0
                                       c.Dxxgunlaw0#c.Dxxgunlaw0 Dxxbeer0
                                       c.Dxxbeer0#c.Dxxbeer0 c.prop0#c.trend
                                       c.prop0#c.trend#c.trend
                                       c.prop0#c.prop0#c.trend
                                       c.prop0#c.prop0#c.trend#c.trend
                                       c.Dprop0#c.trend
                                       c.Dprop0#c.trend#c.trend
                                       c.Dprop0#c.Dprop0#c.trend
                                       c.Dprop0#c.Dprop0#c.trend#c.trend
                                       cD.xxprison#c.trend
                                       cD.xxprison#c.trend#c.trend
                                       cD.xxpolice#c.trend
                                       cD.xxpolice#c.trend#c.trend
                                       cD.xxunemp#c.trend
                                       cD.xxunemp#c.trend#c.trend
                                       cD.xxincome#c.trend
                                       cD.xxincome#c.trend#c.trend
                                       cD.xxpover#c.trend
                                       cD.xxpover#c.trend#c.trend
                                       cD.xxafdc15#c.trend
                                       cD.xxafdc15#c.trend#c.trend
                                       cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#c.trend#c.trend
                                       cD.xxbeer#c.trend
                                       cD.xxbeer#c.trend#c.trend
                                       cD.xxprison#cD.xxprison#c.trend
                                       cD.xxprison#cD.xxprison#c.trend#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend#c.trend
                                       cD.xxprison#cD.xxincome#c.trend
                                       cD.xxprison#cD.xxincome#c.trend#c.trend
                                       cD.xxprison#cD.xxpover#c.trend
                                       cD.xxprison#cD.xxpover#c.trend#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend#c.trend
                                       cD.xxincome#cD.xxincome#c.trend
                                       cD.xxincome#cD.xxincome#c.trend#c.trend
                                       cD.xxincome#cD.xxpover#c.trend
                                       cD.xxincome#cD.xxpover#c.trend#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend#c.trend
                                       cD.xxpover#cD.xxpover#c.trend
                                       cD.xxpover#cD.xxpover#c.trend#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend#c.trend
                                       cL.xxprison#c.trend
                                       cL.xxprison#c.trend#c.trend
                                       cL.xxprison#cL.xxprison#c.trend
                                       cL.xxprison#cL.xxprison#c.trend#c.trend
                                       cL.xxpolice#c.trend
                                       cL.xxpolice#c.trend#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend#c.trend
                                       cL.xxunemp#c.trend
                                       cL.xxunemp#c.trend#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend#c.trend
                                       cL.xxincome#c.trend
                                       cL.xxincome#c.trend#c.trend
                                       cL.xxincome#cL.xxincome#c.trend
                                       cL.xxincome#cL.xxincome#c.trend#c.trend
                                       cL.xxpover#c.trend
                                       cL.xxpover#c.trend#c.trend
                                       cL.xxpover#cL.xxpover#c.trend
                                       cL.xxpover#cL.xxpover#c.trend#c.trend
                                       cL.xxafdc15#c.trend
                                       cL.xxafdc15#c.trend#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend#c.trend
                                       cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#c.trend#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend#c.trend
                                       cL.xxbeer#c.trend
                                       cL.xxbeer#c.trend#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend#c.trend
                                       c.Mxxprison#c.trend
                                       c.Mxxprison#c.trend#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend#c.trend
                                       c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.trend#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend#c.trend
                                       c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.trend#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend#c.trend
                                       c.Mxxincome#c.trend
                                       c.Mxxincome#c.trend#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend#c.trend
                                       c.Mxxpover#c.trend
                                       c.Mxxpover#c.trend#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend#c.trend
                                       c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.trend#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend#c.trend
                                       c.xxprison0#c.trend
                                       c.xxprison0#c.trend#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.xxprison0#c.xxprison0#c.trend#c.trend
                                       c.xxpolice0#c.trend
                                       c.xxpolice0#c.trend#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend#c.trend
                                       c.xxunemp0#c.trend
                                       c.xxunemp0#c.trend#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend#c.trend
                                       c.xxincome0#c.trend
                                       c.xxincome0#c.trend#c.trend
                                       c.xxincome0#c.xxincome0#c.trend
                                       c.xxincome0#c.xxincome0#c.trend#c.trend
                                       c.xxpover0#c.trend
                                       c.xxpover0#c.trend#c.trend
                                       c.xxpover0#c.xxpover0#c.trend
                                       c.xxpover0#c.xxpover0#c.trend#c.trend
                                       c.xxafdc150#c.trend
                                       c.xxafdc150#c.trend#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend#c.trend
                                       c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.trend#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend#c.trend
                                       c.xxbeer0#c.trend
                                       c.xxbeer0#c.trend#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend#c.trend
                                       c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.trend#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend#c.trend
                                       c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.trend#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend#c.trend
                                       c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.trend#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend#c.trend
                                       c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.trend#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend#c.trend
                                       86b.year 87.year 88.year 89.year 90.year
                                       91.year 92.year 93.year 94.year 95.year
                                       96.year 97.year
Selected controls (27):                D.xxincome cD.xxincome#cD.xxincome
                                       L.xxprison cL.xxafdc15#cL.xxafdc15
                                       c.prop0#c.trend c.prop0#c.trend#c.trend
                                       c.prop0#c.prop0#c.trend#c.trend
                                       cL.xxunemp#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend
                                       c.Dxxincome0#c.trend 86b.year 87.year
                                       88.year 89.year 90.year 91.year 92.year
                                       93.year 94.year 95.year 96.year 97.year
  of which, amelioration set (12):     86b.year 87.year 88.year 89.year
                                       90.year 91.year 92.year 93.year 94.year
                                       95.year 96.year 97.year

Structural equation (fixed effects, #groups=50):

OLS using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.1224896    .0505517     -2.42    0.015     -.2215691    -.0234101
-------------+----------------------------------------------------------------

OLS using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.0898873    .0594451     -1.51    0.131     -.2063975     .0266229
-------------+----------------------------------------------------------------

OLS with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.0980909     .064014     -1.53    0.125      -.223556     .0273742
             |
    xxincome |
         D1. |   -10.65165    16.92912     -0.63    0.529     -43.83213     22.52883
             |
 cD.xxincome#|
 cD.xxincome |   -44402.86    31262.22     -1.42    0.156     -105675.7     16869.95
             |
    xxprison |
         L1. |   -.0094006    .0214117     -0.44    0.661     -.0513669     .0325657
             |
 cL.xxafdc15#|
 cL.xxafdc15 |    .0186832    .0171487      1.09    0.276     -.0149278     .0522941
             |
     c.prop0#|
     c.trend |   -.2054358    .2047031     -1.00    0.316     -.6066465     .1957748
             |
     c.prop0#|
     c.trend#|
     c.trend |    .1364936    .2143357      0.64    0.524     -.2835966     .5565839
             |
     c.prop0#|
     c.prop0#|
     c.trend#|
     c.trend |   -.0948657    .2192048     -0.43    0.665     -.5244992     .3347679
             |
  cL.xxunemp#|
     c.trend |   -.4960099    1.520297     -0.33    0.744     -3.475738     2.483718
             |
  cL.xxunemp#|
  cL.xxunemp#|
     c.trend |   -1.867449    11.59353     -0.16    0.872     -24.59035     20.85546
             |
 cL.xxafdc15#|
 cL.xxafdc15#|
     c.trend |    .0336261    .0313697      1.07    0.284     -.0278574     .0951096
             |
   cL.xxbeer#|
   cL.xxbeer#|
     c.trend |    .6952383    .4180451      1.66    0.096      -.124115     1.514592
             |
 c.Mxxpolice#|
 c.Mxxpolice#|
     c.trend |   -.0234749    .0210915     -1.11    0.266     -.0648136     .0178637
             |
 c.xxprison0#|
 c.xxprison0#|
     c.trend |    .0007624    .0230381      0.03    0.974     -.0443915     .0459163
             |
 c.Dxxunemp0#|
 c.Dxxunemp0#|
     c.trend |    7.047113    91.10943      0.08    0.938     -171.5241     185.6183
             |
          c. |
  Dxxincome0#|
     c.trend |   -27.59749      40.551     -0.68    0.496      -107.076     51.88101
             |
        year |
         87  |   -.0207419     .009939     -2.09    0.037      -.040222    -.0012617
         88  |   -.0340968    .0127007     -2.68    0.007     -.0589897    -.0092039
         89  |   -.0171349    .0159894     -1.07    0.284     -.0484736     .0142038
         90  |   -.0149058     .020792     -0.72    0.473     -.0556573     .0258456
         91  |   -.0077583    .0260997     -0.30    0.766     -.0589128     .0433962
         92  |   -.0488697    .0291762     -1.67    0.094      -.106054     .0083147
         93  |   -.0370278    .0328437     -1.13    0.260     -.1014002     .0273446
         94  |   -.0017559    .0369776     -0.05    0.962     -.0742307     .0707189
         95  |    .0152381    .0412686      0.37    0.712     -.0656469     .0961231
         96  |   -.0352492    .0426549     -0.83    0.409     -.1188513     .0483528
         97  |   -.0271296     .047696     -0.57    0.569      -.120612     .0663528
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    D.efaprop
------------------------------------------------------------------------------
Options: aset(i.year) robust nocons
1.  (PDS/CHS) Selecting HD controls for dep var D.lpc_prop...
Selected:  c.prop0#c.trend#c.trend c.xxafdc150#c.xxafdc150#c.trend#c.trend
Also inc:  86b.year 87.year 88.year 89.year 90.year 91.year 92.year 93.year
          94.year 95.year 96.year 97.year
2.  (PDS/CHS) Selecting HD controls for exog regressor D.efaprop...
Selected:  prop0 L.xxprison cL.xxpolice#cL.xxpolice c.Mxxpolice#c.Mxxpolice
          c.xxafdc150#c.xxafdc150 Dxxincome0 cD.xxunemp#cD.xxunemp#c.trend
          cL.xxafdc15#cL.xxafdc15#c.trend cL.xxbeer#cL.xxbeer#c.trend
          c.xxprison0#c.xxprison0#c.trend c.xxbeer0#c.xxbeer0#c.trend
          c.Dxxincome0#c.trend c.Dxxincome0#c.Dxxincome0#c.trend
          c.Dxxbeer0#c.trend 87.year 89.year 90.year 91.year 92.year 93.year
          97.year
Also inc:  86b.year 88.year 94.year 95.year 96.year


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      heteroskedastic
Number of observations:                600
Exogenous (1):                         D.efaprop
High-dim controls (348):               prop0 c.prop0#c.prop0 Dprop0
                                       c.Dprop0#c.Dprop0 D.xxprison D.xxpolice
                                       D.xxunemp D.xxincome D.xxpover
                                       D.xxafdc15 D.xxgunlaw D.xxbeer
                                       cD.xxprison#cD.xxprison
                                       cD.xxprison#cD.xxpolice
                                       cD.xxprison#cD.xxunemp
                                       cD.xxprison#cD.xxincome
                                       cD.xxprison#cD.xxpover
                                       cD.xxprison#cD.xxafdc15
                                       cD.xxprison#cD.xxgunlaw
                                       cD.xxprison#cD.xxbeer
                                       cD.xxpolice#cD.xxpolice
                                       cD.xxpolice#cD.xxunemp
                                       cD.xxpolice#cD.xxincome
                                       cD.xxpolice#cD.xxpover
                                       cD.xxpolice#cD.xxafdc15
                                       cD.xxpolice#cD.xxgunlaw
                                       cD.xxpolice#cD.xxbeer
                                       cD.xxunemp#cD.xxunemp
                                       cD.xxunemp#cD.xxincome
                                       cD.xxunemp#cD.xxpover
                                       cD.xxunemp#cD.xxafdc15
                                       cD.xxunemp#cD.xxgunlaw
                                       cD.xxunemp#cD.xxbeer
                                       cD.xxincome#cD.xxincome
                                       cD.xxincome#cD.xxpover
                                       cD.xxincome#cD.xxafdc15
                                       cD.xxincome#cD.xxgunlaw
                                       cD.xxincome#cD.xxbeer
                                       cD.xxpover#cD.xxpover
                                       cD.xxpover#cD.xxafdc15
                                       cD.xxpover#cD.xxgunlaw
                                       cD.xxpover#cD.xxbeer
                                       cD.xxafdc15#cD.xxafdc15
                                       cD.xxafdc15#cD.xxgunlaw
                                       cD.xxafdc15#cD.xxbeer
                                       cD.xxgunlaw#cD.xxgunlaw
                                       cD.xxgunlaw#cD.xxbeer
                                       cD.xxbeer#cD.xxbeer L.xxprison
                                       cL.xxprison#cL.xxprison L.xxpolice
                                       cL.xxpolice#cL.xxpolice L.xxunemp
                                       cL.xxunemp#cL.xxunemp L.xxincome
                                       cL.xxincome#cL.xxincome L.xxpover
                                       cL.xxpover#cL.xxpover L.xxafdc15
                                       cL.xxafdc15#cL.xxafdc15 L.xxgunlaw
                                       cL.xxgunlaw#cL.xxgunlaw L.xxbeer
                                       cL.xxbeer#cL.xxbeer Mxxprison
                                       c.Mxxprison#c.Mxxprison Mxxpolice
                                       c.Mxxpolice#c.Mxxpolice Mxxunemp
                                       c.Mxxunemp#c.Mxxunemp Mxxincome
                                       c.Mxxincome#c.Mxxincome Mxxpover
                                       c.Mxxpover#c.Mxxpover Mxxafdc15
                                       c.Mxxafdc15#c.Mxxafdc15 Mxxgunlaw
                                       c.Mxxgunlaw#c.Mxxgunlaw Mxxbeer
                                       c.Mxxbeer#c.Mxxbeer xxprison0
                                       c.xxprison0#c.xxprison0 xxpolice0
                                       c.xxpolice0#c.xxpolice0 xxunemp0
                                       c.xxunemp0#c.xxunemp0 xxincome0
                                       c.xxincome0#c.xxincome0 xxpover0
                                       c.xxpover0#c.xxpover0 xxafdc150
                                       c.xxafdc150#c.xxafdc150 xxgunlaw0
                                       c.xxgunlaw0#c.xxgunlaw0 xxbeer0
                                       c.xxbeer0#c.xxbeer0 Dxxprison0
                                       c.Dxxprison0#c.Dxxprison0 Dxxpolice0
                                       c.Dxxpolice0#c.Dxxpolice0 Dxxunemp0
                                       c.Dxxunemp0#c.Dxxunemp0 Dxxincome0
                                       c.Dxxincome0#c.Dxxincome0 Dxxpover0
                                       c.Dxxpover0#c.Dxxpover0 Dxxafdc150
                                       c.Dxxafdc150#c.Dxxafdc150 Dxxgunlaw0
                                       c.Dxxgunlaw0#c.Dxxgunlaw0 Dxxbeer0
                                       c.Dxxbeer0#c.Dxxbeer0 c.prop0#c.trend
                                       c.prop0#c.trend#c.trend
                                       c.prop0#c.prop0#c.trend
                                       c.prop0#c.prop0#c.trend#c.trend
                                       c.Dprop0#c.trend
                                       c.Dprop0#c.trend#c.trend
                                       c.Dprop0#c.Dprop0#c.trend
                                       c.Dprop0#c.Dprop0#c.trend#c.trend
                                       cD.xxprison#c.trend
                                       cD.xxprison#c.trend#c.trend
                                       cD.xxpolice#c.trend
                                       cD.xxpolice#c.trend#c.trend
                                       cD.xxunemp#c.trend
                                       cD.xxunemp#c.trend#c.trend
                                       cD.xxincome#c.trend
                                       cD.xxincome#c.trend#c.trend
                                       cD.xxpover#c.trend
                                       cD.xxpover#c.trend#c.trend
                                       cD.xxafdc15#c.trend
                                       cD.xxafdc15#c.trend#c.trend
                                       cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#c.trend#c.trend
                                       cD.xxbeer#c.trend
                                       cD.xxbeer#c.trend#c.trend
                                       cD.xxprison#cD.xxprison#c.trend
                                       cD.xxprison#cD.xxprison#c.trend#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend#c.trend
                                       cD.xxprison#cD.xxincome#c.trend
                                       cD.xxprison#cD.xxincome#c.trend#c.trend
                                       cD.xxprison#cD.xxpover#c.trend
                                       cD.xxprison#cD.xxpover#c.trend#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend#c.trend
                                       cD.xxincome#cD.xxincome#c.trend
                                       cD.xxincome#cD.xxincome#c.trend#c.trend
                                       cD.xxincome#cD.xxpover#c.trend
                                       cD.xxincome#cD.xxpover#c.trend#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend#c.trend
                                       cD.xxpover#cD.xxpover#c.trend
                                       cD.xxpover#cD.xxpover#c.trend#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend#c.trend
                                       cL.xxprison#c.trend
                                       cL.xxprison#c.trend#c.trend
                                       cL.xxprison#cL.xxprison#c.trend
                                       cL.xxprison#cL.xxprison#c.trend#c.trend
                                       cL.xxpolice#c.trend
                                       cL.xxpolice#c.trend#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend#c.trend
                                       cL.xxunemp#c.trend
                                       cL.xxunemp#c.trend#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend#c.trend
                                       cL.xxincome#c.trend
                                       cL.xxincome#c.trend#c.trend
                                       cL.xxincome#cL.xxincome#c.trend
                                       cL.xxincome#cL.xxincome#c.trend#c.trend
                                       cL.xxpover#c.trend
                                       cL.xxpover#c.trend#c.trend
                                       cL.xxpover#cL.xxpover#c.trend
                                       cL.xxpover#cL.xxpover#c.trend#c.trend
                                       cL.xxafdc15#c.trend
                                       cL.xxafdc15#c.trend#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend#c.trend
                                       cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#c.trend#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend#c.trend
                                       cL.xxbeer#c.trend
                                       cL.xxbeer#c.trend#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend#c.trend
                                       c.Mxxprison#c.trend
                                       c.Mxxprison#c.trend#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend#c.trend
                                       c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.trend#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend#c.trend
                                       c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.trend#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend#c.trend
                                       c.Mxxincome#c.trend
                                       c.Mxxincome#c.trend#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend#c.trend
                                       c.Mxxpover#c.trend
                                       c.Mxxpover#c.trend#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend#c.trend
                                       c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.trend#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend#c.trend
                                       c.xxprison0#c.trend
                                       c.xxprison0#c.trend#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.xxprison0#c.xxprison0#c.trend#c.trend
                                       c.xxpolice0#c.trend
                                       c.xxpolice0#c.trend#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend#c.trend
                                       c.xxunemp0#c.trend
                                       c.xxunemp0#c.trend#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend#c.trend
                                       c.xxincome0#c.trend
                                       c.xxincome0#c.trend#c.trend
                                       c.xxincome0#c.xxincome0#c.trend
                                       c.xxincome0#c.xxincome0#c.trend#c.trend
                                       c.xxpover0#c.trend
                                       c.xxpover0#c.trend#c.trend
                                       c.xxpover0#c.xxpover0#c.trend
                                       c.xxpover0#c.xxpover0#c.trend#c.trend
                                       c.xxafdc150#c.trend
                                       c.xxafdc150#c.trend#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend#c.trend
                                       c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.trend#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend#c.trend
                                       c.xxbeer0#c.trend
                                       c.xxbeer0#c.trend#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend#c.trend
                                       c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.trend#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend#c.trend
                                       c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.trend#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend#c.trend
                                       c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.trend#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend#c.trend
                                       c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.trend#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend#c.trend
                                       86b.year 87.year 88.year 89.year 90.year
                                       91.year 92.year 93.year 94.year 95.year
                                       96.year 97.year
Selected controls (28):                prop0 L.xxprison
                                       cL.xxpolice#cL.xxpolice
                                       c.Mxxpolice#c.Mxxpolice
                                       c.xxafdc150#c.xxafdc150 Dxxincome0
                                       c.prop0#c.trend#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend
                                       c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend
                                       c.Dxxbeer0#c.trend 86b.year 87.year
                                       88.year 89.year 90.year 91.year 92.year
                                       93.year 94.year 95.year 96.year 97.year
  of which, amelioration set (12):     86b.year 87.year 88.year 89.year
                                       90.year 91.year 92.year 93.year 94.year
                                       95.year 96.year 97.year

Structural equation:

OLS using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.1379155    .0367491     -3.75    0.000     -.2099425    -.0658885
-------------+----------------------------------------------------------------

OLS using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.1441071    .0355861     -4.05    0.000     -.2138545    -.0743597
-------------+----------------------------------------------------------------

OLS with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.1756949    .0389296     -4.51    0.000     -.2519955    -.0993943
             |
       prop0 |    .0878677    .0312885      2.81    0.005      .0265434     .1491921
             |
    xxprison |
         L1. |    .0078451     .006634      1.18    0.237     -.0051574     .0208476
             |
 cL.xxpolice#|
 cL.xxpolice |   -.0273387    .0146812     -1.86    0.063     -.0561134     .0014359
             |
 c.Mxxpolice#|
 c.Mxxpolice |    .0355071    .0153168      2.32    0.020      .0054867     .0655275
             |
 c.xxafdc150#|
 c.xxafdc150 |    .0005503    .0095235      0.06    0.954     -.0181153      .019216
             |
  Dxxincome0 |    45.52114    21.45892      2.12    0.034      3.462421     87.57985
             |
     c.prop0#|
     c.trend#|
     c.trend |   -.2163969    .0600685     -3.60    0.000      -.334129    -.0986648
             |
  cD.xxunemp#|
  cD.xxunemp#|
     c.trend |    64.26815    27.35703      2.35    0.019      10.64937     117.8869
             |
 cL.xxafdc15#|
 cL.xxafdc15#|
     c.trend |    .0191785    .0207664      0.92    0.356     -.0215229       .05988
             |
   cL.xxbeer#|
   cL.xxbeer#|
     c.trend |    .7724273    .4826504      1.60    0.110     -.1735501     1.718405
             |
 c.xxprison0#|
 c.xxprison0#|
     c.trend |    .0191752    .0122409      1.57    0.117     -.0048165     .0431669
             |
 c.xxafdc150#|
 c.xxafdc150#|
     c.trend#|
     c.trend |   -.0106037    .0145224     -0.73    0.465     -.0390671     .0178597
             |
   c.xxbeer0#|
   c.xxbeer0#|
     c.trend |   -.7653389    .3911464     -1.96    0.050     -1.531972      .001294
             |
          c. |
  Dxxincome0#|
     c.trend |   -13.15545    32.80894     -0.40    0.688     -77.45979     51.14888
             |
          c. |
  Dxxincome0#|
          c. |
  Dxxincome0#|
     c.trend |   -41148.27    42664.19     -0.96    0.335     -124768.5        42472
             |
  c.Dxxbeer0#|
     c.trend |   -.8481733     .630559     -1.35    0.179     -2.084046     .3876997
             |
        year |
         87  |   -.0061293    .0078926     -0.78    0.437     -.0215986       .00934
         88  |   -.0214414    .0076168     -2.82    0.005     -.0363701    -.0065127
         89  |   -.0015594    .0082539     -0.19    0.850     -.0177367     .0146178
         90  |    .0063722     .009802      0.65    0.516     -.0128393     .0255837
         91  |    .0103287      .01164      0.89    0.375     -.0124852     .0331426
         92  |   -.0366405    .0116247     -3.15    0.002     -.0594244    -.0138565
         93  |   -.0235036    .0129463     -1.82    0.069      -.048878     .0018707
         94  |      .00626    .0132467      0.47    0.637     -.0197031     .0322231
         95  |    .0229921    .0148495      1.55    0.122     -.0061124     .0520966
         96  |   -.0179148    .0151145     -1.19    0.236     -.0475386     .0117089
         97  |     -.00432    .0167742     -0.26    0.797     -.0371968     .0285568
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    D.efaprop
------------------------------------------------------------------------------
Options: aset(i.year) cluster(statenum)
1.  (PDS/CHS) Selecting HD controls for dep var D.lpc_prop...
Selected:  Mxxincome xxincome0 c.prop0#c.trend cL.xxunemp#cL.xxunemp#c.trend
          c.Mxxpolice#c.Mxxpolice#c.trend c.xxafdc150#c.trend
          c.xxafdc150#c.xxafdc150#c.trend 92.year
Also inc:  86b.year 87.year 88.year 89.year 90.year 91.year 93.year 94.year
          95.year 96.year 97.year
2.  (PDS/CHS) Selecting HD controls for exog regressor D.efaprop...
Selected:  prop0 cD.xxprison#cD.xxbeer L.xxincome cD.xxunemp#cD.xxunemp#c.trend
          cD.xxunemp#cD.xxincome#c.trend#c.trend cD.xxgunlaw#cD.xxbeer#c.trend
          c.Dxxincome0#c.trend 87.year 90.year 91.year 92.year 93.year 94.year
          95.year
Also inc:  86b.year 88.year 89.year 96.year 97.year


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      cluster-lasso
Number of observations:                600
Number of clusters:                     50
Exogenous (1):                         D.efaprop
High-dim controls (348):               prop0 c.prop0#c.prop0 Dprop0
                                       c.Dprop0#c.Dprop0 D.xxprison D.xxpolice
                                       D.xxunemp D.xxincome D.xxpover
                                       D.xxafdc15 D.xxgunlaw D.xxbeer
                                       cD.xxprison#cD.xxprison
                                       cD.xxprison#cD.xxpolice
                                       cD.xxprison#cD.xxunemp
                                       cD.xxprison#cD.xxincome
                                       cD.xxprison#cD.xxpover
                                       cD.xxprison#cD.xxafdc15
                                       cD.xxprison#cD.xxgunlaw
                                       cD.xxprison#cD.xxbeer
                                       cD.xxpolice#cD.xxpolice
                                       cD.xxpolice#cD.xxunemp
                                       cD.xxpolice#cD.xxincome
                                       cD.xxpolice#cD.xxpover
                                       cD.xxpolice#cD.xxafdc15
                                       cD.xxpolice#cD.xxgunlaw
                                       cD.xxpolice#cD.xxbeer
                                       cD.xxunemp#cD.xxunemp
                                       cD.xxunemp#cD.xxincome
                                       cD.xxunemp#cD.xxpover
                                       cD.xxunemp#cD.xxafdc15
                                       cD.xxunemp#cD.xxgunlaw
                                       cD.xxunemp#cD.xxbeer
                                       cD.xxincome#cD.xxincome
                                       cD.xxincome#cD.xxpover
                                       cD.xxincome#cD.xxafdc15
                                       cD.xxincome#cD.xxgunlaw
                                       cD.xxincome#cD.xxbeer
                                       cD.xxpover#cD.xxpover
                                       cD.xxpover#cD.xxafdc15
                                       cD.xxpover#cD.xxgunlaw
                                       cD.xxpover#cD.xxbeer
                                       cD.xxafdc15#cD.xxafdc15
                                       cD.xxafdc15#cD.xxgunlaw
                                       cD.xxafdc15#cD.xxbeer
                                       cD.xxgunlaw#cD.xxgunlaw
                                       cD.xxgunlaw#cD.xxbeer
                                       cD.xxbeer#cD.xxbeer L.xxprison
                                       cL.xxprison#cL.xxprison L.xxpolice
                                       cL.xxpolice#cL.xxpolice L.xxunemp
                                       cL.xxunemp#cL.xxunemp L.xxincome
                                       cL.xxincome#cL.xxincome L.xxpover
                                       cL.xxpover#cL.xxpover L.xxafdc15
                                       cL.xxafdc15#cL.xxafdc15 L.xxgunlaw
                                       cL.xxgunlaw#cL.xxgunlaw L.xxbeer
                                       cL.xxbeer#cL.xxbeer Mxxprison
                                       c.Mxxprison#c.Mxxprison Mxxpolice
                                       c.Mxxpolice#c.Mxxpolice Mxxunemp
                                       c.Mxxunemp#c.Mxxunemp Mxxincome
                                       c.Mxxincome#c.Mxxincome Mxxpover
                                       c.Mxxpover#c.Mxxpover Mxxafdc15
                                       c.Mxxafdc15#c.Mxxafdc15 Mxxgunlaw
                                       c.Mxxgunlaw#c.Mxxgunlaw Mxxbeer
                                       c.Mxxbeer#c.Mxxbeer xxprison0
                                       c.xxprison0#c.xxprison0 xxpolice0
                                       c.xxpolice0#c.xxpolice0 xxunemp0
                                       c.xxunemp0#c.xxunemp0 xxincome0
                                       c.xxincome0#c.xxincome0 xxpover0
                                       c.xxpover0#c.xxpover0 xxafdc150
                                       c.xxafdc150#c.xxafdc150 xxgunlaw0
                                       c.xxgunlaw0#c.xxgunlaw0 xxbeer0
                                       c.xxbeer0#c.xxbeer0 Dxxprison0
                                       c.Dxxprison0#c.Dxxprison0 Dxxpolice0
                                       c.Dxxpolice0#c.Dxxpolice0 Dxxunemp0
                                       c.Dxxunemp0#c.Dxxunemp0 Dxxincome0
                                       c.Dxxincome0#c.Dxxincome0 Dxxpover0
                                       c.Dxxpover0#c.Dxxpover0 Dxxafdc150
                                       c.Dxxafdc150#c.Dxxafdc150 Dxxgunlaw0
                                       c.Dxxgunlaw0#c.Dxxgunlaw0 Dxxbeer0
                                       c.Dxxbeer0#c.Dxxbeer0 c.prop0#c.trend
                                       c.prop0#c.trend#c.trend
                                       c.prop0#c.prop0#c.trend
                                       c.prop0#c.prop0#c.trend#c.trend
                                       c.Dprop0#c.trend
                                       c.Dprop0#c.trend#c.trend
                                       c.Dprop0#c.Dprop0#c.trend
                                       c.Dprop0#c.Dprop0#c.trend#c.trend
                                       cD.xxprison#c.trend
                                       cD.xxprison#c.trend#c.trend
                                       cD.xxpolice#c.trend
                                       cD.xxpolice#c.trend#c.trend
                                       cD.xxunemp#c.trend
                                       cD.xxunemp#c.trend#c.trend
                                       cD.xxincome#c.trend
                                       cD.xxincome#c.trend#c.trend
                                       cD.xxpover#c.trend
                                       cD.xxpover#c.trend#c.trend
                                       cD.xxafdc15#c.trend
                                       cD.xxafdc15#c.trend#c.trend
                                       cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#c.trend#c.trend
                                       cD.xxbeer#c.trend
                                       cD.xxbeer#c.trend#c.trend
                                       cD.xxprison#cD.xxprison#c.trend
                                       cD.xxprison#cD.xxprison#c.trend#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend#c.trend
                                       cD.xxprison#cD.xxincome#c.trend
                                       cD.xxprison#cD.xxincome#c.trend#c.trend
                                       cD.xxprison#cD.xxpover#c.trend
                                       cD.xxprison#cD.xxpover#c.trend#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend#c.trend
                                       cD.xxincome#cD.xxincome#c.trend
                                       cD.xxincome#cD.xxincome#c.trend#c.trend
                                       cD.xxincome#cD.xxpover#c.trend
                                       cD.xxincome#cD.xxpover#c.trend#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend#c.trend
                                       cD.xxpover#cD.xxpover#c.trend
                                       cD.xxpover#cD.xxpover#c.trend#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend#c.trend
                                       cL.xxprison#c.trend
                                       cL.xxprison#c.trend#c.trend
                                       cL.xxprison#cL.xxprison#c.trend
                                       cL.xxprison#cL.xxprison#c.trend#c.trend
                                       cL.xxpolice#c.trend
                                       cL.xxpolice#c.trend#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend#c.trend
                                       cL.xxunemp#c.trend
                                       cL.xxunemp#c.trend#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend#c.trend
                                       cL.xxincome#c.trend
                                       cL.xxincome#c.trend#c.trend
                                       cL.xxincome#cL.xxincome#c.trend
                                       cL.xxincome#cL.xxincome#c.trend#c.trend
                                       cL.xxpover#c.trend
                                       cL.xxpover#c.trend#c.trend
                                       cL.xxpover#cL.xxpover#c.trend
                                       cL.xxpover#cL.xxpover#c.trend#c.trend
                                       cL.xxafdc15#c.trend
                                       cL.xxafdc15#c.trend#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend#c.trend
                                       cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#c.trend#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend#c.trend
                                       cL.xxbeer#c.trend
                                       cL.xxbeer#c.trend#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend#c.trend
                                       c.Mxxprison#c.trend
                                       c.Mxxprison#c.trend#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend#c.trend
                                       c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.trend#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend#c.trend
                                       c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.trend#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend#c.trend
                                       c.Mxxincome#c.trend
                                       c.Mxxincome#c.trend#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend#c.trend
                                       c.Mxxpover#c.trend
                                       c.Mxxpover#c.trend#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend#c.trend
                                       c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.trend#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend#c.trend
                                       c.xxprison0#c.trend
                                       c.xxprison0#c.trend#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.xxprison0#c.xxprison0#c.trend#c.trend
                                       c.xxpolice0#c.trend
                                       c.xxpolice0#c.trend#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend#c.trend
                                       c.xxunemp0#c.trend
                                       c.xxunemp0#c.trend#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend#c.trend
                                       c.xxincome0#c.trend
                                       c.xxincome0#c.trend#c.trend
                                       c.xxincome0#c.xxincome0#c.trend
                                       c.xxincome0#c.xxincome0#c.trend#c.trend
                                       c.xxpover0#c.trend
                                       c.xxpover0#c.trend#c.trend
                                       c.xxpover0#c.xxpover0#c.trend
                                       c.xxpover0#c.xxpover0#c.trend#c.trend
                                       c.xxafdc150#c.trend
                                       c.xxafdc150#c.trend#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend#c.trend
                                       c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.trend#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend#c.trend
                                       c.xxbeer0#c.trend
                                       c.xxbeer0#c.trend#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend#c.trend
                                       c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.trend#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend#c.trend
                                       c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.trend#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend#c.trend
                                       c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.trend#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend#c.trend
                                       c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.trend#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend#c.trend
                                       86b.year 87.year 88.year 89.year 90.year
                                       91.year 92.year 93.year 94.year 95.year
                                       96.year 97.year
Selected controls (26):                prop0 cD.xxprison#cD.xxbeer L.xxincome
                                       Mxxincome xxincome0 c.prop0#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend
                                       c.xxafdc150#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend
                                       c.Dxxincome0#c.trend 86b.year 87.year
                                       88.year 89.year 90.year 91.year 92.year
                                       93.year 94.year 95.year 96.year 97.year
  of which, amelioration set (12):     86b.year 87.year 88.year 89.year
                                       90.year 91.year 92.year 93.year 94.year
                                       95.year 96.year 97.year
Unpenalized controls (1):              _cons

Structural equation:

OLS using CHS lasso-orthogonalized vars
(Std. Err. adjusted for 50 clusters in statenum)
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.1089538    .0375056     -2.90    0.004     -.1824634    -.0354441
-------------+----------------------------------------------------------------

OLS using CHS post-lasso-orthogonalized vars
(Std. Err. adjusted for 50 clusters in statenum)
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.0812192    .0462104     -1.76    0.079       -.17179     .0093516
-------------+----------------------------------------------------------------

OLS with PDS-selected variables and full regressor set
(Std. Err. adjusted for 50 clusters in statenum)
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |     -.09251    .0456967     -2.02    0.043     -.1820739    -.0029461
             |
       prop0 |    .0681508    .0364219      1.87    0.061     -.0032348     .1395364
             |
 cD.xxprison#|
   cD.xxbeer |    -.213217    2.513952     -0.08    0.932     -5.140473     4.714039
             |
    xxincome |
         L1. |    29.84207    8.963678      3.33    0.001      12.27358     47.41056
             |
   Mxxincome |     -11.289    10.37651     -1.09    0.277     -31.62658     9.048588
   xxincome0 |    -18.9608    4.762599     -3.98    0.000     -28.29532    -9.626274
             |
     c.prop0#|
     c.trend |   -.0966492      .05907     -1.64    0.102     -.2124243     .0191259
             |
  cD.xxunemp#|
  cD.xxunemp#|
     c.trend |    88.87148    26.67365      3.33    0.001      36.59209     141.1509
             |
  cD.xxunemp#|
 cD.xxincome#|
     c.trend#|
     c.trend |    3519.228    2810.658      1.25    0.211      -1989.56     9028.016
             |
 cD.xxgunlaw#|
   cD.xxbeer#|
     c.trend |   -.0435517    2.268508     -0.02    0.985     -4.489745     4.402642
             |
  cL.xxunemp#|
  cL.xxunemp#|
     c.trend |   -2.800648    1.290272     -2.17    0.030     -5.329534    -.2717619
             |
 c.Mxxpolice#|
 c.Mxxpolice#|
     c.trend |   -.0022476    .0084517     -0.27    0.790     -.0188126     .0143175
             |
 c.xxafdc150#|
     c.trend |   -.0025678    .0440245     -0.06    0.953     -.0888542     .0837185
             |
 c.xxafdc150#|
 c.xxafdc150#|
     c.trend |   -.0189278    .0286736     -0.66    0.509      -.075127     .0372714
             |
          c. |
  Dxxincome0#|
     c.trend |   -29.49446    23.87461     -1.24    0.217     -76.28783     17.29892
             |
        year |
         87  |   -.0222934    .0088506     -2.52    0.012     -.0396403    -.0049465
         88  |   -.0394781    .0095354     -4.14    0.000     -.0581671    -.0207891
         89  |   -.0265678    .0133001     -2.00    0.046     -.0526355    -.0005002
         90  |   -.0257258    .0176849     -1.45    0.146     -.0603876     .0089361
         91  |   -.0225386    .0190857     -1.18    0.238     -.0599458     .0148686
         92  |   -.0662145    .0200385     -3.30    0.001     -.1054893    -.0269397
         93  |   -.0566603    .0230567     -2.46    0.014     -.1018506    -.0114701
         94  |   -.0260171    .0253288     -1.03    0.304     -.0756607     .0236265
         95  |   -.0193705    .0287688     -0.67    0.501     -.0757563     .0370152
         96  |   -.0767345    .0322089     -2.38    0.017     -.1398628    -.0136062
         97  |   -.0720818    .0340447     -2.12    0.034     -.1388082    -.0053554
             |
       _cons |     .091145    .1643923      0.55    0.579      -.231058      .413348
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    D.efaprop
------------------------------------------------------------------------------
Options: aset(i.year) cluster(statenum) fe
Fixed effects transformation...
1.  (PDS/CHS) Selecting HD controls for dep var D.lpc_prop...
Selected:  L.xxprison cL.xxafdc15#cL.xxafdc15 L.xxbeer
          cL.xxunemp#cL.xxunemp#c.trend
          c.Dxxincome0#c.Dxxincome0#c.trend#c.trend
Also inc:  86b.year 87.year 88.year 89.year 90.year 91.year 92.year 93.year
          94.year 95.year 96.year 97.year
2.  (PDS/CHS) Selecting HD controls for exog regressor D.efaprop...
Selected:  cD.xxincome#cD.xxincome cD.xxunemp#cD.xxincome#c.trend#c.trend
          cD.xxincome#cD.xxgunlaw#c.trend#c.trend cL.xxbeer#cL.xxbeer#c.trend
          87.year 89.year 90.year 91.year 92.year 93.year 94.year
Also inc:  86b.year 88.year 95.year 96.year 97.year


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      cluster-lasso
Number of observations:                600
Number of clusters:                     50
Number of fixed effects:                50
Exogenous (1):                         D.efaprop
High-dim controls (348):               prop0 c.prop0#c.prop0 Dprop0
                                       c.Dprop0#c.Dprop0 D.xxprison D.xxpolice
                                       D.xxunemp D.xxincome D.xxpover
                                       D.xxafdc15 D.xxgunlaw D.xxbeer
                                       cD.xxprison#cD.xxprison
                                       cD.xxprison#cD.xxpolice
                                       cD.xxprison#cD.xxunemp
                                       cD.xxprison#cD.xxincome
                                       cD.xxprison#cD.xxpover
                                       cD.xxprison#cD.xxafdc15
                                       cD.xxprison#cD.xxgunlaw
                                       cD.xxprison#cD.xxbeer
                                       cD.xxpolice#cD.xxpolice
                                       cD.xxpolice#cD.xxunemp
                                       cD.xxpolice#cD.xxincome
                                       cD.xxpolice#cD.xxpover
                                       cD.xxpolice#cD.xxafdc15
                                       cD.xxpolice#cD.xxgunlaw
                                       cD.xxpolice#cD.xxbeer
                                       cD.xxunemp#cD.xxunemp
                                       cD.xxunemp#cD.xxincome
                                       cD.xxunemp#cD.xxpover
                                       cD.xxunemp#cD.xxafdc15
                                       cD.xxunemp#cD.xxgunlaw
                                       cD.xxunemp#cD.xxbeer
                                       cD.xxincome#cD.xxincome
                                       cD.xxincome#cD.xxpover
                                       cD.xxincome#cD.xxafdc15
                                       cD.xxincome#cD.xxgunlaw
                                       cD.xxincome#cD.xxbeer
                                       cD.xxpover#cD.xxpover
                                       cD.xxpover#cD.xxafdc15
                                       cD.xxpover#cD.xxgunlaw
                                       cD.xxpover#cD.xxbeer
                                       cD.xxafdc15#cD.xxafdc15
                                       cD.xxafdc15#cD.xxgunlaw
                                       cD.xxafdc15#cD.xxbeer
                                       cD.xxgunlaw#cD.xxgunlaw
                                       cD.xxgunlaw#cD.xxbeer
                                       cD.xxbeer#cD.xxbeer L.xxprison
                                       cL.xxprison#cL.xxprison L.xxpolice
                                       cL.xxpolice#cL.xxpolice L.xxunemp
                                       cL.xxunemp#cL.xxunemp L.xxincome
                                       cL.xxincome#cL.xxincome L.xxpover
                                       cL.xxpover#cL.xxpover L.xxafdc15
                                       cL.xxafdc15#cL.xxafdc15 L.xxgunlaw
                                       cL.xxgunlaw#cL.xxgunlaw L.xxbeer
                                       cL.xxbeer#cL.xxbeer Mxxprison
                                       c.Mxxprison#c.Mxxprison Mxxpolice
                                       c.Mxxpolice#c.Mxxpolice Mxxunemp
                                       c.Mxxunemp#c.Mxxunemp Mxxincome
                                       c.Mxxincome#c.Mxxincome Mxxpover
                                       c.Mxxpover#c.Mxxpover Mxxafdc15
                                       c.Mxxafdc15#c.Mxxafdc15 Mxxgunlaw
                                       c.Mxxgunlaw#c.Mxxgunlaw Mxxbeer
                                       c.Mxxbeer#c.Mxxbeer xxprison0
                                       c.xxprison0#c.xxprison0 xxpolice0
                                       c.xxpolice0#c.xxpolice0 xxunemp0
                                       c.xxunemp0#c.xxunemp0 xxincome0
                                       c.xxincome0#c.xxincome0 xxpover0
                                       c.xxpover0#c.xxpover0 xxafdc150
                                       c.xxafdc150#c.xxafdc150 xxgunlaw0
                                       c.xxgunlaw0#c.xxgunlaw0 xxbeer0
                                       c.xxbeer0#c.xxbeer0 Dxxprison0
                                       c.Dxxprison0#c.Dxxprison0 Dxxpolice0
                                       c.Dxxpolice0#c.Dxxpolice0 Dxxunemp0
                                       c.Dxxunemp0#c.Dxxunemp0 Dxxincome0
                                       c.Dxxincome0#c.Dxxincome0 Dxxpover0
                                       c.Dxxpover0#c.Dxxpover0 Dxxafdc150
                                       c.Dxxafdc150#c.Dxxafdc150 Dxxgunlaw0
                                       c.Dxxgunlaw0#c.Dxxgunlaw0 Dxxbeer0
                                       c.Dxxbeer0#c.Dxxbeer0 c.prop0#c.trend
                                       c.prop0#c.trend#c.trend
                                       c.prop0#c.prop0#c.trend
                                       c.prop0#c.prop0#c.trend#c.trend
                                       c.Dprop0#c.trend
                                       c.Dprop0#c.trend#c.trend
                                       c.Dprop0#c.Dprop0#c.trend
                                       c.Dprop0#c.Dprop0#c.trend#c.trend
                                       cD.xxprison#c.trend
                                       cD.xxprison#c.trend#c.trend
                                       cD.xxpolice#c.trend
                                       cD.xxpolice#c.trend#c.trend
                                       cD.xxunemp#c.trend
                                       cD.xxunemp#c.trend#c.trend
                                       cD.xxincome#c.trend
                                       cD.xxincome#c.trend#c.trend
                                       cD.xxpover#c.trend
                                       cD.xxpover#c.trend#c.trend
                                       cD.xxafdc15#c.trend
                                       cD.xxafdc15#c.trend#c.trend
                                       cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#c.trend#c.trend
                                       cD.xxbeer#c.trend
                                       cD.xxbeer#c.trend#c.trend
                                       cD.xxprison#cD.xxprison#c.trend
                                       cD.xxprison#cD.xxprison#c.trend#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend#c.trend
                                       cD.xxprison#cD.xxincome#c.trend
                                       cD.xxprison#cD.xxincome#c.trend#c.trend
                                       cD.xxprison#cD.xxpover#c.trend
                                       cD.xxprison#cD.xxpover#c.trend#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend#c.trend
                                       cD.xxincome#cD.xxincome#c.trend
                                       cD.xxincome#cD.xxincome#c.trend#c.trend
                                       cD.xxincome#cD.xxpover#c.trend
                                       cD.xxincome#cD.xxpover#c.trend#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend#c.trend
                                       cD.xxpover#cD.xxpover#c.trend
                                       cD.xxpover#cD.xxpover#c.trend#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend#c.trend
                                       cL.xxprison#c.trend
                                       cL.xxprison#c.trend#c.trend
                                       cL.xxprison#cL.xxprison#c.trend
                                       cL.xxprison#cL.xxprison#c.trend#c.trend
                                       cL.xxpolice#c.trend
                                       cL.xxpolice#c.trend#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend#c.trend
                                       cL.xxunemp#c.trend
                                       cL.xxunemp#c.trend#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend#c.trend
                                       cL.xxincome#c.trend
                                       cL.xxincome#c.trend#c.trend
                                       cL.xxincome#cL.xxincome#c.trend
                                       cL.xxincome#cL.xxincome#c.trend#c.trend
                                       cL.xxpover#c.trend
                                       cL.xxpover#c.trend#c.trend
                                       cL.xxpover#cL.xxpover#c.trend
                                       cL.xxpover#cL.xxpover#c.trend#c.trend
                                       cL.xxafdc15#c.trend
                                       cL.xxafdc15#c.trend#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend#c.trend
                                       cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#c.trend#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend#c.trend
                                       cL.xxbeer#c.trend
                                       cL.xxbeer#c.trend#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend#c.trend
                                       c.Mxxprison#c.trend
                                       c.Mxxprison#c.trend#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend#c.trend
                                       c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.trend#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend#c.trend
                                       c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.trend#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend#c.trend
                                       c.Mxxincome#c.trend
                                       c.Mxxincome#c.trend#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend#c.trend
                                       c.Mxxpover#c.trend
                                       c.Mxxpover#c.trend#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend#c.trend
                                       c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.trend#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend#c.trend
                                       c.xxprison0#c.trend
                                       c.xxprison0#c.trend#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.xxprison0#c.xxprison0#c.trend#c.trend
                                       c.xxpolice0#c.trend
                                       c.xxpolice0#c.trend#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend#c.trend
                                       c.xxunemp0#c.trend
                                       c.xxunemp0#c.trend#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend#c.trend
                                       c.xxincome0#c.trend
                                       c.xxincome0#c.trend#c.trend
                                       c.xxincome0#c.xxincome0#c.trend
                                       c.xxincome0#c.xxincome0#c.trend#c.trend
                                       c.xxpover0#c.trend
                                       c.xxpover0#c.trend#c.trend
                                       c.xxpover0#c.xxpover0#c.trend
                                       c.xxpover0#c.xxpover0#c.trend#c.trend
                                       c.xxafdc150#c.trend
                                       c.xxafdc150#c.trend#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend#c.trend
                                       c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.trend#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend#c.trend
                                       c.xxbeer0#c.trend
                                       c.xxbeer0#c.trend#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend#c.trend
                                       c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.trend#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend#c.trend
                                       c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.trend#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend#c.trend
                                       c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.trend#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend#c.trend
                                       c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.trend#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend#c.trend
                                       86b.year 87.year 88.year 89.year 90.year
                                       91.year 92.year 93.year 94.year 95.year
                                       96.year 97.year
Selected controls (21):                cD.xxincome#cD.xxincome L.xxprison
                                       cL.xxafdc15#cL.xxafdc15 L.xxbeer
                                       cD.xxunemp#cD.xxincome#c.trend#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend#c.trend
                                       86b.year 87.year 88.year 89.year 90.year
                                       91.year 92.year 93.year 94.year 95.year
                                       96.year 97.year
  of which, amelioration set (12):     86b.year 87.year 88.year 89.year
                                       90.year 91.year 92.year 93.year 94.year
                                       95.year 96.year 97.year

Structural equation (fixed effects, #groups=50):

OLS using CHS lasso-orthogonalized vars
(Std. Err. adjusted for 50 clusters in statenum)
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.0900702     .059069     -1.52    0.127     -.2058433      .025703
-------------+----------------------------------------------------------------

OLS using CHS post-lasso-orthogonalized vars
(Std. Err. adjusted for 50 clusters in statenum)
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.0525198    .0658428     -0.80    0.425     -.1815692     .0765297
-------------+----------------------------------------------------------------

OLS with PDS-selected variables and full regressor set
(Std. Err. adjusted for 50 clusters in statenum)
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.0539441    .0603449     -0.89    0.371      -.172218     .0643298
             |
 cD.xxincome#|
 cD.xxincome |   -58459.87     27497.9     -2.13    0.034     -112354.8    -4564.977
             |
    xxprison |
         L1. |   -.0023046    .0197134     -0.12    0.907     -.0409421     .0363329
             |
 cL.xxafdc15#|
 cL.xxafdc15 |    .0252871    .0106392      2.38    0.017      .0044347     .0461396
             |
      xxbeer |
         L1. |    .1508921    .1636813      0.92    0.357     -.1699174     .4717016
             |
  cD.xxunemp#|
 cD.xxincome#|
     c.trend#|
     c.trend |   -150.5244      3175.5     -0.05    0.962      -6374.39     6073.341
             |
 cD.xxincome#|
 cD.xxgunlaw#|
     c.trend#|
     c.trend |   -36.82332    63.06559     -0.58    0.559     -160.4296     86.78296
             |
  cL.xxunemp#|
  cL.xxunemp#|
     c.trend |   -6.818322    3.013377     -2.26    0.024     -12.72443    -.9122111
             |
   cL.xxbeer#|
   cL.xxbeer#|
     c.trend |     .609076     .332413      1.83    0.067     -.0424415     1.260593
             |
          c. |
  Dxxincome0#|
          c. |
  Dxxincome0#|
     c.trend#|
     c.trend |   -84812.14    52159.29     -1.63    0.104     -187042.5      17418.2
             |
        year |
         87  |   -.0246111    .0090742     -2.71    0.007     -.0423962     -.006826
         88  |   -.0416168    .0090774     -4.58    0.000     -.0594081    -.0238254
         89  |   -.0288543    .0093909     -3.07    0.002       -.04726    -.0104486
         90  |    -.028393    .0127361     -2.23    0.026     -.0533554    -.0034306
         91  |   -.0247627    .0148907     -1.66    0.096     -.0539479     .0044225
         92  |   -.0683384    .0172454     -3.96    0.000     -.1021388    -.0345381
         93  |   -.0556809    .0183814     -3.03    0.002     -.0917078    -.0196539
         94  |   -.0228592    .0174864     -1.31    0.191     -.0571318     .0114135
         95  |   -.0059622    .0200234     -0.30    0.766     -.0452074     .0332831
         96  |   -.0588694    .0215545     -2.73    0.006     -.1011154    -.0166234
         97  |   -.0502835    .0235444     -2.14    0.033     -.0964298    -.0041373
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    D.efaprop
------------------------------------------------------------------------------
Options: aset(i.year) cluster(statenum) nocons
1.  (PDS/CHS) Selecting HD controls for dep var D.lpc_prop...
Selected:  c.prop0#c.prop0#c.trend#c.trend
          cL.xxpolice#cL.xxpolice#c.trend#c.trend
          c.xxafdc150#c.xxafdc150#c.trend#c.trend
          c.Dxxincome0#c.Dxxincome0#c.trend#c.trend
Also inc:  86b.year 87.year 88.year 89.year 90.year 91.year 92.year 93.year
          94.year 95.year 96.year 97.year
2.  (PDS/CHS) Selecting HD controls for exog regressor D.efaprop...
Selected:  prop0 L.xxprison cL.xxpolice#cL.xxpolice cL.xxafdc15#cL.xxafdc15
          Dxxincome0 c.Dxxincome0#c.Dxxincome0 cD.xxprison#c.trend
          cD.xxprison#cD.xxprison#c.trend
          cD.xxprison#cD.xxincome#c.trend#c.trend cD.xxunemp#cD.xxunemp#c.trend
          c.xxbeer0#c.trend c.Dxxincome0#c.trend
          c.Dxxincome0#c.Dxxincome0#c.trend 89.year 90.year 91.year 92.year
          93.year 94.year 95.year
Also inc:  86b.year 87.year 88.year 96.year 97.year


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      cluster-lasso
Number of observations:                600
Number of clusters:                     50
Exogenous (1):                         D.efaprop
High-dim controls (348):               prop0 c.prop0#c.prop0 Dprop0
                                       c.Dprop0#c.Dprop0 D.xxprison D.xxpolice
                                       D.xxunemp D.xxincome D.xxpover
                                       D.xxafdc15 D.xxgunlaw D.xxbeer
                                       cD.xxprison#cD.xxprison
                                       cD.xxprison#cD.xxpolice
                                       cD.xxprison#cD.xxunemp
                                       cD.xxprison#cD.xxincome
                                       cD.xxprison#cD.xxpover
                                       cD.xxprison#cD.xxafdc15
                                       cD.xxprison#cD.xxgunlaw
                                       cD.xxprison#cD.xxbeer
                                       cD.xxpolice#cD.xxpolice
                                       cD.xxpolice#cD.xxunemp
                                       cD.xxpolice#cD.xxincome
                                       cD.xxpolice#cD.xxpover
                                       cD.xxpolice#cD.xxafdc15
                                       cD.xxpolice#cD.xxgunlaw
                                       cD.xxpolice#cD.xxbeer
                                       cD.xxunemp#cD.xxunemp
                                       cD.xxunemp#cD.xxincome
                                       cD.xxunemp#cD.xxpover
                                       cD.xxunemp#cD.xxafdc15
                                       cD.xxunemp#cD.xxgunlaw
                                       cD.xxunemp#cD.xxbeer
                                       cD.xxincome#cD.xxincome
                                       cD.xxincome#cD.xxpover
                                       cD.xxincome#cD.xxafdc15
                                       cD.xxincome#cD.xxgunlaw
                                       cD.xxincome#cD.xxbeer
                                       cD.xxpover#cD.xxpover
                                       cD.xxpover#cD.xxafdc15
                                       cD.xxpover#cD.xxgunlaw
                                       cD.xxpover#cD.xxbeer
                                       cD.xxafdc15#cD.xxafdc15
                                       cD.xxafdc15#cD.xxgunlaw
                                       cD.xxafdc15#cD.xxbeer
                                       cD.xxgunlaw#cD.xxgunlaw
                                       cD.xxgunlaw#cD.xxbeer
                                       cD.xxbeer#cD.xxbeer L.xxprison
                                       cL.xxprison#cL.xxprison L.xxpolice
                                       cL.xxpolice#cL.xxpolice L.xxunemp
                                       cL.xxunemp#cL.xxunemp L.xxincome
                                       cL.xxincome#cL.xxincome L.xxpover
                                       cL.xxpover#cL.xxpover L.xxafdc15
                                       cL.xxafdc15#cL.xxafdc15 L.xxgunlaw
                                       cL.xxgunlaw#cL.xxgunlaw L.xxbeer
                                       cL.xxbeer#cL.xxbeer Mxxprison
                                       c.Mxxprison#c.Mxxprison Mxxpolice
                                       c.Mxxpolice#c.Mxxpolice Mxxunemp
                                       c.Mxxunemp#c.Mxxunemp Mxxincome
                                       c.Mxxincome#c.Mxxincome Mxxpover
                                       c.Mxxpover#c.Mxxpover Mxxafdc15
                                       c.Mxxafdc15#c.Mxxafdc15 Mxxgunlaw
                                       c.Mxxgunlaw#c.Mxxgunlaw Mxxbeer
                                       c.Mxxbeer#c.Mxxbeer xxprison0
                                       c.xxprison0#c.xxprison0 xxpolice0
                                       c.xxpolice0#c.xxpolice0 xxunemp0
                                       c.xxunemp0#c.xxunemp0 xxincome0
                                       c.xxincome0#c.xxincome0 xxpover0
                                       c.xxpover0#c.xxpover0 xxafdc150
                                       c.xxafdc150#c.xxafdc150 xxgunlaw0
                                       c.xxgunlaw0#c.xxgunlaw0 xxbeer0
                                       c.xxbeer0#c.xxbeer0 Dxxprison0
                                       c.Dxxprison0#c.Dxxprison0 Dxxpolice0
                                       c.Dxxpolice0#c.Dxxpolice0 Dxxunemp0
                                       c.Dxxunemp0#c.Dxxunemp0 Dxxincome0
                                       c.Dxxincome0#c.Dxxincome0 Dxxpover0
                                       c.Dxxpover0#c.Dxxpover0 Dxxafdc150
                                       c.Dxxafdc150#c.Dxxafdc150 Dxxgunlaw0
                                       c.Dxxgunlaw0#c.Dxxgunlaw0 Dxxbeer0
                                       c.Dxxbeer0#c.Dxxbeer0 c.prop0#c.trend
                                       c.prop0#c.trend#c.trend
                                       c.prop0#c.prop0#c.trend
                                       c.prop0#c.prop0#c.trend#c.trend
                                       c.Dprop0#c.trend
                                       c.Dprop0#c.trend#c.trend
                                       c.Dprop0#c.Dprop0#c.trend
                                       c.Dprop0#c.Dprop0#c.trend#c.trend
                                       cD.xxprison#c.trend
                                       cD.xxprison#c.trend#c.trend
                                       cD.xxpolice#c.trend
                                       cD.xxpolice#c.trend#c.trend
                                       cD.xxunemp#c.trend
                                       cD.xxunemp#c.trend#c.trend
                                       cD.xxincome#c.trend
                                       cD.xxincome#c.trend#c.trend
                                       cD.xxpover#c.trend
                                       cD.xxpover#c.trend#c.trend
                                       cD.xxafdc15#c.trend
                                       cD.xxafdc15#c.trend#c.trend
                                       cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#c.trend#c.trend
                                       cD.xxbeer#c.trend
                                       cD.xxbeer#c.trend#c.trend
                                       cD.xxprison#cD.xxprison#c.trend
                                       cD.xxprison#cD.xxprison#c.trend#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend#c.trend
                                       cD.xxprison#cD.xxincome#c.trend
                                       cD.xxprison#cD.xxincome#c.trend#c.trend
                                       cD.xxprison#cD.xxpover#c.trend
                                       cD.xxprison#cD.xxpover#c.trend#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend#c.trend
                                       cD.xxincome#cD.xxincome#c.trend
                                       cD.xxincome#cD.xxincome#c.trend#c.trend
                                       cD.xxincome#cD.xxpover#c.trend
                                       cD.xxincome#cD.xxpover#c.trend#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend#c.trend
                                       cD.xxpover#cD.xxpover#c.trend
                                       cD.xxpover#cD.xxpover#c.trend#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend#c.trend
                                       cL.xxprison#c.trend
                                       cL.xxprison#c.trend#c.trend
                                       cL.xxprison#cL.xxprison#c.trend
                                       cL.xxprison#cL.xxprison#c.trend#c.trend
                                       cL.xxpolice#c.trend
                                       cL.xxpolice#c.trend#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend#c.trend
                                       cL.xxunemp#c.trend
                                       cL.xxunemp#c.trend#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend#c.trend
                                       cL.xxincome#c.trend
                                       cL.xxincome#c.trend#c.trend
                                       cL.xxincome#cL.xxincome#c.trend
                                       cL.xxincome#cL.xxincome#c.trend#c.trend
                                       cL.xxpover#c.trend
                                       cL.xxpover#c.trend#c.trend
                                       cL.xxpover#cL.xxpover#c.trend
                                       cL.xxpover#cL.xxpover#c.trend#c.trend
                                       cL.xxafdc15#c.trend
                                       cL.xxafdc15#c.trend#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend#c.trend
                                       cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#c.trend#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend#c.trend
                                       cL.xxbeer#c.trend
                                       cL.xxbeer#c.trend#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend#c.trend
                                       c.Mxxprison#c.trend
                                       c.Mxxprison#c.trend#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend#c.trend
                                       c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.trend#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend#c.trend
                                       c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.trend#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend#c.trend
                                       c.Mxxincome#c.trend
                                       c.Mxxincome#c.trend#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend#c.trend
                                       c.Mxxpover#c.trend
                                       c.Mxxpover#c.trend#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend#c.trend
                                       c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.trend#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend#c.trend
                                       c.xxprison0#c.trend
                                       c.xxprison0#c.trend#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.xxprison0#c.xxprison0#c.trend#c.trend
                                       c.xxpolice0#c.trend
                                       c.xxpolice0#c.trend#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend#c.trend
                                       c.xxunemp0#c.trend
                                       c.xxunemp0#c.trend#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend#c.trend
                                       c.xxincome0#c.trend
                                       c.xxincome0#c.trend#c.trend
                                       c.xxincome0#c.xxincome0#c.trend
                                       c.xxincome0#c.xxincome0#c.trend#c.trend
                                       c.xxpover0#c.trend
                                       c.xxpover0#c.trend#c.trend
                                       c.xxpover0#c.xxpover0#c.trend
                                       c.xxpover0#c.xxpover0#c.trend#c.trend
                                       c.xxafdc150#c.trend
                                       c.xxafdc150#c.trend#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend#c.trend
                                       c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.trend#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend#c.trend
                                       c.xxbeer0#c.trend
                                       c.xxbeer0#c.trend#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend#c.trend
                                       c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.trend#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend#c.trend
                                       c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.trend#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend#c.trend
                                       c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.trend#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend#c.trend
                                       c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.trend#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend#c.trend
                                       86b.year 87.year 88.year 89.year 90.year
                                       91.year 92.year 93.year 94.year 95.year
                                       96.year 97.year
Selected controls (29):                prop0 L.xxprison
                                       cL.xxpolice#cL.xxpolice
                                       cL.xxafdc15#cL.xxafdc15 Dxxincome0
                                       c.Dxxincome0#c.Dxxincome0
                                       c.prop0#c.prop0#c.trend#c.trend
                                       cD.xxprison#c.trend
                                       cD.xxprison#cD.xxprison#c.trend
                                       cD.xxprison#cD.xxincome#c.trend#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend#c.trend
                                       c.xxbeer0#c.trend c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend#c.trend
                                       86b.year 87.year 88.year 89.year 90.year
                                       91.year 92.year 93.year 94.year 95.year
                                       96.year 97.year
  of which, amelioration set (12):     86b.year 87.year 88.year 89.year
                                       90.year 91.year 92.year 93.year 94.year
                                       95.year 96.year 97.year

Structural equation:

OLS using CHS lasso-orthogonalized vars
(Std. Err. adjusted for 50 clusters in statenum)
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.1416696     .039261     -3.61    0.000     -.2186197    -.0647195
-------------+----------------------------------------------------------------

OLS using CHS post-lasso-orthogonalized vars
(Std. Err. adjusted for 50 clusters in statenum)
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.1436651    .0422845     -3.40    0.001     -.2265413     -.060789
-------------+----------------------------------------------------------------

OLS with PDS-selected variables and full regressor set
(Std. Err. adjusted for 50 clusters in statenum)
-------------+----------------------------------------------------------------
             |               Robust
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.1748775    .0482561     -3.62    0.000     -.2694577    -.0802973
             |
       prop0 |    .0729424    .0313256      2.33    0.020      .0115454     .1343394
             |
    xxprison |
         L1. |     .011286    .0054586      2.07    0.039      .0005874     .0219846
             |
 cL.xxpolice#|
 cL.xxpolice |     .016199    .0094892      1.71    0.088     -.0023996     .0347975
             |
 cL.xxafdc15#|
 cL.xxafdc15 |    .0007529     .007643      0.10    0.922      -.014227     .0157329
             |
  Dxxincome0 |    50.62028    20.37634      2.48    0.013       10.6834     90.55716
             |
          c. |
  Dxxincome0#|
c.Dxxincome0 |   -3634.061    69024.61     -0.05    0.958     -138919.8     131651.7
             |
     c.prop0#|
     c.prop0#|
     c.trend#|
     c.trend |   -.2475365     .079677     -3.11    0.002     -.4037006    -.0913724
             |
 cD.xxprison#|
     c.trend |   -.0506313    .1412457     -0.36    0.720     -.3274678     .2262051
             |
 cD.xxprison#|
 cD.xxprison#|
     c.trend |    .3838315    .3325887      1.15    0.248     -.2680303     1.035693
             |
 cD.xxprison#|
 cD.xxincome#|
     c.trend#|
     c.trend |   -146.1816     122.259     -1.20    0.232     -385.8049     93.44176
             |
  cD.xxunemp#|
  cD.xxunemp#|
     c.trend |    59.57671     27.2401      2.19    0.029      6.187103     112.9663
             |
 cL.xxpolice#|
 cL.xxpolice#|
     c.trend#|
     c.trend |   -.0301998    .0148523     -2.03    0.042     -.0593098    -.0010899
             |
 c.xxafdc150#|
 c.xxafdc150#|
     c.trend#|
     c.trend |   -.0171357    .0094388     -1.82    0.069     -.0356354     .0013641
             |
   c.xxbeer0#|
     c.trend |   -.0412105    .0512532     -0.80    0.421     -.1416648     .0592438
             |
          c. |
  Dxxincome0#|
     c.trend |   -31.44817    38.11101     -0.83    0.409     -106.1444     43.24803
             |
          c. |
  Dxxincome0#|
          c. |
  Dxxincome0#|
     c.trend |    25870.44    259632.5      0.10    0.921       -483000     534740.9
             |
          c. |
  Dxxincome0#|
          c. |
  Dxxincome0#|
     c.trend#|
     c.trend |   -97532.35    223747.1     -0.44    0.663     -536068.7       341004
             |
        year |
         87  |   -.0043278    .0087984     -0.49    0.623     -.0215724     .0129168
         88  |   -.0182113    .0084819     -2.15    0.032     -.0348355    -.0015871
         89  |    .0031423    .0087781      0.36    0.720     -.0140626     .0203471
         90  |    .0125046    .0107599      1.16    0.245     -.0085843     .0335936
         91  |    .0209187    .0105838      1.98    0.048      .0001748     .0416627
         92  |   -.0225708    .0124263     -1.82    0.069     -.0469259     .0017844
         93  |   -.0070234    .0122133     -0.58    0.565      -.030961     .0169143
         94  |    .0279266    .0128971      2.17    0.030      .0026487     .0532044
         95  |    .0485939    .0167224      2.91    0.004      .0158185     .0813693
         96  |    .0126351    .0190001      0.67    0.506     -.0246045     .0498747
         97  |    .0301299    .0216382      1.39    0.164     -.0122802     .0725401
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    D.efaprop
------------------------------------------------------------------------------
r; t=311.94 21:47:36

.
.
. // FE and no ftools
. pdslasso D.lpc_prop D.efaprop                                                                           ///
>                 (                                                                                                                       /// no trend
>                 c.prop0##c.prop0                                                                                        ///
>                 c.Dprop0##c.Dprop0                                                                                      ///
>                 c.(D.($xx))##c.(D.($xx))                                                                        /// note macro
>                 c.(L.xxprison)##c.(L.xxprison)                                                          ///
>                 c.(L.xxpolice)##c.(L.xxpolice)                                                          ///
>                 c.(L.xxunemp)##c.(L.xxunemp)                                                            ///
>                 c.(L.xxincome)##c.(L.xxincome)                                                          ///
>                 c.(L.xxpover)##c.(L.xxpover)                                                            ///
>                 c.(L.xxafdc15)##c.(L.xxafdc15)                                                          ///
>                 c.(L.xxgunlaw)##c.(L.xxgunlaw)                                                          ///
>                 c.(L.xxbeer)##c.(L.xxbeer)                                                                      ///
>                 c.Mxxprison##c.Mxxprison                                                                        ///
>                 c.Mxxpolice##c.Mxxpolice                                                                        ///
>                 c.Mxxunemp##c.Mxxunemp                                                                          ///
>                 c.Mxxincome##c.Mxxincome                                                                        ///
>                 c.Mxxpover##c.Mxxpover                                                                          ///
>                 c.Mxxafdc15##c.Mxxafdc15                                                                        ///
>                 c.Mxxgunlaw##c.Mxxgunlaw                                                                        ///
>                 c.Mxxbeer##c.Mxxbeer                                                                            ///
>                 c.xxprison0##c.xxprison0                                                                        ///
>                 c.xxpolice0##c.xxpolice0                                                                        ///
>                 c.xxunemp0##c.xxunemp0                                                                          ///
>                 c.xxincome0##c.xxincome0                                                                        ///
>                 c.xxpover0##c.xxpover0                                                                          ///
>                 c.xxafdc150##c.xxafdc150                                                                        ///
>                 c.xxgunlaw0##c.xxgunlaw0                                                                        ///
>                 c.xxbeer0##c.xxbeer0                                                                            ///
>                 c.Dxxprison0##c.Dxxprison0                                                                      ///
>                 c.Dxxpolice0##c.Dxxpolice0                                                                      ///
>                 c.Dxxunemp0##c.Dxxunemp0                                                                        ///
>                 c.Dxxincome0##c.Dxxincome0                                                                      ///
>                 c.Dxxpover0##c.Dxxpover0                                                                        ///
>                 c.Dxxafdc150##c.Dxxafdc150                                                                      ///
>                 c.Dxxgunlaw0##c.Dxxgunlaw0                                                                      ///
>                 c.Dxxbeer0##c.Dxxbeer0                                                                          ///
>                                                                                                                                         ///
>                 (c.prop0##c.prop0)#(c.trend##c.trend)                                           /// now interacted with trend
>                 (c.Dprop0##c.Dprop0)#(c.trend##c.trend)                                         ///
>                 (c.(D.($xx))##c.(D.($xx)))#(c.trend##c.trend)                           /// note macro
>                 (c.(L.xxprison)##c.(L.xxprison))#(c.trend##c.trend)                     ///
>                 (c.(L.xxpolice)##c.(L.xxpolice))#(c.trend##c.trend)                     ///
>                 (c.(L.xxunemp)##c.(L.xxunemp))#(c.trend##c.trend)                       ///
>                 (c.(L.xxincome)##c.(L.xxincome))#(c.trend##c.trend)                     ///
>                 (c.(L.xxpover)##c.(L.xxpover))#(c.trend##c.trend)                       ///
>                 (c.(L.xxafdc15)##c.(L.xxafdc15))#(c.trend##c.trend)                     ///
>                 (c.(L.xxgunlaw)##c.(L.xxgunlaw))#(c.trend##c.trend)                     ///
>                 (c.(L.xxbeer)##c.(L.xxbeer))#(c.trend##c.trend)                         ///
>                 (c.Mxxprison##c.Mxxprison)#(c.trend##c.trend)                           ///
>                 (c.Mxxpolice##c.Mxxpolice)#(c.trend##c.trend)                           ///
>                 (c.Mxxunemp##c.Mxxunemp )#(c.trend##c.trend)                            ///
>                 (c.Mxxincome##c.Mxxincome)#(c.trend##c.trend)                           ///
>                 (c.Mxxpover##c.Mxxpover )#(c.trend##c.trend)                            ///
>                 (c.Mxxafdc15##c.Mxxafdc15)#(c.trend##c.trend)                           ///
>                 (c.Mxxgunlaw##c.Mxxgunlaw)#(c.trend##c.trend)                           ///
>                 (c.Mxxbeer##c.Mxxbeer)#(c.trend##c.trend)                                       ///
>                 (c.xxprison0##c.xxprison0)#(c.trend##c.trend)                           ///
>                 (c.xxpolice0##c.xxpolice0)#(c.trend##c.trend)                           ///
>                 (c.xxunemp0##c.xxunemp0)#(c.trend##c.trend)                                     ///
>                 (c.xxincome0##c.xxincome0)#(c.trend##c.trend)                           ///
>                 (c.xxpover0##c.xxpover0)#(c.trend##c.trend)                                     ///
>                 (c.xxafdc150##c.xxafdc150)#(c.trend##c.trend)                           ///
>                 (c.xxgunlaw0##c.xxgunlaw0)#(c.trend##c.trend)                           ///
>                 (c.xxbeer0##c.xxbeer0)#(c.trend##c.trend)                                       ///
>                 (c.Dxxprison0##c.Dxxprison0)#(c.trend##c.trend)                         ///
>                 (c.Dxxpolice0##c.Dxxpolice0)#(c.trend##c.trend)                         ///
>                 (c.Dxxunemp0##c.Dxxunemp0)#(c.trend##c.trend)                           ///
>                 (c.Dxxincome0##c.Dxxincome0)#(c.trend##c.trend)                         ///
>                 (c.Dxxpover0##c.Dxxpover0)#(c.trend##c.trend)                           ///
>                 (c.Dxxafdc150##c.Dxxafdc150)#(c.trend##c.trend)                         ///
>                 (c.Dxxgunlaw0##c.Dxxgunlaw0)#(c.trend##c.trend)                         ///
>                 (c.Dxxbeer0##c.Dxxbeer0 )#(c.trend##c.trend)                            ///
>                 i.year                                                                                                          ///
>                 )                                                                                                                       ///
>                 , fe
Fixed effects transformation...
1.  (PDS/CHS) Selecting HD controls for dep var D.lpc_prop...
Selected:  cL.xxafdc15#cL.xxafdc15 cL.xxunemp#c.trend
          cL.xxunemp#cL.xxunemp#c.trend 92.year
2.  (PDS/CHS) Selecting HD controls for exog regressor D.efaprop...
Selected:  D.xxincome cD.xxprison#cD.xxunemp c.prop0#c.trend#c.trend
          c.prop0#c.prop0#c.trend#c.trend cL.xxunemp#cL.xxunemp#c.trend
          cL.xxafdc15#cL.xxafdc15#c.trend cL.xxbeer#cL.xxbeer#c.trend
          c.xxprison0#c.xxprison0#c.trend c.Dxxunemp0#c.Dxxunemp0#c.trend
          c.Dxxincome0#c.trend c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
          89.year 90.year 91.year 92.year 93.year 96.year 97.year


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      homoskedastic
Number of observations:                600
Number of fixed effects:                50
Exogenous (1):                         D.efaprop
High-dim controls (348):               prop0 c.prop0#c.prop0 Dprop0
                                       c.Dprop0#c.Dprop0 D.xxprison D.xxpolice
                                       D.xxunemp D.xxincome D.xxpover
                                       D.xxafdc15 D.xxgunlaw D.xxbeer
                                       cD.xxprison#cD.xxprison
                                       cD.xxprison#cD.xxpolice
                                       cD.xxprison#cD.xxunemp
                                       cD.xxprison#cD.xxincome
                                       cD.xxprison#cD.xxpover
                                       cD.xxprison#cD.xxafdc15
                                       cD.xxprison#cD.xxgunlaw
                                       cD.xxprison#cD.xxbeer
                                       cD.xxpolice#cD.xxpolice
                                       cD.xxpolice#cD.xxunemp
                                       cD.xxpolice#cD.xxincome
                                       cD.xxpolice#cD.xxpover
                                       cD.xxpolice#cD.xxafdc15
                                       cD.xxpolice#cD.xxgunlaw
                                       cD.xxpolice#cD.xxbeer
                                       cD.xxunemp#cD.xxunemp
                                       cD.xxunemp#cD.xxincome
                                       cD.xxunemp#cD.xxpover
                                       cD.xxunemp#cD.xxafdc15
                                       cD.xxunemp#cD.xxgunlaw
                                       cD.xxunemp#cD.xxbeer
                                       cD.xxincome#cD.xxincome
                                       cD.xxincome#cD.xxpover
                                       cD.xxincome#cD.xxafdc15
                                       cD.xxincome#cD.xxgunlaw
                                       cD.xxincome#cD.xxbeer
                                       cD.xxpover#cD.xxpover
                                       cD.xxpover#cD.xxafdc15
                                       cD.xxpover#cD.xxgunlaw
                                       cD.xxpover#cD.xxbeer
                                       cD.xxafdc15#cD.xxafdc15
                                       cD.xxafdc15#cD.xxgunlaw
                                       cD.xxafdc15#cD.xxbeer
                                       cD.xxgunlaw#cD.xxgunlaw
                                       cD.xxgunlaw#cD.xxbeer
                                       cD.xxbeer#cD.xxbeer L.xxprison
                                       cL.xxprison#cL.xxprison L.xxpolice
                                       cL.xxpolice#cL.xxpolice L.xxunemp
                                       cL.xxunemp#cL.xxunemp L.xxincome
                                       cL.xxincome#cL.xxincome L.xxpover
                                       cL.xxpover#cL.xxpover L.xxafdc15
                                       cL.xxafdc15#cL.xxafdc15 L.xxgunlaw
                                       cL.xxgunlaw#cL.xxgunlaw L.xxbeer
                                       cL.xxbeer#cL.xxbeer Mxxprison
                                       c.Mxxprison#c.Mxxprison Mxxpolice
                                       c.Mxxpolice#c.Mxxpolice Mxxunemp
                                       c.Mxxunemp#c.Mxxunemp Mxxincome
                                       c.Mxxincome#c.Mxxincome Mxxpover
                                       c.Mxxpover#c.Mxxpover Mxxafdc15
                                       c.Mxxafdc15#c.Mxxafdc15 Mxxgunlaw
                                       c.Mxxgunlaw#c.Mxxgunlaw Mxxbeer
                                       c.Mxxbeer#c.Mxxbeer xxprison0
                                       c.xxprison0#c.xxprison0 xxpolice0
                                       c.xxpolice0#c.xxpolice0 xxunemp0
                                       c.xxunemp0#c.xxunemp0 xxincome0
                                       c.xxincome0#c.xxincome0 xxpover0
                                       c.xxpover0#c.xxpover0 xxafdc150
                                       c.xxafdc150#c.xxafdc150 xxgunlaw0
                                       c.xxgunlaw0#c.xxgunlaw0 xxbeer0
                                       c.xxbeer0#c.xxbeer0 Dxxprison0
                                       c.Dxxprison0#c.Dxxprison0 Dxxpolice0
                                       c.Dxxpolice0#c.Dxxpolice0 Dxxunemp0
                                       c.Dxxunemp0#c.Dxxunemp0 Dxxincome0
                                       c.Dxxincome0#c.Dxxincome0 Dxxpover0
                                       c.Dxxpover0#c.Dxxpover0 Dxxafdc150
                                       c.Dxxafdc150#c.Dxxafdc150 Dxxgunlaw0
                                       c.Dxxgunlaw0#c.Dxxgunlaw0 Dxxbeer0
                                       c.Dxxbeer0#c.Dxxbeer0 c.prop0#c.trend
                                       c.prop0#c.trend#c.trend
                                       c.prop0#c.prop0#c.trend
                                       c.prop0#c.prop0#c.trend#c.trend
                                       c.Dprop0#c.trend
                                       c.Dprop0#c.trend#c.trend
                                       c.Dprop0#c.Dprop0#c.trend
                                       c.Dprop0#c.Dprop0#c.trend#c.trend
                                       cD.xxprison#c.trend
                                       cD.xxprison#c.trend#c.trend
                                       cD.xxpolice#c.trend
                                       cD.xxpolice#c.trend#c.trend
                                       cD.xxunemp#c.trend
                                       cD.xxunemp#c.trend#c.trend
                                       cD.xxincome#c.trend
                                       cD.xxincome#c.trend#c.trend
                                       cD.xxpover#c.trend
                                       cD.xxpover#c.trend#c.trend
                                       cD.xxafdc15#c.trend
                                       cD.xxafdc15#c.trend#c.trend
                                       cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#c.trend#c.trend
                                       cD.xxbeer#c.trend
                                       cD.xxbeer#c.trend#c.trend
                                       cD.xxprison#cD.xxprison#c.trend
                                       cD.xxprison#cD.xxprison#c.trend#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend#c.trend
                                       cD.xxprison#cD.xxincome#c.trend
                                       cD.xxprison#cD.xxincome#c.trend#c.trend
                                       cD.xxprison#cD.xxpover#c.trend
                                       cD.xxprison#cD.xxpover#c.trend#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend#c.trend
                                       cD.xxincome#cD.xxincome#c.trend
                                       cD.xxincome#cD.xxincome#c.trend#c.trend
                                       cD.xxincome#cD.xxpover#c.trend
                                       cD.xxincome#cD.xxpover#c.trend#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend#c.trend
                                       cD.xxpover#cD.xxpover#c.trend
                                       cD.xxpover#cD.xxpover#c.trend#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend#c.trend
                                       cL.xxprison#c.trend
                                       cL.xxprison#c.trend#c.trend
                                       cL.xxprison#cL.xxprison#c.trend
                                       cL.xxprison#cL.xxprison#c.trend#c.trend
                                       cL.xxpolice#c.trend
                                       cL.xxpolice#c.trend#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend#c.trend
                                       cL.xxunemp#c.trend
                                       cL.xxunemp#c.trend#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend#c.trend
                                       cL.xxincome#c.trend
                                       cL.xxincome#c.trend#c.trend
                                       cL.xxincome#cL.xxincome#c.trend
                                       cL.xxincome#cL.xxincome#c.trend#c.trend
                                       cL.xxpover#c.trend
                                       cL.xxpover#c.trend#c.trend
                                       cL.xxpover#cL.xxpover#c.trend
                                       cL.xxpover#cL.xxpover#c.trend#c.trend
                                       cL.xxafdc15#c.trend
                                       cL.xxafdc15#c.trend#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend#c.trend
                                       cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#c.trend#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend#c.trend
                                       cL.xxbeer#c.trend
                                       cL.xxbeer#c.trend#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend#c.trend
                                       c.Mxxprison#c.trend
                                       c.Mxxprison#c.trend#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend#c.trend
                                       c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.trend#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend#c.trend
                                       c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.trend#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend#c.trend
                                       c.Mxxincome#c.trend
                                       c.Mxxincome#c.trend#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend#c.trend
                                       c.Mxxpover#c.trend
                                       c.Mxxpover#c.trend#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend#c.trend
                                       c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.trend#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend#c.trend
                                       c.xxprison0#c.trend
                                       c.xxprison0#c.trend#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.xxprison0#c.xxprison0#c.trend#c.trend
                                       c.xxpolice0#c.trend
                                       c.xxpolice0#c.trend#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend#c.trend
                                       c.xxunemp0#c.trend
                                       c.xxunemp0#c.trend#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend#c.trend
                                       c.xxincome0#c.trend
                                       c.xxincome0#c.trend#c.trend
                                       c.xxincome0#c.xxincome0#c.trend
                                       c.xxincome0#c.xxincome0#c.trend#c.trend
                                       c.xxpover0#c.trend
                                       c.xxpover0#c.trend#c.trend
                                       c.xxpover0#c.xxpover0#c.trend
                                       c.xxpover0#c.xxpover0#c.trend#c.trend
                                       c.xxafdc150#c.trend
                                       c.xxafdc150#c.trend#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend#c.trend
                                       c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.trend#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend#c.trend
                                       c.xxbeer0#c.trend
                                       c.xxbeer0#c.trend#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend#c.trend
                                       c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.trend#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend#c.trend
                                       c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.trend#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend#c.trend
                                       c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.trend#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend#c.trend
                                       c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.trend#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend#c.trend
                                       86b.year 87.year 88.year 89.year 90.year
                                       91.year 92.year 93.year 94.year 95.year
                                       96.year 97.year
Selected controls (20):                D.xxincome cD.xxprison#cD.xxunemp
                                       cL.xxafdc15#cL.xxafdc15
                                       c.prop0#c.trend#c.trend
                                       c.prop0#c.prop0#c.trend#c.trend
                                       cL.xxunemp#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend
                                       c.Dxxincome0#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       89.year 90.year 91.year 92.year 93.year
                                       96.year 97.year

Structural equation (fixed effects, #groups=50):

OLS using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.1564198    .0617164     -2.53    0.011     -.2773818    -.0354578
-------------+----------------------------------------------------------------

OLS using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |    -.184829    .0751541     -2.46    0.014     -.3321284    -.0375297
-------------+----------------------------------------------------------------

OLS with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.2107865    .0756391     -2.79    0.005     -.3590364    -.0625366
             |
    xxincome |
         D1. |   -13.59428    11.57446     -1.17    0.240     -36.27981     9.091248
             |
 cD.xxprison#|
  cD.xxunemp |    4.446929    3.248478      1.37    0.171      -1.91997     10.81383
             |
 cL.xxafdc15#|
 cL.xxafdc15 |    .0131344    .0186569      0.70    0.481     -.0234325     .0497014
             |
     c.prop0#|
     c.trend#|
     c.trend |    .0494942    .1851277      0.27    0.789     -.3133495     .4123379
             |
     c.prop0#|
     c.prop0#|
     c.trend#|
     c.trend |   -.3519988    .2631329     -1.34    0.181     -.8677299     .1637323
             |
  cL.xxunemp#|
     c.trend |   -.0282544    .8961037     -0.03    0.975     -1.784585     1.728077
             |
  cL.xxunemp#|
  cL.xxunemp#|
     c.trend |   -4.940899    8.467639     -0.58    0.560     -21.53717     11.65537
             |
 cL.xxafdc15#|
 cL.xxafdc15#|
     c.trend |    .0105381     .030399      0.35    0.729     -.0490429      .070119
             |
   cL.xxbeer#|
   cL.xxbeer#|
     c.trend |    .8260327    .4004716      2.06    0.039      .0411228     1.610943
             |
 c.xxprison0#|
 c.xxprison0#|
     c.trend |   -.0051437    .0224803     -0.23    0.819     -.0492042     .0389168
             |
 c.Dxxunemp0#|
 c.Dxxunemp0#|
     c.trend |   -4.841663    96.97646     -0.05    0.960      -194.912     185.2287
             |
          c. |
  Dxxincome0#|
     c.trend |   -12.36979    36.82629     -0.34    0.737     -84.54799     59.80842
             |
          c. |
  Dxxafdc150#|
          c. |
  Dxxafdc150#|
     c.trend#|
     c.trend |   -1.304046    1.039637     -1.25    0.210     -3.341697     .7336055
             |
        year |
         89  |   -.0002653    .0079841     -0.03    0.973     -.0159139     .0153833
         90  |   -.0004137    .0084958     -0.05    0.961     -.0170651     .0162377
         91  |    .0020101    .0090243      0.22    0.824     -.0156772     .0196973
         92  |   -.0411255    .0082625     -4.98    0.000     -.0573198    -.0249313
         93  |   -.0296378    .0084574     -3.50    0.000      -.046214    -.0130616
         96  |   -.0458827    .0094947     -4.83    0.000     -.0644919    -.0272735
         97  |   -.0407131    .0121748     -3.34    0.001     -.0645752     -.016851
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    D.efaprop
------------------------------------------------------------------------------
r; t=3.47 21:47:40

. savedresults save ftools e()
r; t=0.01 21:47:40

. cap noi assert "`e(noftools)'"==""  // will be error if ftools not installed
r; t=0.00 21:47:40

. pdslasso D.lpc_prop D.efaprop                                                                           ///
>                 (                                                                                                                       /// no trend
>                 c.prop0##c.prop0                                                                                        ///
>                 c.Dprop0##c.Dprop0                                                                                      ///
>                 c.(D.($xx))##c.(D.($xx))                                                                        /// note macro
>                 c.(L.xxprison)##c.(L.xxprison)                                                          ///
>                 c.(L.xxpolice)##c.(L.xxpolice)                                                          ///
>                 c.(L.xxunemp)##c.(L.xxunemp)                                                            ///
>                 c.(L.xxincome)##c.(L.xxincome)                                                          ///
>                 c.(L.xxpover)##c.(L.xxpover)                                                            ///
>                 c.(L.xxafdc15)##c.(L.xxafdc15)                                                          ///
>                 c.(L.xxgunlaw)##c.(L.xxgunlaw)                                                          ///
>                 c.(L.xxbeer)##c.(L.xxbeer)                                                                      ///
>                 c.Mxxprison##c.Mxxprison                                                                        ///
>                 c.Mxxpolice##c.Mxxpolice                                                                        ///
>                 c.Mxxunemp##c.Mxxunemp                                                                          ///
>                 c.Mxxincome##c.Mxxincome                                                                        ///
>                 c.Mxxpover##c.Mxxpover                                                                          ///
>                 c.Mxxafdc15##c.Mxxafdc15                                                                        ///
>                 c.Mxxgunlaw##c.Mxxgunlaw                                                                        ///
>                 c.Mxxbeer##c.Mxxbeer                                                                            ///
>                 c.xxprison0##c.xxprison0                                                                        ///
>                 c.xxpolice0##c.xxpolice0                                                                        ///
>                 c.xxunemp0##c.xxunemp0                                                                          ///
>                 c.xxincome0##c.xxincome0                                                                        ///
>                 c.xxpover0##c.xxpover0                                                                          ///
>                 c.xxafdc150##c.xxafdc150                                                                        ///
>                 c.xxgunlaw0##c.xxgunlaw0                                                                        ///
>                 c.xxbeer0##c.xxbeer0                                                                            ///
>                 c.Dxxprison0##c.Dxxprison0                                                                      ///
>                 c.Dxxpolice0##c.Dxxpolice0                                                                      ///
>                 c.Dxxunemp0##c.Dxxunemp0                                                                        ///
>                 c.Dxxincome0##c.Dxxincome0                                                                      ///
>                 c.Dxxpover0##c.Dxxpover0                                                                        ///
>                 c.Dxxafdc150##c.Dxxafdc150                                                                      ///
>                 c.Dxxgunlaw0##c.Dxxgunlaw0                                                                      ///
>                 c.Dxxbeer0##c.Dxxbeer0                                                                          ///
>                                                                                                                                         ///
>                 (c.prop0##c.prop0)#(c.trend##c.trend)                                           /// now interacted with trend
>                 (c.Dprop0##c.Dprop0)#(c.trend##c.trend)                                         ///
>                 (c.(D.($xx))##c.(D.($xx)))#(c.trend##c.trend)                           /// note macro
>                 (c.(L.xxprison)##c.(L.xxprison))#(c.trend##c.trend)                     ///
>                 (c.(L.xxpolice)##c.(L.xxpolice))#(c.trend##c.trend)                     ///
>                 (c.(L.xxunemp)##c.(L.xxunemp))#(c.trend##c.trend)                       ///
>                 (c.(L.xxincome)##c.(L.xxincome))#(c.trend##c.trend)                     ///
>                 (c.(L.xxpover)##c.(L.xxpover))#(c.trend##c.trend)                       ///
>                 (c.(L.xxafdc15)##c.(L.xxafdc15))#(c.trend##c.trend)                     ///
>                 (c.(L.xxgunlaw)##c.(L.xxgunlaw))#(c.trend##c.trend)                     ///
>                 (c.(L.xxbeer)##c.(L.xxbeer))#(c.trend##c.trend)                         ///
>                 (c.Mxxprison##c.Mxxprison)#(c.trend##c.trend)                           ///
>                 (c.Mxxpolice##c.Mxxpolice)#(c.trend##c.trend)                           ///
>                 (c.Mxxunemp##c.Mxxunemp )#(c.trend##c.trend)                            ///
>                 (c.Mxxincome##c.Mxxincome)#(c.trend##c.trend)                           ///
>                 (c.Mxxpover##c.Mxxpover )#(c.trend##c.trend)                            ///
>                 (c.Mxxafdc15##c.Mxxafdc15)#(c.trend##c.trend)                           ///
>                 (c.Mxxgunlaw##c.Mxxgunlaw)#(c.trend##c.trend)                           ///
>                 (c.Mxxbeer##c.Mxxbeer)#(c.trend##c.trend)                                       ///
>                 (c.xxprison0##c.xxprison0)#(c.trend##c.trend)                           ///
>                 (c.xxpolice0##c.xxpolice0)#(c.trend##c.trend)                           ///
>                 (c.xxunemp0##c.xxunemp0)#(c.trend##c.trend)                                     ///
>                 (c.xxincome0##c.xxincome0)#(c.trend##c.trend)                           ///
>                 (c.xxpover0##c.xxpover0)#(c.trend##c.trend)                                     ///
>                 (c.xxafdc150##c.xxafdc150)#(c.trend##c.trend)                           ///
>                 (c.xxgunlaw0##c.xxgunlaw0)#(c.trend##c.trend)                           ///
>                 (c.xxbeer0##c.xxbeer0)#(c.trend##c.trend)                                       ///
>                 (c.Dxxprison0##c.Dxxprison0)#(c.trend##c.trend)                         ///
>                 (c.Dxxpolice0##c.Dxxpolice0)#(c.trend##c.trend)                         ///
>                 (c.Dxxunemp0##c.Dxxunemp0)#(c.trend##c.trend)                           ///
>                 (c.Dxxincome0##c.Dxxincome0)#(c.trend##c.trend)                         ///
>                 (c.Dxxpover0##c.Dxxpover0)#(c.trend##c.trend)                           ///
>                 (c.Dxxafdc150##c.Dxxafdc150)#(c.trend##c.trend)                         ///
>                 (c.Dxxgunlaw0##c.Dxxgunlaw0)#(c.trend##c.trend)                         ///
>                 (c.Dxxbeer0##c.Dxxbeer0 )#(c.trend##c.trend)                            ///
>                 i.year                                                                                                          ///
>                 )                                                                                                                       ///
>                 , fe noftools
Fixed effects transformation...
1.  (PDS/CHS) Selecting HD controls for dep var D.lpc_prop...
Selected:  cL.xxafdc15#cL.xxafdc15 cL.xxunemp#c.trend
          cL.xxunemp#cL.xxunemp#c.trend 92.year
2.  (PDS/CHS) Selecting HD controls for exog regressor D.efaprop...
Selected:  D.xxincome cD.xxprison#cD.xxunemp c.prop0#c.trend#c.trend
          c.prop0#c.prop0#c.trend#c.trend cL.xxunemp#cL.xxunemp#c.trend
          cL.xxafdc15#cL.xxafdc15#c.trend cL.xxbeer#cL.xxbeer#c.trend
          c.xxprison0#c.xxprison0#c.trend c.Dxxunemp0#c.Dxxunemp0#c.trend
          c.Dxxincome0#c.trend c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
          89.year 90.year 91.year 92.year 93.year 96.year 97.year


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      homoskedastic
Number of observations:                600
Number of fixed effects:                50
Exogenous (1):                         D.efaprop
High-dim controls (348):               prop0 c.prop0#c.prop0 Dprop0
                                       c.Dprop0#c.Dprop0 D.xxprison D.xxpolice
                                       D.xxunemp D.xxincome D.xxpover
                                       D.xxafdc15 D.xxgunlaw D.xxbeer
                                       cD.xxprison#cD.xxprison
                                       cD.xxprison#cD.xxpolice
                                       cD.xxprison#cD.xxunemp
                                       cD.xxprison#cD.xxincome
                                       cD.xxprison#cD.xxpover
                                       cD.xxprison#cD.xxafdc15
                                       cD.xxprison#cD.xxgunlaw
                                       cD.xxprison#cD.xxbeer
                                       cD.xxpolice#cD.xxpolice
                                       cD.xxpolice#cD.xxunemp
                                       cD.xxpolice#cD.xxincome
                                       cD.xxpolice#cD.xxpover
                                       cD.xxpolice#cD.xxafdc15
                                       cD.xxpolice#cD.xxgunlaw
                                       cD.xxpolice#cD.xxbeer
                                       cD.xxunemp#cD.xxunemp
                                       cD.xxunemp#cD.xxincome
                                       cD.xxunemp#cD.xxpover
                                       cD.xxunemp#cD.xxafdc15
                                       cD.xxunemp#cD.xxgunlaw
                                       cD.xxunemp#cD.xxbeer
                                       cD.xxincome#cD.xxincome
                                       cD.xxincome#cD.xxpover
                                       cD.xxincome#cD.xxafdc15
                                       cD.xxincome#cD.xxgunlaw
                                       cD.xxincome#cD.xxbeer
                                       cD.xxpover#cD.xxpover
                                       cD.xxpover#cD.xxafdc15
                                       cD.xxpover#cD.xxgunlaw
                                       cD.xxpover#cD.xxbeer
                                       cD.xxafdc15#cD.xxafdc15
                                       cD.xxafdc15#cD.xxgunlaw
                                       cD.xxafdc15#cD.xxbeer
                                       cD.xxgunlaw#cD.xxgunlaw
                                       cD.xxgunlaw#cD.xxbeer
                                       cD.xxbeer#cD.xxbeer L.xxprison
                                       cL.xxprison#cL.xxprison L.xxpolice
                                       cL.xxpolice#cL.xxpolice L.xxunemp
                                       cL.xxunemp#cL.xxunemp L.xxincome
                                       cL.xxincome#cL.xxincome L.xxpover
                                       cL.xxpover#cL.xxpover L.xxafdc15
                                       cL.xxafdc15#cL.xxafdc15 L.xxgunlaw
                                       cL.xxgunlaw#cL.xxgunlaw L.xxbeer
                                       cL.xxbeer#cL.xxbeer Mxxprison
                                       c.Mxxprison#c.Mxxprison Mxxpolice
                                       c.Mxxpolice#c.Mxxpolice Mxxunemp
                                       c.Mxxunemp#c.Mxxunemp Mxxincome
                                       c.Mxxincome#c.Mxxincome Mxxpover
                                       c.Mxxpover#c.Mxxpover Mxxafdc15
                                       c.Mxxafdc15#c.Mxxafdc15 Mxxgunlaw
                                       c.Mxxgunlaw#c.Mxxgunlaw Mxxbeer
                                       c.Mxxbeer#c.Mxxbeer xxprison0
                                       c.xxprison0#c.xxprison0 xxpolice0
                                       c.xxpolice0#c.xxpolice0 xxunemp0
                                       c.xxunemp0#c.xxunemp0 xxincome0
                                       c.xxincome0#c.xxincome0 xxpover0
                                       c.xxpover0#c.xxpover0 xxafdc150
                                       c.xxafdc150#c.xxafdc150 xxgunlaw0
                                       c.xxgunlaw0#c.xxgunlaw0 xxbeer0
                                       c.xxbeer0#c.xxbeer0 Dxxprison0
                                       c.Dxxprison0#c.Dxxprison0 Dxxpolice0
                                       c.Dxxpolice0#c.Dxxpolice0 Dxxunemp0
                                       c.Dxxunemp0#c.Dxxunemp0 Dxxincome0
                                       c.Dxxincome0#c.Dxxincome0 Dxxpover0
                                       c.Dxxpover0#c.Dxxpover0 Dxxafdc150
                                       c.Dxxafdc150#c.Dxxafdc150 Dxxgunlaw0
                                       c.Dxxgunlaw0#c.Dxxgunlaw0 Dxxbeer0
                                       c.Dxxbeer0#c.Dxxbeer0 c.prop0#c.trend
                                       c.prop0#c.trend#c.trend
                                       c.prop0#c.prop0#c.trend
                                       c.prop0#c.prop0#c.trend#c.trend
                                       c.Dprop0#c.trend
                                       c.Dprop0#c.trend#c.trend
                                       c.Dprop0#c.Dprop0#c.trend
                                       c.Dprop0#c.Dprop0#c.trend#c.trend
                                       cD.xxprison#c.trend
                                       cD.xxprison#c.trend#c.trend
                                       cD.xxpolice#c.trend
                                       cD.xxpolice#c.trend#c.trend
                                       cD.xxunemp#c.trend
                                       cD.xxunemp#c.trend#c.trend
                                       cD.xxincome#c.trend
                                       cD.xxincome#c.trend#c.trend
                                       cD.xxpover#c.trend
                                       cD.xxpover#c.trend#c.trend
                                       cD.xxafdc15#c.trend
                                       cD.xxafdc15#c.trend#c.trend
                                       cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#c.trend#c.trend
                                       cD.xxbeer#c.trend
                                       cD.xxbeer#c.trend#c.trend
                                       cD.xxprison#cD.xxprison#c.trend
                                       cD.xxprison#cD.xxprison#c.trend#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend
                                       cD.xxprison#cD.xxpolice#c.trend#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend
                                       cD.xxprison#cD.xxunemp#c.trend#c.trend
                                       cD.xxprison#cD.xxincome#c.trend
                                       cD.xxprison#cD.xxincome#c.trend#c.trend
                                       cD.xxprison#cD.xxpover#c.trend
                                       cD.xxprison#cD.xxpover#c.trend#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend
                                       cD.xxprison#cD.xxafdc15#c.trend#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend
                                       cD.xxprison#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend
                                       cD.xxprison#cD.xxbeer#c.trend#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend
                                       cD.xxpolice#cD.xxpolice#c.trend#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend
                                       cD.xxpolice#cD.xxunemp#c.trend#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend
                                       cD.xxpolice#cD.xxincome#c.trend#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend
                                       cD.xxpolice#cD.xxpover#c.trend#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend
                                       cD.xxpolice#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend
                                       cD.xxpolice#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend
                                       cD.xxpolice#cD.xxbeer#c.trend#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend
                                       cD.xxunemp#cD.xxunemp#c.trend#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend
                                       cD.xxunemp#cD.xxincome#c.trend#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend
                                       cD.xxunemp#cD.xxpover#c.trend#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend
                                       cD.xxunemp#cD.xxafdc15#c.trend#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend
                                       cD.xxunemp#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend
                                       cD.xxunemp#cD.xxbeer#c.trend#c.trend
                                       cD.xxincome#cD.xxincome#c.trend
                                       cD.xxincome#cD.xxincome#c.trend#c.trend
                                       cD.xxincome#cD.xxpover#c.trend
                                       cD.xxincome#cD.xxpover#c.trend#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend
                                       cD.xxincome#cD.xxafdc15#c.trend#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend
                                       cD.xxincome#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend
                                       cD.xxincome#cD.xxbeer#c.trend#c.trend
                                       cD.xxpover#cD.xxpover#c.trend
                                       cD.xxpover#cD.xxpover#c.trend#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend
                                       cD.xxpover#cD.xxafdc15#c.trend#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend
                                       cD.xxpover#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend
                                       cD.xxpover#cD.xxbeer#c.trend#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend
                                       cD.xxafdc15#cD.xxafdc15#c.trend#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend
                                       cD.xxafdc15#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend
                                       cD.xxafdc15#cD.xxbeer#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend
                                       cD.xxgunlaw#cD.xxgunlaw#c.trend#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend
                                       cD.xxgunlaw#cD.xxbeer#c.trend#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend
                                       cD.xxbeer#cD.xxbeer#c.trend#c.trend
                                       cL.xxprison#c.trend
                                       cL.xxprison#c.trend#c.trend
                                       cL.xxprison#cL.xxprison#c.trend
                                       cL.xxprison#cL.xxprison#c.trend#c.trend
                                       cL.xxpolice#c.trend
                                       cL.xxpolice#c.trend#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend
                                       cL.xxpolice#cL.xxpolice#c.trend#c.trend
                                       cL.xxunemp#c.trend
                                       cL.xxunemp#c.trend#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend#c.trend
                                       cL.xxincome#c.trend
                                       cL.xxincome#c.trend#c.trend
                                       cL.xxincome#cL.xxincome#c.trend
                                       cL.xxincome#cL.xxincome#c.trend#c.trend
                                       cL.xxpover#c.trend
                                       cL.xxpover#c.trend#c.trend
                                       cL.xxpover#cL.xxpover#c.trend
                                       cL.xxpover#cL.xxpover#c.trend#c.trend
                                       cL.xxafdc15#c.trend
                                       cL.xxafdc15#c.trend#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend#c.trend
                                       cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#c.trend#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend
                                       cL.xxgunlaw#cL.xxgunlaw#c.trend#c.trend
                                       cL.xxbeer#c.trend
                                       cL.xxbeer#c.trend#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend#c.trend
                                       c.Mxxprison#c.trend
                                       c.Mxxprison#c.trend#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend
                                       c.Mxxprison#c.Mxxprison#c.trend#c.trend
                                       c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.trend#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend
                                       c.Mxxpolice#c.Mxxpolice#c.trend#c.trend
                                       c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.trend#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend
                                       c.Mxxunemp#c.Mxxunemp#c.trend#c.trend
                                       c.Mxxincome#c.trend
                                       c.Mxxincome#c.trend#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend
                                       c.Mxxincome#c.Mxxincome#c.trend#c.trend
                                       c.Mxxpover#c.trend
                                       c.Mxxpover#c.trend#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend
                                       c.Mxxpover#c.Mxxpover#c.trend#c.trend
                                       c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend
                                       c.Mxxafdc15#c.Mxxafdc15#c.trend#c.trend
                                       c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend
                                       c.Mxxgunlaw#c.Mxxgunlaw#c.trend#c.trend
                                       c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.trend#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend
                                       c.Mxxbeer#c.Mxxbeer#c.trend#c.trend
                                       c.xxprison0#c.trend
                                       c.xxprison0#c.trend#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.xxprison0#c.xxprison0#c.trend#c.trend
                                       c.xxpolice0#c.trend
                                       c.xxpolice0#c.trend#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend
                                       c.xxpolice0#c.xxpolice0#c.trend#c.trend
                                       c.xxunemp0#c.trend
                                       c.xxunemp0#c.trend#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend
                                       c.xxunemp0#c.xxunemp0#c.trend#c.trend
                                       c.xxincome0#c.trend
                                       c.xxincome0#c.trend#c.trend
                                       c.xxincome0#c.xxincome0#c.trend
                                       c.xxincome0#c.xxincome0#c.trend#c.trend
                                       c.xxpover0#c.trend
                                       c.xxpover0#c.trend#c.trend
                                       c.xxpover0#c.xxpover0#c.trend
                                       c.xxpover0#c.xxpover0#c.trend#c.trend
                                       c.xxafdc150#c.trend
                                       c.xxafdc150#c.trend#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend
                                       c.xxafdc150#c.xxafdc150#c.trend#c.trend
                                       c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.trend#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend
                                       c.xxgunlaw0#c.xxgunlaw0#c.trend#c.trend
                                       c.xxbeer0#c.trend
                                       c.xxbeer0#c.trend#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend
                                       c.xxbeer0#c.xxbeer0#c.trend#c.trend
                                       c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.trend#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend
                                       c.Dxxprison0#c.Dxxprison0#c.trend#c.trend
                                       c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend
                                       c.Dxxpolice0#c.Dxxpolice0#c.trend#c.trend
                                       c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend#c.trend
                                       c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.trend#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend
                                       c.Dxxincome0#c.Dxxincome0#c.trend#c.trend
                                       c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.trend#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend
                                       c.Dxxpover0#c.Dxxpover0#c.trend#c.trend
                                       c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend
                                       c.Dxxgunlaw0#c.Dxxgunlaw0#c.trend#c.trend
                                       c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.trend#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend
                                       c.Dxxbeer0#c.Dxxbeer0#c.trend#c.trend
                                       86b.year 87.year 88.year 89.year 90.year
                                       91.year 92.year 93.year 94.year 95.year
                                       96.year 97.year
Selected controls (20):                D.xxincome cD.xxprison#cD.xxunemp
                                       cL.xxafdc15#cL.xxafdc15
                                       c.prop0#c.trend#c.trend
                                       c.prop0#c.prop0#c.trend#c.trend
                                       cL.xxunemp#c.trend
                                       cL.xxunemp#cL.xxunemp#c.trend
                                       cL.xxafdc15#cL.xxafdc15#c.trend
                                       cL.xxbeer#cL.xxbeer#c.trend
                                       c.xxprison0#c.xxprison0#c.trend
                                       c.Dxxunemp0#c.Dxxunemp0#c.trend
                                       c.Dxxincome0#c.trend
                                       c.Dxxafdc150#c.Dxxafdc150#c.trend#c.trend
                                       89.year 90.year 91.year 92.year 93.year
                                       96.year 97.year

Structural equation (fixed effects, #groups=50):

OLS using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.1564198    .0617164     -2.53    0.011     -.2773818    -.0354578
-------------+----------------------------------------------------------------

OLS using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |    -.184829    .0751541     -2.46    0.014     -.3321284    -.0375297
-------------+----------------------------------------------------------------

OLS with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
   D.lpc_prop |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
     efaprop |
         D1. |   -.2107865    .0756391     -2.79    0.005     -.3590364    -.0625366
             |
    xxincome |
         D1. |   -13.59428    11.57446     -1.17    0.240     -36.27981     9.091248
             |
 cD.xxprison#|
  cD.xxunemp |    4.446929    3.248478      1.37    0.171      -1.91997     10.81383
             |
 cL.xxafdc15#|
 cL.xxafdc15 |    .0131344    .0186569      0.70    0.481     -.0234325     .0497014
             |
     c.prop0#|
     c.trend#|
     c.trend |    .0494942    .1851277      0.27    0.789     -.3133495     .4123379
             |
     c.prop0#|
     c.prop0#|
     c.trend#|
     c.trend |   -.3519988    .2631329     -1.34    0.181     -.8677299     .1637323
             |
  cL.xxunemp#|
     c.trend |   -.0282544    .8961037     -0.03    0.975     -1.784585     1.728077
             |
  cL.xxunemp#|
  cL.xxunemp#|
     c.trend |   -4.940899    8.467639     -0.58    0.560     -21.53717     11.65537
             |
 cL.xxafdc15#|
 cL.xxafdc15#|
     c.trend |    .0105381     .030399      0.35    0.729     -.0490429      .070119
             |
   cL.xxbeer#|
   cL.xxbeer#|
     c.trend |    .8260327    .4004716      2.06    0.039      .0411228     1.610943
             |
 c.xxprison0#|
 c.xxprison0#|
     c.trend |   -.0051437    .0224803     -0.23    0.819     -.0492042     .0389168
             |
 c.Dxxunemp0#|
 c.Dxxunemp0#|
     c.trend |   -4.841663    96.97646     -0.05    0.960      -194.912     185.2287
             |
          c. |
  Dxxincome0#|
     c.trend |   -12.36979    36.82629     -0.34    0.737     -84.54799     59.80842
             |
          c. |
  Dxxafdc150#|
          c. |
  Dxxafdc150#|
     c.trend#|
     c.trend |   -1.304046    1.039637     -1.25    0.210     -3.341697     .7336055
             |
        year |
         89  |   -.0002653    .0079841     -0.03    0.973     -.0159139     .0153833
         90  |   -.0004137    .0084958     -0.05    0.961     -.0170651     .0162377
         91  |    .0020101    .0090243      0.22    0.824     -.0156772     .0196973
         92  |   -.0411255    .0082625     -4.98    0.000     -.0573198    -.0249313
         93  |   -.0296378    .0084574     -3.50    0.000      -.046214    -.0130616
         96  |   -.0458827    .0094947     -4.83    0.000     -.0644919    -.0272735
         97  |   -.0407131    .0121748     -3.34    0.001     -.0645752     -.016851
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    D.efaprop
------------------------------------------------------------------------------
r; t=4.82 21:47:45

. assert "`e(noftools)'"=="noftools"
r; t=0.00 21:47:45

. savedresults comp ftools e()
r; t=0.00 21:47:45

.
. // ***************** END LEVITT DATASET ************************* //
.
.
. // ***************** BLP DATASET ************************* //
.
. * follows/replicates Matlab code/results from Belloni et. al 2012.
.
. // dataset separately constructed from Matalab data and code
. use Data\BLP, clear
r; t=0.19 21:47:45

.
. gen double y = ln(share) - ln(outshr)
r; t=0.00 21:47:45

.
. // Matlab feasiblePostLasso code description:
. // default lambda is 2.2*sqrt(n)*norminv(1-(1/log(n))/(2*p))
. // i.e. "gamma" is 1 not 0.1 as in rlasso.
. // default is het-rob loadings
. // default max ups iter = 15
. // default ups tol = 1e-6
. // default zero tol = 1e-4 (not settable in feasiblePostLasso)
. // default opt tol = 1e-5 (not settable in feasilblePostLasso)
. // 6 results replicated, 3 with tol 1e-3, 3 with tol 1e-5
. // Would possibly replicate more closely if Matlab tolerances were tighter.
.
. ******************************
. ******** Small set ***********
. ******************************
.
. // lasso, price (line 72)
. // Matlab output:
. // bDzx =
. //  -0.027187307080839
. //                   0
. //   0.140573386182651
. //                   0
. //  -0.040297610145709
. //   0.043091980749192
. //                   0
. //                   0
. //                   0
. //                   0
. //  22.361611212285307
. //   8.864499676282328
. //  -2.336920687857595
. //   1.571888537853250
. mat b_matlab =                          ///
>         (                                               ///
>   -0.027187307080839,           ///
>                    0,           ///
>    0.140573386182651,           ///
>                    0,           ///
>   -0.040297610145709,           ///
>    0.043091980749192,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>   22.361611212285307,           ///
>    8.864499676282328,           ///
>   -2.336920687857595,           ///
>    1.571888537853250            ///
>    )
r; t=0.00 21:47:45

.
. rlasso price                                                                                                                            ///
>                 sum_othbig_1 sum_othbig_2 sum_othbig_3 sum_othbig_4 sum_othbig_5        ///
>                 sum_rivbig_1 sum_rivbig_2 sum_rivbig_3 sum_rivbig_4 sum_rivbig_5        ///
>                 hpwt air mpd space                                                                                                      ///
>                 , displayall gamma(1) rob maxupsiter(15)                                                        ///
>                 tolups(1e-6) tolzero(1e-4) tolopt(1e-5)

------------------+--------------------------------
         Selected |           Lasso   Post-est OLS
------------------+--------------------------------
     sum_othbig_1 |      -0.0272571     -0.4374508
     sum_othbig_2 |  (not selected) (not selected)
     sum_othbig_3 |       0.1406422      0.4608627
     sum_othbig_4 |  (not selected) (not selected)
     sum_othbig_5 |      -0.0402651      0.1780889
     sum_rivbig_1 |       0.0430951      0.0607921
     sum_rivbig_2 |  (not selected) (not selected)
     sum_rivbig_3 |  (not selected) (not selected)
     sum_rivbig_4 |  (not selected) (not selected)
     sum_rivbig_5 |  (not selected) (not selected)
             hpwt |      22.3623884     25.9292369
              air |       8.8643947      8.5010834
              mpd |      -2.3370630     -3.0185721
            space |       1.5723379      2.9226899
            _cons |*       0.0048033     -2.9963539
------------------+--------------------------------
*Not penalized
r; t=0.12 21:47:45

.
. mat b_rlasso = e(betaAll)
r; t=0.00 21:47:45

. mat b_rlasso = b_rlasso[1,1..colsof(b_rlasso)-1]
r; t=0.00 21:47:45

. // note looser tolerance
. assert mreldif(b_rlasso,b_matlab)<1e-3
r; t=0.00 21:47:45

.
.
. // lasso, dep var (line 83)
. // Matlab output:
. // bYx =
. //  -2.226431503473688
. //  -0.894181896404704
. //   0.234706642184791
. //   1.782524104280113
. mat b_matlab =                          ///
>         (                                               ///
>   -2.226431503473688,           ///
>   -0.894181896404704,           ///
>    0.234706642184791,           ///
>    1.782524104280113            ///
>    )
r; t=0.00 21:47:45

.
. rlasso y                                                                                                                                        ///
>                 hpwt air mpd space                                                                                                      ///
>                 , displayall gamma(1) rob maxupsiter(15)                                                        ///
>                 tolups(1e-6) tolzero(1e-4) tolopt(1e-5)

------------------+--------------------------------
         Selected |           Lasso   Post-est OLS
------------------+--------------------------------
             hpwt |      -2.2264354     -2.6668706
              air |      -0.8941844     -1.0147559
              mpd |       0.2347080      0.4410037
            space |       1.7825423      2.4371977
            _cons |*      -9.2809016    -10.3658574
------------------+--------------------------------
*Not penalized
r; t=0.03 21:47:45

.
. mat b_rlasso = e(betaAll)
r; t=0.00 21:47:45

. mat b_rlasso = b_rlasso[1,1..colsof(b_rlasso)-1]
r; t=0.00 21:47:45

. // note tougher tolerance
. assert mreldif(b_rlasso,b_matlab)<1e-5
r; t=0.00 21:47:45

.
.
. // post-regularization IV (line 94)
. // post-lasso-orthogonalized replicates
. // Matlab output:
. // aL =
. //   -0.184934034947562
. ivlasso y (price=                                                                                                                       ///
>                 sum_othbig_1 sum_othbig_2 sum_othbig_3 sum_othbig_4 sum_othbig_5        ///
>                 sum_rivbig_1 sum_rivbig_2 sum_rivbig_3 sum_rivbig_4 sum_rivbig_5        ///
>                 )                                                                                                                                       ///
>                 (hpwt air mpd space)                                                                                            ///
>                 , rob lopt(gamma(1) maxupsiter(15) tolups(1e-6))
1.  (PDS/CHS) Selecting HD controls for dep var y...
Selected:  hpwt air mpd space
3.  (PDS) Selecting HD controls for endog regressor price...
Selected:  hpwt air mpd
5.  (PDS/CHS) Selecting HD controls/IVs for endog regressor price...
Selected:  hpwt air mpd space sum_othbig_1 sum_othbig_3 sum_othbig_5
          sum_rivbig_1
6a. (CHS) Selecting lasso HD controls and creating optimal IV for endog regressor price...
Selected:  hpwt air mpd space
6b. (CHS) Selecting post-lasso HD controls and creating optimal IV for endog regressor price...
Selected:  hpwt air mpd
7.  (CHS) Creating orthogonalized endogenous regressor price...


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      heteroskedastic
Number of observations:                2,217
Endogenous (1):                        price
High-dim controls (4):                 hpwt air mpd space
Selected controls, PDS (4):            hpwt air mpd space
Selected controls, CHS-L (4):          hpwt air mpd space
Selected controls, CHS-PL (4):         hpwt air mpd space
Unpenalized controls (1):              _cons
High-dim instruments (10):             sum_othbig_1 sum_othbig_2 sum_othbig_3
                                       sum_othbig_4 sum_othbig_5 sum_rivbig_1
                                       sum_rivbig_2 sum_rivbig_3 sum_rivbig_4
                                       sum_rivbig_5
Selected instruments (4):              sum_othbig_1 sum_othbig_3 sum_othbig_5
                                       sum_rivbig_1

Structural equation:

IV using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
            y |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
       price |    -.226732    .0167435    -13.54    0.000     -.2595487    -.1939153
-------------+----------------------------------------------------------------

IV using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
            y |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
       price |   -.1849353    .0141731    -13.05    0.000      -.212714    -.1571566
-------------+----------------------------------------------------------------

IV with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
             |               Robust
            y |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
       price |   -.1867778     .014296    -13.07    0.000     -.2147975    -.1587581
        hpwt |    2.690695     .495631      5.43    0.000      1.719276     3.662114
         air |    1.051139    .1602466      6.56    0.000      .7370616     1.365217
         mpd |    .0701803    .0506931      1.38    0.166     -.0291762     .1695369
       space |    2.236855    .1370175     16.33    0.000      1.968305     2.505404
       _cons |   -9.745845    .2848143    -34.22    0.000     -10.30407    -9.187619
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    price
------------------------------------------------------------------------------
r; t=0.35 21:47:45

. // note tougher tolerance
. assert reldif(el(e(beta_plasso),1,1), -0.184934034947562)<1e-5
r; t=0.00 21:47:45

.
. ******************************
. ******** Big set *************
. ******************************
.
. // lasso, price (line 135)
. // Matlab output:
. /*
> bDzx =
>
>   -0.026309868626536
>                    0
>    0.064576639402394
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>   -0.061816175757360
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>    0.057797411950973
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>  -14.890463278505399
>                    0
>                    0
>                    0
>   20.239078392116543
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>   15.468957465755846
>                    0
>    3.499130491002932
>                    0
>                    0
>    6.172115587542651
>                    0
>                    0
>                    0
>    1.525359161441577
>  */
. mat b_matlab =                          ///
>         (                                               ///
>   -0.026309868626536,           ///
>                    0,           ///
>    0.064576639402394,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>   -0.061816175757360,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>    0.057797411950973,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>  -14.890463278505399,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>   20.239078392116543,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>   15.468957465755846,           ///
>                    0,           ///
>    3.499130491002932,           ///
>                    0,           ///
>                    0,           ///
>    6.172115587542651,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>    1.525359161441577            ///
>    )
r; t=0.00 21:47:45

.
. rlasso price                                                                                                                            ///
>                 Z*                                                                                                                                      ///
>                 hpwt air mpdu spaceu tu                                                                                         ///
>                 hpwt_sq-spaceu_tu                                                                                                       ///
>                 , displayall gamma(1) rob maxupsiter(15)                                                        ///
>                 tolups(1e-6) tolzero(1e-4) tolopt(1e-5)

------------------+--------------------------------
         Selected |           Lasso   Post-est OLS
------------------+--------------------------------
              Z_1 |      -0.0263504     -0.2195643
              Z_2 |  (not selected) (not selected)
              Z_3 |       0.0646406      0.3465790
              Z_4 |  (not selected) (not selected)
              Z_5 |  (not selected) (not selected)
              Z_6 |  (not selected) (not selected)
              Z_7 |  (not selected) (not selected)
              Z_8 |  (not selected) (not selected)
              Z_9 |  (not selected) (not selected)
             Z_10 |  (not selected) (not selected)
             Z_11 |      -0.0617943      0.0382309
             Z_12 |  (not selected) (not selected)
             Z_13 |  (not selected) (not selected)
             Z_14 |  (not selected) (not selected)
             Z_15 |  (not selected) (not selected)
             Z_16 |  (not selected) (not selected)
             Z_17 |  (not selected) (not selected)
             Z_18 |  (not selected) (not selected)
             Z_19 |  (not selected) (not selected)
             Z_20 |  (not selected) (not selected)
             Z_21 |  (not selected) (not selected)
             Z_22 |  (not selected) (not selected)
             Z_23 |  (not selected) (not selected)
             Z_24 |  (not selected) (not selected)
             Z_25 |  (not selected) (not selected)
             Z_26 |  (not selected) (not selected)
             Z_27 |  (not selected) (not selected)
             Z_28 |  (not selected) (not selected)
             Z_29 |       0.0577900      0.0145323
             Z_30 |  (not selected) (not selected)
             Z_31 |  (not selected) (not selected)
             Z_32 |  (not selected) (not selected)
             Z_33 |  (not selected) (not selected)
             Z_34 |  (not selected) (not selected)
             Z_35 |  (not selected) (not selected)
             Z_36 |  (not selected) (not selected)
             Z_37 |  (not selected) (not selected)
             Z_38 |  (not selected) (not selected)
             Z_39 |  (not selected) (not selected)
             Z_40 |  (not selected) (not selected)
             Z_41 |  (not selected) (not selected)
             Z_42 |  (not selected) (not selected)
             Z_43 |  (not selected) (not selected)
             Z_44 |  (not selected) (not selected)
             Z_45 |  (not selected) (not selected)
             Z_46 |  (not selected) (not selected)
             Z_47 |  (not selected) (not selected)
             Z_48 |  (not selected) (not selected)
             hpwt |  (not selected) (not selected)
              air |  (not selected) (not selected)
             mpdu |     -14.8918883    -20.3265239
           spaceu |  (not selected) (not selected)
               tu |  (not selected) (not selected)
          hpwt_sq |  (not selected) (not selected)
          hpwt_cu |      20.2415617     29.4116519
          mpdu_sq |  (not selected) (not selected)
          mpdu_cu |  (not selected) (not selected)
        spaceu_sq |  (not selected) (not selected)
        spaceu_cu |  (not selected) (not selected)
            tu_sq |  (not selected) (not selected)
            tu_cu |  (not selected) (not selected)
         hpwt_air |      15.4677213     11.0026026
         mpdu_air |  (not selected) (not selected)
       spaceu_air |       3.4997957      5.8396319
           tu_air |  (not selected) (not selected)
        hpwt_mpdu |  (not selected) (not selected)
      hpwt_spaceu |       6.1717599      6.2193114
          hpwt_tu |  (not selected) (not selected)
      mpdu_spaceu |  (not selected) (not selected)
          mpdu_tu |  (not selected) (not selected)
        spaceu_tu |       1.5261598      5.5650409
            _cons |*       7.1982652     10.6090725
------------------+--------------------------------
*Not penalized
r; t=0.53 21:47:46

.
. mat b_rlasso = e(betaAll)
r; t=0.00 21:47:46

. mat b_rlasso = b_rlasso[1,1..colsof(b_rlasso)-1]
r; t=0.00 21:47:46

. // note looser tolerance
. assert mreldif(b_rlasso,b_matlab)<1e-3
r; t=0.00 21:47:46

.
. // lasso, dep var (line 146)
. // Matlab output:
. /*
> bYx =
>                    0
>   -0.448213818098585
>                    0
>                    0
>                    0
>                    0
>   -2.798818364136941
>                    0
>                    0
>    0.849364554746214
>    1.079486139873257
>                    0
>                    0
>   -0.748743293530742
>   -0.289563827442536
>                    0
>                    0
>                    0
>                    0
>                    0
>    3.512233383389987
>                    0
>                    0
> */
.
. mat b_matlab =                          ///
>         (                                               ///
>                    0,           ///
>   -0.448213818098585,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>   -2.798818364136941,           ///
>                    0,           ///
>                    0,           ///
>    0.849364554746214,           ///
>    1.079486139873257,           ///
>                    0,           ///
>                    0,           ///
>   -0.748743293530742,           ///
>   -0.289563827442536,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>    3.512233383389987,           ///
>                    0,           ///
>                    0            ///
>         )
r; t=0.00 21:47:46

.
. rlasso y                                                                                                                                        ///
>                 hpwt air mpdu spaceu tu                                                                                         ///
>                 hpwt_sq-spaceu_tu                                                                                                       ///
>                 , displayall gamma(1) rob maxupsiter(15)                                                        ///
>                 tolups(1e-6) tolzero(1e-4) tolopt(1e-5)

------------------+--------------------------------
         Selected |           Lasso   Post-est OLS
------------------+--------------------------------
             hpwt |  (not selected) (not selected)
              air |      -0.4482835     -0.8314957
             mpdu |  (not selected) (not selected)
           spaceu |  (not selected) (not selected)
               tu |  (not selected) (not selected)
          hpwt_sq |  (not selected) (not selected)
          hpwt_cu |      -2.7990523     -3.9442645
          mpdu_sq |  (not selected) (not selected)
          mpdu_cu |  (not selected) (not selected)
        spaceu_sq |       0.8504198      3.3325056
        spaceu_cu |       1.0786201     -0.6726752
            tu_sq |  (not selected) (not selected)
            tu_cu |  (not selected) (not selected)
         hpwt_air |      -0.7485333      0.3980872
         mpdu_air |      -0.2898074     -1.3746496
       spaceu_air |  (not selected) (not selected)
           tu_air |  (not selected) (not selected)
        hpwt_mpdu |  (not selected) (not selected)
      hpwt_spaceu |  (not selected) (not selected)
          hpwt_tu |  (not selected) (not selected)
      mpdu_spaceu |       3.5127542      5.7909368
          mpdu_tu |  (not selected) (not selected)
        spaceu_tu |  (not selected) (not selected)
            _cons |*      -8.5048572     -9.3657310
------------------+--------------------------------
*Not penalized
r; t=0.13 21:47:46

.
. mat b_rlasso = e(betaAll)
r; t=0.00 21:47:46

. mat b_rlasso = b_rlasso[1,1..colsof(b_rlasso)-1]
r; t=0.00 21:47:46

. // note looser tolerance
. assert mreldif(b_rlasso,b_matlab)<1e-3
r; t=0.00 21:47:46

.
. // post-regularization IV (line 157)
. // post-lasso-orthogonalized replicates
. // Matlab output:
. // aB =
. //  -0.221208122513718
. ivlasso y (price=                                                                                                                       ///
>                 Z*                                                                                                                                      ///
>                 )                                                                                                                                       ///
>                 (hpwt air mpdu spaceu tu                                                                                        ///
>                 hpwt_sq-spaceu_tu)                                                                                                      ///
>                 , rob lopt(gamma(1) maxupsiter(15) tolups(1e-6))
1.  (PDS/CHS) Selecting HD controls for dep var y...
Selected:  air hpwt_cu spaceu_sq spaceu_cu hpwt_air mpdu_air mpdu_spaceu
3.  (PDS) Selecting HD controls for endog regressor price...
Selected:  mpdu hpwt_cu hpwt_air spaceu_air hpwt_tu spaceu_tu
5.  (PDS/CHS) Selecting HD controls/IVs for endog regressor price...
Selected:  mpdu hpwt_cu hpwt_air spaceu_air hpwt_spaceu spaceu_tu Z_1 Z_3 Z_11
          Z_29
6a. (CHS) Selecting lasso HD controls and creating optimal IV for endog regressor price...
Selected:  air mpdu hpwt_sq hpwt_cu mpdu_cu hpwt_air mpdu_air spaceu_air
          hpwt_tu mpdu_spaceu spaceu_tu
6b. (CHS) Selecting post-lasso HD controls and creating optimal IV for endog regressor price...
Selected:  mpdu hpwt_sq hpwt_cu mpdu_sq tu_cu hpwt_air mpdu_air spaceu_air
          tu_air hpwt_tu mpdu_spaceu spaceu_tu
7.  (CHS) Creating orthogonalized endogenous regressor price...


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      heteroskedastic
Number of observations:                2,217
Endogenous (1):                        price
High-dim controls (23):                hpwt air mpdu spaceu tu hpwt_sq hpwt_cu
                                       mpdu_sq mpdu_cu spaceu_sq spaceu_cu
                                       tu_sq tu_cu hpwt_air mpdu_air spaceu_air
                                       tu_air hpwt_mpdu hpwt_spaceu hpwt_tu
                                       mpdu_spaceu mpdu_tu spaceu_tu
Selected controls, PDS (12):           air mpdu hpwt_cu spaceu_sq spaceu_cu
                                       hpwt_air mpdu_air spaceu_air hpwt_spaceu
                                       hpwt_tu mpdu_spaceu spaceu_tu
Selected controls, CHS-L (14):         air mpdu hpwt_sq hpwt_cu mpdu_cu
                                       spaceu_sq spaceu_cu hpwt_air mpdu_air
                                       spaceu_air hpwt_spaceu hpwt_tu
                                       mpdu_spaceu spaceu_tu
Selected controls, CHS-PL (16):        air mpdu hpwt_sq hpwt_cu mpdu_sq
                                       spaceu_sq spaceu_cu tu_cu hpwt_air
                                       mpdu_air spaceu_air tu_air hpwt_spaceu
                                       hpwt_tu mpdu_spaceu spaceu_tu
Unpenalized controls (1):              _cons
High-dim instruments (48):             Z_1 Z_2 Z_3 Z_4 Z_5 Z_6 Z_7 Z_8 Z_9
                                       Z_10 Z_11 Z_12 Z_13 Z_14 Z_15 Z_16 Z_17
                                       Z_18 Z_19 Z_20 Z_21 Z_22 Z_23 Z_24 Z_25
                                       Z_26 Z_27 Z_28 Z_29 Z_30 Z_31 Z_32 Z_33
                                       Z_34 Z_35 Z_36 Z_37 Z_38 Z_39 Z_40 Z_41
                                       Z_42 Z_43 Z_44 Z_45 Z_46 Z_47 Z_48
Selected instruments (4):              Z_1 Z_3 Z_11 Z_29

Structural equation:

IV using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
            y |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
       price |   -.2854954    .0216236    -13.20    0.000     -.3278768     -.243114
-------------+----------------------------------------------------------------

IV using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
            y |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
       price |     -.22121    .0163464    -13.53    0.000     -.2532483    -.1891716
-------------+----------------------------------------------------------------

IV with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
             |               Robust
            y |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
       price |   -.2400588    .0165342    -14.52    0.000     -.2724653    -.2076523
         air |   -.7516704    1.152868     -0.65    0.514      -3.01125     1.507909
        mpdu |    .6372987    2.025019      0.31    0.753     -3.331665     4.606262
     hpwt_cu |    3.547906    1.628053      2.18    0.029      .3569812     6.738831
   spaceu_sq |    21.12323    3.749161      5.63    0.000      13.77501     28.47145
   spaceu_cu |   -17.08911    3.063951     -5.58    0.000     -23.09434    -11.08387
    hpwt_air |    5.263331    1.276285      4.12    0.000      2.761858     7.764805
    mpdu_air |   -6.733311    1.319556     -5.10    0.000     -9.319593    -4.147029
  spaceu_air |    2.509731    1.049038      2.39    0.017      .4536542     4.565807
 hpwt_spaceu |    .7423877    1.540128      0.48    0.630     -2.276208     3.760983
     hpwt_tu |     .023687    .9754441      0.02    0.981     -1.888148     1.935522
 mpdu_spaceu |   -.0483206    3.673517     -0.01    0.990     -7.248282     7.151641
   spaceu_tu |    .7363435    .6167486      1.19    0.233     -.4724615     1.945149
       _cons |   -10.06004    .6846313    -14.69    0.000      -11.4019     -8.71819
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    price
------------------------------------------------------------------------------
r; t=1.79 21:47:48

. // note tougher tolerance
. assert reldif(el(e(beta_plasso),1,1), -0.221208122513718)<1e-5
r; t=0.00 21:47:48

.
.
. // now results from Chernoznukov et al. AER 2015.
. // 6 results replicated, 3 with tol 1e-3, 3 with tol 1e-5
. // Would possibly replicate more closely if Matlab tolerances were tighter.
.
. ******************************
. ******** Small set ***********
. ******************************
.
. // lasso, price (line 72)
. // Matlab output:
. // bDzx =
. //  -0.027187307080839
. //                   0
. //   0.140573386182651
. //                   0
. //  -0.040297610145709
. //   0.043091980749192
. //                   0
. //                   0
. //                   0
. //                   0
. //  22.361611212285307
. //   8.864499676282328
. //  -2.336920687857595
. //   1.571888537853250
. mat b_matlab =                          ///
>         (                                               ///
>   -0.027187307080839,           ///
>                    0,           ///
>    0.140573386182651,           ///
>                    0,           ///
>   -0.040297610145709,           ///
>    0.043091980749192,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>   22.361611212285307,           ///
>    8.864499676282328,           ///
>   -2.336920687857595,           ///
>    1.571888537853250            ///
>    )
r; t=0.00 21:47:48

.
. rlasso price                                                                                                                            ///
>                 sum_othbig_1 sum_othbig_2 sum_othbig_3 sum_othbig_4 sum_othbig_5        ///
>                 sum_rivbig_1 sum_rivbig_2 sum_rivbig_3 sum_rivbig_4 sum_rivbig_5        ///
>                 hpwt air mpd space                                                                                                      ///
>                 , displayall gamma(1) rob maxupsiter(15)                                                        ///
>                 tolups(1e-6) tolzero(1e-4) tolopt(1e-5)

------------------+--------------------------------
         Selected |           Lasso   Post-est OLS
------------------+--------------------------------
     sum_othbig_1 |      -0.0272571     -0.4374508
     sum_othbig_2 |  (not selected) (not selected)
     sum_othbig_3 |       0.1406422      0.4608627
     sum_othbig_4 |  (not selected) (not selected)
     sum_othbig_5 |      -0.0402651      0.1780889
     sum_rivbig_1 |       0.0430951      0.0607921
     sum_rivbig_2 |  (not selected) (not selected)
     sum_rivbig_3 |  (not selected) (not selected)
     sum_rivbig_4 |  (not selected) (not selected)
     sum_rivbig_5 |  (not selected) (not selected)
             hpwt |      22.3623884     25.9292369
              air |       8.8643947      8.5010834
              mpd |      -2.3370630     -3.0185721
            space |       1.5723379      2.9226899
            _cons |*       0.0048033     -2.9963539
------------------+--------------------------------
*Not penalized
r; t=0.08 21:47:48

.
. mat b_rlasso = e(betaAll)
r; t=0.00 21:47:48

. mat b_rlasso = b_rlasso[1,1..colsof(b_rlasso)-1]
r; t=0.00 21:47:48

. // note looser tolerance
. assert mreldif(b_rlasso,b_matlab)<1e-3
r; t=0.00 21:47:48

.
.
. // lasso, dep var (line 83)
. // Matlab output:
. // bYx =
. //  -2.226431503473688
. //  -0.894181896404704
. //   0.234706642184791
. //   1.782524104280113
. mat b_matlab =                          ///
>         (                                               ///
>   -2.226431503473688,           ///
>   -0.894181896404704,           ///
>    0.234706642184791,           ///
>    1.782524104280113            ///
>    )
r; t=0.00 21:47:48

.
. rlasso y                                                                                                                                        ///
>                 hpwt air mpd space                                                                                                      ///
>                 , displayall gamma(1) rob maxupsiter(15)                                                        ///
>                 tolups(1e-6) tolzero(1e-4) tolopt(1e-5)

------------------+--------------------------------
         Selected |           Lasso   Post-est OLS
------------------+--------------------------------
             hpwt |      -2.2264354     -2.6668706
              air |      -0.8941844     -1.0147559
              mpd |       0.2347080      0.4410037
            space |       1.7825423      2.4371977
            _cons |*      -9.2809016    -10.3658574
------------------+--------------------------------
*Not penalized
r; t=0.03 21:47:48

.
. mat b_rlasso = e(betaAll)
r; t=0.00 21:47:48

. mat b_rlasso = b_rlasso[1,1..colsof(b_rlasso)-1]
r; t=0.00 21:47:48

. // note tougher tolerance
. assert mreldif(b_rlasso,b_matlab)<1e-5
r; t=0.00 21:47:48

.
.
. // post-regularization IV (line 94)
. // post-lasso-orthogonalized replicates
. // Matlab output:
. // aL =
. //   -0.184934034947562
. ivlasso y (price=                                                                                                                       ///
>                 sum_othbig_1 sum_othbig_2 sum_othbig_3 sum_othbig_4 sum_othbig_5        ///
>                 sum_rivbig_1 sum_rivbig_2 sum_rivbig_3 sum_rivbig_4 sum_rivbig_5        ///
>                 )                                                                                                                                       ///
>                 (hpwt air mpd space)                                                                                            ///
>                 , rob lopt(gamma(1) maxupsiter(15) tolups(1e-6))
1.  (PDS/CHS) Selecting HD controls for dep var y...
Selected:  hpwt air mpd space
3.  (PDS) Selecting HD controls for endog regressor price...
Selected:  hpwt air mpd
5.  (PDS/CHS) Selecting HD controls/IVs for endog regressor price...
Selected:  hpwt air mpd space sum_othbig_1 sum_othbig_3 sum_othbig_5
          sum_rivbig_1
6a. (CHS) Selecting lasso HD controls and creating optimal IV for endog regressor price...
Selected:  hpwt air mpd space
6b. (CHS) Selecting post-lasso HD controls and creating optimal IV for endog regressor price...
Selected:  hpwt air mpd
7.  (CHS) Creating orthogonalized endogenous regressor price...


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      heteroskedastic
Number of observations:                2,217
Endogenous (1):                        price
High-dim controls (4):                 hpwt air mpd space
Selected controls, PDS (4):            hpwt air mpd space
Selected controls, CHS-L (4):          hpwt air mpd space
Selected controls, CHS-PL (4):         hpwt air mpd space
Unpenalized controls (1):              _cons
High-dim instruments (10):             sum_othbig_1 sum_othbig_2 sum_othbig_3
                                       sum_othbig_4 sum_othbig_5 sum_rivbig_1
                                       sum_rivbig_2 sum_rivbig_3 sum_rivbig_4
                                       sum_rivbig_5
Selected instruments (4):              sum_othbig_1 sum_othbig_3 sum_othbig_5
                                       sum_rivbig_1

Structural equation:

IV using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
            y |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
       price |    -.226732    .0167435    -13.54    0.000     -.2595487    -.1939153
-------------+----------------------------------------------------------------

IV using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
            y |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
       price |   -.1849353    .0141731    -13.05    0.000      -.212714    -.1571566
-------------+----------------------------------------------------------------

IV with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
             |               Robust
            y |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
       price |   -.1867778     .014296    -13.07    0.000     -.2147975    -.1587581
        hpwt |    2.690695     .495631      5.43    0.000      1.719276     3.662114
         air |    1.051139    .1602466      6.56    0.000      .7370616     1.365217
         mpd |    .0701803    .0506931      1.38    0.166     -.0291762     .1695369
       space |    2.236855    .1370175     16.33    0.000      1.968305     2.505404
       _cons |   -9.745845    .2848143    -34.22    0.000     -10.30407    -9.187619
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    price
------------------------------------------------------------------------------
r; t=0.36 21:47:48

. // note tougher tolerance
. assert reldif(el(e(beta_plasso),1,1), -0.184934034947562)<1e-5
r; t=0.00 21:47:48

.
. ******************************
. ******** Big set *************
. ******************************
.
. // lasso, price (line 135)
. // Matlab output:
. /*
> bDzx =
>
>   -0.026309868626536
>                    0
>    0.064576639402394
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>   -0.061816175757360
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>    0.057797411950973
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>  -14.890463278505399
>                    0
>                    0
>                    0
>   20.239078392116543
>                    0
>                    0
>                    0
>                    0
>                    0
>                    0
>   15.468957465755846
>                    0
>    3.499130491002932
>                    0
>                    0
>    6.172115587542651
>                    0
>                    0
>                    0
>    1.525359161441577
>  */
. mat b_matlab =                          ///
>         (                                               ///
>   -0.026309868626536,           ///
>                    0,           ///
>    0.064576639402394,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>   -0.061816175757360,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>    0.057797411950973,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>  -14.890463278505399,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>   20.239078392116543,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>   15.468957465755846,           ///
>                    0,           ///
>    3.499130491002932,           ///
>                    0,           ///
>                    0,           ///
>    6.172115587542651,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>    1.525359161441577            ///
>    )
r; t=0.00 21:47:48

.
. rlasso price                                                                                                                            ///
>                 Z*                                                                                                                                      ///
>                 hpwt air mpdu spaceu tu                                                                                         ///
>                 hpwt_sq-spaceu_tu                                                                                                       ///
>                 , displayall gamma(1) rob maxupsiter(15)                                                        ///
>                 tolups(1e-6) tolzero(1e-4) tolopt(1e-5)

------------------+--------------------------------
         Selected |           Lasso   Post-est OLS
------------------+--------------------------------
              Z_1 |      -0.0263504     -0.2195643
              Z_2 |  (not selected) (not selected)
              Z_3 |       0.0646406      0.3465790
              Z_4 |  (not selected) (not selected)
              Z_5 |  (not selected) (not selected)
              Z_6 |  (not selected) (not selected)
              Z_7 |  (not selected) (not selected)
              Z_8 |  (not selected) (not selected)
              Z_9 |  (not selected) (not selected)
             Z_10 |  (not selected) (not selected)
             Z_11 |      -0.0617943      0.0382309
             Z_12 |  (not selected) (not selected)
             Z_13 |  (not selected) (not selected)
             Z_14 |  (not selected) (not selected)
             Z_15 |  (not selected) (not selected)
             Z_16 |  (not selected) (not selected)
             Z_17 |  (not selected) (not selected)
             Z_18 |  (not selected) (not selected)
             Z_19 |  (not selected) (not selected)
             Z_20 |  (not selected) (not selected)
             Z_21 |  (not selected) (not selected)
             Z_22 |  (not selected) (not selected)
             Z_23 |  (not selected) (not selected)
             Z_24 |  (not selected) (not selected)
             Z_25 |  (not selected) (not selected)
             Z_26 |  (not selected) (not selected)
             Z_27 |  (not selected) (not selected)
             Z_28 |  (not selected) (not selected)
             Z_29 |       0.0577900      0.0145323
             Z_30 |  (not selected) (not selected)
             Z_31 |  (not selected) (not selected)
             Z_32 |  (not selected) (not selected)
             Z_33 |  (not selected) (not selected)
             Z_34 |  (not selected) (not selected)
             Z_35 |  (not selected) (not selected)
             Z_36 |  (not selected) (not selected)
             Z_37 |  (not selected) (not selected)
             Z_38 |  (not selected) (not selected)
             Z_39 |  (not selected) (not selected)
             Z_40 |  (not selected) (not selected)
             Z_41 |  (not selected) (not selected)
             Z_42 |  (not selected) (not selected)
             Z_43 |  (not selected) (not selected)
             Z_44 |  (not selected) (not selected)
             Z_45 |  (not selected) (not selected)
             Z_46 |  (not selected) (not selected)
             Z_47 |  (not selected) (not selected)
             Z_48 |  (not selected) (not selected)
             hpwt |  (not selected) (not selected)
              air |  (not selected) (not selected)
             mpdu |     -14.8918883    -20.3265239
           spaceu |  (not selected) (not selected)
               tu |  (not selected) (not selected)
          hpwt_sq |  (not selected) (not selected)
          hpwt_cu |      20.2415617     29.4116519
          mpdu_sq |  (not selected) (not selected)
          mpdu_cu |  (not selected) (not selected)
        spaceu_sq |  (not selected) (not selected)
        spaceu_cu |  (not selected) (not selected)
            tu_sq |  (not selected) (not selected)
            tu_cu |  (not selected) (not selected)
         hpwt_air |      15.4677213     11.0026026
         mpdu_air |  (not selected) (not selected)
       spaceu_air |       3.4997957      5.8396319
           tu_air |  (not selected) (not selected)
        hpwt_mpdu |  (not selected) (not selected)
      hpwt_spaceu |       6.1717599      6.2193114
          hpwt_tu |  (not selected) (not selected)
      mpdu_spaceu |  (not selected) (not selected)
          mpdu_tu |  (not selected) (not selected)
        spaceu_tu |       1.5261598      5.5650409
            _cons |*       7.1982652     10.6090725
------------------+--------------------------------
*Not penalized
r; t=0.56 21:47:49

.
. mat b_rlasso = e(betaAll)
r; t=0.00 21:47:49

. mat b_rlasso = b_rlasso[1,1..colsof(b_rlasso)-1]
r; t=0.00 21:47:49

. // note looser tolerance
. assert mreldif(b_rlasso,b_matlab)<1e-3
r; t=0.00 21:47:49

.
. // lasso, dep var (line 146)
. // Matlab output:
. /*
> bYx =
>                    0
>   -0.448213818098585
>                    0
>                    0
>                    0
>                    0
>   -2.798818364136941
>                    0
>                    0
>    0.849364554746214
>    1.079486139873257
>                    0
>                    0
>   -0.748743293530742
>   -0.289563827442536
>                    0
>                    0
>                    0
>                    0
>                    0
>    3.512233383389987
>                    0
>                    0
> */
.
. mat b_matlab =                          ///
>         (                                               ///
>                    0,           ///
>   -0.448213818098585,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>   -2.798818364136941,           ///
>                    0,           ///
>                    0,           ///
>    0.849364554746214,           ///
>    1.079486139873257,           ///
>                    0,           ///
>                    0,           ///
>   -0.748743293530742,           ///
>   -0.289563827442536,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>                    0,           ///
>    3.512233383389987,           ///
>                    0,           ///
>                    0            ///
>         )
r; t=0.00 21:47:49

.
. rlasso y                                                                                                                                        ///
>                 hpwt air mpdu spaceu tu                                                                                         ///
>                 hpwt_sq-spaceu_tu                                                                                                       ///
>                 , displayall gamma(1) rob maxupsiter(15)                                                        ///
>                 tolups(1e-6) tolzero(1e-4) tolopt(1e-5)

------------------+--------------------------------
         Selected |           Lasso   Post-est OLS
------------------+--------------------------------
             hpwt |  (not selected) (not selected)
              air |      -0.4482835     -0.8314957
             mpdu |  (not selected) (not selected)
           spaceu |  (not selected) (not selected)
               tu |  (not selected) (not selected)
          hpwt_sq |  (not selected) (not selected)
          hpwt_cu |      -2.7990523     -3.9442645
          mpdu_sq |  (not selected) (not selected)
          mpdu_cu |  (not selected) (not selected)
        spaceu_sq |       0.8504198      3.3325056
        spaceu_cu |       1.0786201     -0.6726752
            tu_sq |  (not selected) (not selected)
            tu_cu |  (not selected) (not selected)
         hpwt_air |      -0.7485333      0.3980872
         mpdu_air |      -0.2898074     -1.3746496
       spaceu_air |  (not selected) (not selected)
           tu_air |  (not selected) (not selected)
        hpwt_mpdu |  (not selected) (not selected)
      hpwt_spaceu |  (not selected) (not selected)
          hpwt_tu |  (not selected) (not selected)
      mpdu_spaceu |       3.5127542      5.7909368
          mpdu_tu |  (not selected) (not selected)
        spaceu_tu |  (not selected) (not selected)
            _cons |*      -8.5048572     -9.3657310
------------------+--------------------------------
*Not penalized
r; t=0.12 21:47:49

.
. mat b_rlasso = e(betaAll)
r; t=0.00 21:47:49

. mat b_rlasso = b_rlasso[1,1..colsof(b_rlasso)-1]
r; t=0.00 21:47:49

. // note looser tolerance
. assert mreldif(b_rlasso,b_matlab)<1e-3
r; t=0.00 21:47:49

.
. // post-regularization IV (line 157)
. // post-lasso-orthogonalized replicates
. // Matlab output:
. // aB =
. //  -0.221208122513718
. ivlasso y (price=                                                                                                                       ///
>                 Z*                                                                                                                                      ///
>                 )                                                                                                                                       ///
>                 (hpwt air mpdu spaceu tu                                                                                        ///
>                 hpwt_sq-spaceu_tu)                                                                                                      ///
>                 , rob lopt(gamma(1) maxupsiter(15) tolups(1e-6))
1.  (PDS/CHS) Selecting HD controls for dep var y...
Selected:  air hpwt_cu spaceu_sq spaceu_cu hpwt_air mpdu_air mpdu_spaceu
3.  (PDS) Selecting HD controls for endog regressor price...
Selected:  mpdu hpwt_cu hpwt_air spaceu_air hpwt_tu spaceu_tu
5.  (PDS/CHS) Selecting HD controls/IVs for endog regressor price...
Selected:  mpdu hpwt_cu hpwt_air spaceu_air hpwt_spaceu spaceu_tu Z_1 Z_3 Z_11
          Z_29
6a. (CHS) Selecting lasso HD controls and creating optimal IV for endog regressor price...
Selected:  air mpdu hpwt_sq hpwt_cu mpdu_cu hpwt_air mpdu_air spaceu_air
          hpwt_tu mpdu_spaceu spaceu_tu
6b. (CHS) Selecting post-lasso HD controls and creating optimal IV for endog regressor price...
Selected:  mpdu hpwt_sq hpwt_cu mpdu_sq tu_cu hpwt_air mpdu_air spaceu_air
          tu_air hpwt_tu mpdu_spaceu spaceu_tu
7.  (CHS) Creating orthogonalized endogenous regressor price...


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      heteroskedastic
Number of observations:                2,217
Endogenous (1):                        price
High-dim controls (23):                hpwt air mpdu spaceu tu hpwt_sq hpwt_cu
                                       mpdu_sq mpdu_cu spaceu_sq spaceu_cu
                                       tu_sq tu_cu hpwt_air mpdu_air spaceu_air
                                       tu_air hpwt_mpdu hpwt_spaceu hpwt_tu
                                       mpdu_spaceu mpdu_tu spaceu_tu
Selected controls, PDS (12):           air mpdu hpwt_cu spaceu_sq spaceu_cu
                                       hpwt_air mpdu_air spaceu_air hpwt_spaceu
                                       hpwt_tu mpdu_spaceu spaceu_tu
Selected controls, CHS-L (14):         air mpdu hpwt_sq hpwt_cu mpdu_cu
                                       spaceu_sq spaceu_cu hpwt_air mpdu_air
                                       spaceu_air hpwt_spaceu hpwt_tu
                                       mpdu_spaceu spaceu_tu
Selected controls, CHS-PL (16):        air mpdu hpwt_sq hpwt_cu mpdu_sq
                                       spaceu_sq spaceu_cu tu_cu hpwt_air
                                       mpdu_air spaceu_air tu_air hpwt_spaceu
                                       hpwt_tu mpdu_spaceu spaceu_tu
Unpenalized controls (1):              _cons
High-dim instruments (48):             Z_1 Z_2 Z_3 Z_4 Z_5 Z_6 Z_7 Z_8 Z_9
                                       Z_10 Z_11 Z_12 Z_13 Z_14 Z_15 Z_16 Z_17
                                       Z_18 Z_19 Z_20 Z_21 Z_22 Z_23 Z_24 Z_25
                                       Z_26 Z_27 Z_28 Z_29 Z_30 Z_31 Z_32 Z_33
                                       Z_34 Z_35 Z_36 Z_37 Z_38 Z_39 Z_40 Z_41
                                       Z_42 Z_43 Z_44 Z_45 Z_46 Z_47 Z_48
Selected instruments (4):              Z_1 Z_3 Z_11 Z_29

Structural equation:

IV using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
            y |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
       price |   -.2854954    .0216236    -13.20    0.000     -.3278768     -.243114
-------------+----------------------------------------------------------------

IV using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
            y |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
       price |     -.22121    .0163464    -13.53    0.000     -.2532483    -.1891716
-------------+----------------------------------------------------------------

IV with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
             |               Robust
            y |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
       price |   -.2400588    .0165342    -14.52    0.000     -.2724653    -.2076523
         air |   -.7516704    1.152868     -0.65    0.514      -3.01125     1.507909
        mpdu |    .6372987    2.025019      0.31    0.753     -3.331665     4.606262
     hpwt_cu |    3.547906    1.628053      2.18    0.029      .3569812     6.738831
   spaceu_sq |    21.12323    3.749161      5.63    0.000      13.77501     28.47145
   spaceu_cu |   -17.08911    3.063951     -5.58    0.000     -23.09434    -11.08387
    hpwt_air |    5.263331    1.276285      4.12    0.000      2.761858     7.764805
    mpdu_air |   -6.733311    1.319556     -5.10    0.000     -9.319593    -4.147029
  spaceu_air |    2.509731    1.049038      2.39    0.017      .4536542     4.565807
 hpwt_spaceu |    .7423877    1.540128      0.48    0.630     -2.276208     3.760983
     hpwt_tu |     .023687    .9754441      0.02    0.981     -1.888148     1.935522
 mpdu_spaceu |   -.0483206    3.673517     -0.01    0.990     -7.248282     7.151641
   spaceu_tu |    .7363435    .6167486      1.19    0.233     -.4724615     1.945149
       _cons |   -10.06004    .6846313    -14.69    0.000      -11.4019     -8.71819
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    price
------------------------------------------------------------------------------
r; t=1.86 21:47:51

. // note tougher tolerance
. assert reldif(el(e(beta_plasso),1,1), -0.221208122513718)<1e-5
r; t=0.00 21:47:51

.
. // ***************** END BLP DATASET ************************* //
.
. // ***************** AJR DATASET ************************* //
.
. // used to check options etc.; no replication.
. // datasets separately downloaded from economics.mit.edu; see help ivlasso.
. clear
r; t=0.01 21:47:51

. use Data\maketable6
r; t=0.09 21:47:51

. merge 1:1 shortnam using Data\maketable8

    Result                           # of obs.
    -----------------------------------------
    not matched                             0
    matched                               163  (_merge==3)
    -----------------------------------------
r; t=0.24 21:47:51

. keep if baseco==1
(99 observations deleted)
r; t=0.00 21:47:51

. order shortnam logpgp95 avexpr lat_abst logem4 edes1975 avelf, first
r; t=0.11 21:47:51

. order indtime euro1900 democ1 cons1 democ00a cons00a, last
r; t=0.01 21:47:51

.
. // examples based on those in ivlasso help file.
.
. //Examples with exogenous regressors:
.
. // Basic usage: select from high-dim controls.
. pdslasso logpgp95 avexpr                                                                                ///
>         (lat_abst edes1975 avelf temp* humid* steplow-oilres)
1.  (PDS/CHS) Selecting HD controls for dep var logpgp95...
Selected:  edes1975 avelf
2.  (PDS/CHS) Selecting HD controls for exog regressor avexpr...
Selected:  edes1975 zinc


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      homoskedastic
Number of observations:                64
Exogenous (1):                         avexpr
High-dim controls (24):                lat_abst edes1975 avelf temp1 temp2
                                       temp3 temp4 temp5 humid1 humid2 humid3
                                       humid4 steplow deslow stepmid desmid
                                       drystep drywint landlock goldm iron silv
                                       zinc oilres
Selected controls (3):                 edes1975 avelf zinc
Unpenalized controls (1):              _cons

Structural equation:

OLS using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |    .4187502    .0536084      7.81    0.000      .3136796     .5238207
-------------+----------------------------------------------------------------

OLS using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |     .391257    .0574894      6.81    0.000      .2785799      .503934
-------------+----------------------------------------------------------------

OLS with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |    .3913455    .0561862      6.97    0.000      .2812225     .5014684
    edes1975 |    .0091289     .003184      2.87    0.004      .0028883     .0153694
       avelf |   -.9974943    .2474453     -4.03    0.000     -1.482478    -.5125104
        zinc |   -.0079226    .0280604     -0.28    0.778     -.0629201     .0470748
       _cons |    5.764133    .3773706     15.27    0.000      5.024501     6.503766
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    avexpr
------------------------------------------------------------------------------
r; t=0.22 21:47:51

.
. // As above, hetoroskedastic-robust.
. pdslasso logpgp95 avexpr                                                                                ///
>         (lat_abst edes1975 avelf temp* humid* steplow-oilres)           ///
>         , rob
1.  (PDS/CHS) Selecting HD controls for dep var logpgp95...
Selected:  edes1975 avelf drystep landlock silv
2.  (PDS/CHS) Selecting HD controls for exog regressor avexpr...
Selected:  edes1975 stepmid landlock iron zinc


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      heteroskedastic
Number of observations:                64
Exogenous (1):                         avexpr
High-dim controls (24):                lat_abst edes1975 avelf temp1 temp2
                                       temp3 temp4 temp5 humid1 humid2 humid3
                                       humid4 steplow deslow stepmid desmid
                                       drystep drywint landlock goldm iron silv
                                       zinc oilres
Selected controls (8):                 edes1975 avelf stepmid drystep landlock
                                       iron silv zinc
Unpenalized controls (1):              _cons

Structural equation:

OLS using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |    .3877013    .0609796      6.36    0.000      .2681836     .5072191
-------------+----------------------------------------------------------------

OLS using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |    .3786846    .0745483      5.08    0.000      .2325726     .5247966
-------------+----------------------------------------------------------------

OLS with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
             |               Robust
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |    .3941882    .0775025      5.09    0.000      .2422862     .5460903
    edes1975 |    .0090592    .0028737      3.15    0.002      .0034269     .0146915
       avelf |   -.9536871    .3248062     -2.94    0.003     -1.590296    -.3170787
     stepmid |    .1397762      .13014      1.07    0.283     -.1152934     .3948459
     drystep |      .00409     .209989      0.02    0.984      -.407481      .415661
    landlock |    .0223137    .1595841      0.14    0.889     -.2904654     .3350929
        iron |    .0115941     .044112      0.26    0.793      -.074864     .0980521
        silv |    .0573208     .035967      1.59    0.111     -.0131733     .1278149
        zinc |   -.0666105    .0614861     -1.08    0.279     -.1871209        .0539
       _cons |    5.722393    .4621069     12.38    0.000       4.81668     6.628106
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    avexpr
------------------------------------------------------------------------------
r; t=0.19 21:47:52

.
. // Specify that latitude is an unpenalized control to be partialled out.
. pdslasso logpgp95 avexpr                                                                                ///
>         (lat_abst edes1975 avelf temp* humid* steplow-oilres)   ///
>         , partial(lat_abst)
Partialling out unpenalized controls...
1.  (PDS/CHS) Selecting HD controls for dep var logpgp95...
Selected:  edes1975 avelf humid3
2.  (PDS/CHS) Selecting HD controls for exog regressor avexpr...
Selected:


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      homoskedastic
Number of observations:                64
Exogenous (1):                         avexpr
High-dim controls (23):                edes1975 avelf temp1 temp2 temp3 temp4
                                       temp5 humid1 humid2 humid3 humid4
                                       steplow deslow stepmid desmid drystep
                                       drywint landlock goldm iron silv zinc
                                       oilres
Selected controls (3):                 edes1975 avelf humid3
Partialled-out controls (1):           lat_abst

Structural equation:

OLS using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |    .4009515    .0542295      7.39    0.000      .2946637     .5072393
-------------+----------------------------------------------------------------

OLS using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |     .293103    .0509508      5.75    0.000      .1932412     .3929648
-------------+----------------------------------------------------------------

OLS with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |    .3596855    .0530236      6.78    0.000      .2557612     .4636099
    edes1975 |    .0084385    .0031334      2.69    0.007      .0022973     .0145798
       avelf |   -.9903407    .2365126     -4.19    0.000     -1.453897    -.5267845
      humid3 |     .010625    .0043199      2.46    0.014      .0021583     .0190918
    lat_abst |    .1868175    .6963272      0.27    0.788     -1.177959     1.551594
       _cons |    5.403213    .3926628     13.76    0.000      4.633608     6.172818
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    avexpr
------------------------------------------------------------------------------
r; t=0.15 21:47:52

.
. // Specify that latitude is an unpenalized control using the notpen option (equivalent).
. pdslasso logpgp95 avexpr                                                                                ///
>         (lat_abst edes1975 avelf temp* humid* steplow-oilres)   ///
>         , pnotpen(lat_abst)
1.  (PDS/CHS) Selecting HD controls for dep var logpgp95...
Selected:  edes1975 avelf humid3
Also inc:  lat_abst
2.  (PDS/CHS) Selecting HD controls for exog regressor avexpr...
Selected:
Also inc:  lat_abst


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      homoskedastic
Number of observations:                64
Exogenous (1):                         avexpr
High-dim controls (23):                edes1975 avelf temp1 temp2 temp3 temp4
                                       temp5 humid1 humid2 humid3 humid4
                                       steplow deslow stepmid desmid drystep
                                       drywint landlock goldm iron silv zinc
                                       oilres
Selected controls (4):                 edes1975 avelf humid3 lat_abst
Unpenalized controls (2):              lat_abst _cons

Structural equation:

OLS using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |    .4009514    .0542295      7.39    0.000      .2946636     .5072392
-------------+----------------------------------------------------------------

OLS using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |     .293103    .0509508      5.75    0.000      .1932412     .3929648
-------------+----------------------------------------------------------------

OLS with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |    .3596855    .0530236      6.78    0.000      .2557612     .4636099
    edes1975 |    .0084385    .0031334      2.69    0.007      .0022973     .0145798
       avelf |   -.9903407    .2365126     -4.19    0.000     -1.453897    -.5267845
      humid3 |     .010625    .0043199      2.46    0.014      .0021583     .0190918
    lat_abst |    .1868175    .6963272      0.27    0.788     -1.177959     1.551594
       _cons |    5.403213    .3926628     13.76    0.000      4.633608     6.172818
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    avexpr
------------------------------------------------------------------------------
r; t=0.88 21:47:53

.
. // Specify that latitude is in the amelioration set.
. pdslasso logpgp95 avexpr                                                                                ///
>         (lat_abst edes1975 avelf temp* humid* steplow-oilres)   ///
>         , aset(lat_abst)
1.  (PDS/CHS) Selecting HD controls for dep var logpgp95...
Selected:  edes1975 avelf
Also inc:  lat_abst
2.  (PDS/CHS) Selecting HD controls for exog regressor avexpr...
Selected:  edes1975 zinc
Also inc:  lat_abst


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      homoskedastic
Number of observations:                64
Exogenous (1):                         avexpr
High-dim controls (24):                lat_abst edes1975 avelf temp1 temp2
                                       temp3 temp4 temp5 humid1 humid2 humid3
                                       humid4 steplow deslow stepmid desmid
                                       drystep drywint landlock goldm iron silv
                                       zinc oilres
Selected controls (4):                 lat_abst edes1975 avelf zinc
  of which, amelioration set (1):      lat_abst
Unpenalized controls (1):              _cons

Structural equation:

OLS using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |    .4187502    .0536084      7.81    0.000      .3136796     .5238207
-------------+----------------------------------------------------------------

OLS using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |    .3930771    .0574059      6.85    0.000      .2805636     .5055906
-------------+----------------------------------------------------------------

OLS with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |    .3925992    .0560087      7.01    0.000      .2828241     .5023743
    lat_abst |   -.4760682    .6912343     -0.69    0.491     -1.830863     .8787262
    edes1975 |    .0099183     .003373      2.94    0.003      .0033073     .0165293
       avelf |   -1.044795     .255921     -4.08    0.000     -1.546391    -.5431993
        zinc |   -.0028598    .0289073     -0.10    0.921     -.0595171     .0537975
       _cons |    5.842409    .3927825     14.87    0.000       5.07257     6.612249
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    avexpr
------------------------------------------------------------------------------
r; t=0.29 21:47:53

.
. // Example with endogenous regressor, high-dimensional controls
. // and low-dimensional instrument:
.
. // Select controls; specify that logem4 is an unpenalized instrument
. // to be partialled out.
. ivlasso logpgp95 (avexpr=logem4)                                                        ///
>         (lat_abst edes1975 avelf temp* humid* steplow-oilres)   ///
>         , partial(logem4)
1.  (PDS/CHS) Selecting HD controls for dep var logpgp95...
Selected:  lat_abst edes1975 temp3 humid2 humid3
3.  (PDS) Selecting HD controls for endog regressor avexpr...
Selected:  lat_abst edes1975 temp3 humid1 humid2 humid3 humid4 iron zinc
4.  (PDS) Selecting HD controls for IV logem4...
Selected:  avelf temp2 temp5 humid2
5.  (CHS) Selecting HD controls and IVs for endog regressor avexpr...
Selected:
Also inc:  logem4
6a. (CHS) Selecting lasso HD controls and creating optimal IV for endog regressor avexpr...
Selected:  lat_abst edes1975 temp3 humid2 humid3
6b. (CHS) Selecting post-lasso HD controls and creating optimal IV for endog regressor avexpr...
Selected:  lat_abst edes1975 temp3 humid2 humid3
7.  (CHS) Creating orthogonalized endogenous regressor avexpr...


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      homoskedastic
Number of observations:                64
Endogenous (1):                        avexpr
High-dim controls (24):                lat_abst edes1975 avelf temp1 temp2
                                       temp3 temp4 temp5 humid1 humid2 humid3
                                       humid4 steplow deslow stepmid desmid
                                       drystep drywint landlock goldm iron silv
                                       zinc oilres
Selected controls, PDS (12):           lat_abst edes1975 avelf temp2 temp3
                                       temp5 humid1 humid2 humid3 humid4 iron
                                       zinc
Selected controls, CHS-L (5):          lat_abst edes1975 temp3 humid2 humid3
Selected controls, CHS-PL (5):         lat_abst edes1975 temp3 humid2 humid3
Partialled-out instruments (1):        logem4

Structural equation:

IV using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |     .977766    .1708062      5.72    0.000      .6429919      1.31254
-------------+----------------------------------------------------------------

IV using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |    1.139098    .2782736      4.09    0.000      .5936921     1.684505
-------------+----------------------------------------------------------------

IV with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |     .765767    .2020636      3.79    0.000      .3697296     1.161804
    lat_abst |   -1.348873    1.369259     -0.99    0.325     -4.032571     1.334824
    edes1975 |    .0019131    .0049826      0.38    0.701     -.0078525     .0116788
       avelf |   -1.131221     .337874     -3.35    0.001     -1.793442    -.4690002
       temp2 |   -.0249502    .0326909     -0.76    0.445     -.0890232     .0391229
       temp3 |     .021731     .026079      0.83    0.405     -.0293829      .072845
       temp5 |   -.0183963    .0227653     -0.81    0.419     -.0630154     .0262228
      humid1 |   -.0432292    .0184622     -2.34    0.019     -.0794144     -.007044
      humid2 |    .0651965    .0290922      2.24    0.025      .0081767     .1222162
      humid3 |    .0458411    .0170148      2.69    0.007      .0124928     .0791895
      humid4 |    -.043253    .0205977     -2.10    0.036     -.0836239    -.0028822
        iron |   -.1437898    .0835631     -1.72    0.085     -.3075705     .0199909
        zinc |    .0531055    .0584786      0.91    0.364     -.0615104     .1677214
       _cons |    2.157911     2.00102      1.08    0.281     -1.764016     6.079839
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    avexpr
------------------------------------------------------------------------------
r; t=0.84 21:47:54

.
. // Example with endogenous regressor and high-dimensional instruments and controls:
.
. // Select controls and instruments; specify that logem4 is an unpenalized
. // instrument and lat_abst is an unpenalized control; request weak
. // identification stats and first-stage results.
. ivlasso logpgp95                                                                                        ///
>         (lat_abst edes1975 avelf temp* humid* steplow-oilres)   ///
>         (avexpr=logem4 euro1900-cons00a)                                                ///
>         , partial(logem4 lat_abst) idstats first
Partialling out unpenalized controls...
1.  (PDS/CHS) Selecting HD controls for dep var logpgp95...
Selected:  edes1975 humid3
3.  (PDS) Selecting HD controls for endog regressor avexpr...
Selected:  edes1975
5.  (PDS/CHS) Selecting HD controls/IVs for endog regressor avexpr...
Selected:
Also inc:  logem4
6a. (CHS) Selecting lasso HD controls and creating optimal IV for endog regressor avexpr...
Selected:  edes1975 avelf temp2 drystep
6b. (CHS) Selecting post-lasso HD controls and creating optimal IV for endog regressor avexpr...
Selected:  edes1975 avelf temp2 drystep
7.  (CHS) Creating orthogonalized endogenous regressor avexpr...


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      homoskedastic
Number of observations:                59
Endogenous (1):                        avexpr
High-dim controls (23):                edes1975 avelf temp1 temp2 temp3 temp4
                                       temp5 humid1 humid2 humid3 humid4
                                       steplow deslow stepmid desmid drystep
                                       drywint landlock goldm iron silv zinc
                                       oilres
Selected controls, PDS (2):            edes1975 humid3
Selected controls, CHS-L (5):          edes1975 avelf temp2 humid3 drystep
Selected controls, CHS-PL (5):         edes1975 avelf temp2 humid3 drystep
Partialled-out controls (1):           lat_abst
High-dim instruments (5):              euro1900 democ1 cons1 democ00a cons00a
Selected instruments (1):              logem4
Partialled-out instruments (1):        logem4

First-stage estimation(s):
-------------+----------------------------------------------------------------
       avexpr |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
    edes1975 |    .0156071    .0074681      2.09    0.037        .00097     .0302442
      humid3 |     .016044    .0096802      1.66    0.097     -.0029289     .0350168
      logem4 |   -.3705068    .1450972     -2.55    0.011      -.654892    -.0861216
-------------+----------------------------------------------------------------

Weak identification F stats (i.i.d.):
  Optimal Lasso IV(s):        19.85
  Optimal Post-Lasso IV(s):    13.24
  Full IV set:                 6.08

Structural equation:

IV using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |    .7667961    .1914687      4.00    0.000      .3915242     1.142068
-------------+----------------------------------------------------------------

IV using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |    .8394174     .362614      2.31    0.021       .128707     1.550128
-------------+----------------------------------------------------------------

IV with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |    .8735301    .2929925      2.98    0.003      .2992753     1.447785
    edes1975 |    .0013051    .0083678      0.16    0.876     -.0150955     .0177057
      humid3 |    .0031166    .0087269      0.36    0.721     -.0139878      .020221
    lat_abst |   -.5020038    1.254352     -0.40    0.689     -2.960489     1.956482
       _cons |    2.253524    1.528477      1.47    0.140     -.7422353     5.249283
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    avexpr
------------------------------------------------------------------------------
r; t=1.13 21:47:55

.
. // Select controls and instruments; specify that lat_abst
. // is an unpenalized control; request weak identification
. // stats and sup-score confidence sets.
. ivlasso logpgp95                                                                                        ///
>         (lat_abst edes1975 avelf temp* humid* steplow-oilres)   ///
>         (avexpr=logem4 euro1900-cons00a)                                                ///
>         ,partial(lat_abst) idstats sscset
Partialling out unpenalized controls...
1.  (PDS/CHS) Selecting HD controls for dep var logpgp95...
Selected:  edes1975 humid3
3.  (PDS) Selecting HD controls for endog regressor avexpr...
Selected:  edes1975
5.  (PDS/CHS) Selecting HD controls/IVs for endog regressor avexpr...
Selected:  logem4 euro1900
6a. (CHS) Selecting lasso HD controls and creating optimal IV for endog regressor avexpr...
Selected:  edes1975 temp3 iron zinc
6b. (CHS) Selecting post-lasso HD controls and creating optimal IV for endog regressor avexpr...
Selected:  edes1975 temp3 drystep iron
7.  (CHS) Creating orthogonalized endogenous regressor avexpr...
8.  (PDS/CHS) Performing sup-score test(s)
Estimating sup-score confidence set over 100 grid points
----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5
..................................................    50
..................................................   100


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      homoskedastic
Number of observations:                59
Endogenous (1):                        avexpr
High-dim controls (23):                edes1975 avelf temp1 temp2 temp3 temp4
                                       temp5 humid1 humid2 humid3 humid4
                                       steplow deslow stepmid desmid drystep
                                       drywint landlock goldm iron silv zinc
                                       oilres
Selected controls, PDS (2):            edes1975 humid3
Selected controls, CHS-L (5):          edes1975 temp3 humid3 iron zinc
Selected controls, CHS-PL (5):         edes1975 temp3 humid3 drystep iron
Partialled-out controls (1):           lat_abst
High-dim instruments (6):              logem4 euro1900 democ1 cons1 democ00a
                                       cons00a
Selected instruments (2):              logem4 euro1900

Weak identification F stats (i.i.d.):
  Optimal Lasso IV(s):        14.38
  Optimal Post-Lasso IV(s):    15.23
  Full IV set:                 3.67

Sup-score weak-identification-robust tests (method=abound)
H0: b(avexpr)=0   (5% significance level)
  Lasso-orthogonalized:      reject
  Post-lasso-orthogonalized: reject
  No orthogonalization:      n.a.
95% confidence set (grid min=-0.77, max=1.68, points=100):
  Lasso-orthogonalized:      [ .393885,   ...  ]
  Post-lasso-orthogonalized: [ .319881,   ...  ]
  No orthogonalization:      n.a.

Structural equation:

IV using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |    .7953799    .2096509      3.79    0.000      .3844716     1.206288
-------------+----------------------------------------------------------------

IV using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |    1.208319    .6336821      1.91    0.057     -.0336749     2.450313
-------------+----------------------------------------------------------------

IV with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |    .8149497    .2499039      3.26    0.001       .325147     1.304752
    edes1975 |    .0026105     .007416      0.35    0.725     -.0119247     .0171457
      humid3 |    .0040908    .0079481      0.51    0.607     -.0114872     .0196688
    lat_abst |   -.4028061    1.158143     -0.35    0.728     -2.672724     1.867112
       _cons |     2.54553     1.31519      1.94    0.053     -.0321958     5.123256
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    avexpr
------------------------------------------------------------------------------
r; t=3.24 21:47:58

.
. // As above but heteroskedastic-robust and use grid options
. // to control grid search and test level; also set seed in rlasso
. // options to make multiplier-bootstrap p-values replicable.
. ivlasso logpgp95                                                                                        ///
>         (lat_abst edes1975 avelf temp* humid* steplow-oilres)   ///
>         (avexpr=logem4 euro1900-cons00a)                                                ///
>         ,partial(lat_abst) rob idstats                                                  ///
>         sscset ssgridmin(0) ssgridmax(2) ssgamma(0.1)                   ///
>         lopt(seed(1))
Partialling out unpenalized controls...
1.  (PDS/CHS) Selecting HD controls for dep var logpgp95...
Selected:  edes1975 humid3 landlock
3.  (PDS) Selecting HD controls for endog regressor avexpr...
Selected:  edes1975 landlock
5.  (PDS/CHS) Selecting HD controls/IVs for endog regressor avexpr...
Selected:  landlock iron euro1900 cons00a
6a. (CHS) Selecting lasso HD controls and creating optimal IV for endog regressor avexpr...
Selected:  edes1975 temp3 landlock iron
6b. (CHS) Selecting post-lasso HD controls and creating optimal IV for endog regressor avexpr...
Selected:  edes1975 temp3 stepmid landlock iron
7.  (CHS) Creating orthogonalized endogenous regressor avexpr...
8.  (PDS/CHS) Performing sup-score test(s)
Estimating sup-score confidence set over 100 grid points
----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5
..................................................    50
..................................................   100


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      heteroskedastic
Number of observations:                59
Endogenous (1):                        avexpr
High-dim controls (23):                edes1975 avelf temp1 temp2 temp3 temp4
                                       temp5 humid1 humid2 humid3 humid4
                                       steplow deslow stepmid desmid drystep
                                       drywint landlock goldm iron silv zinc
                                       oilres
Selected controls, PDS (4):            edes1975 humid3 landlock iron
Selected controls, CHS-L (5):          edes1975 temp3 humid3 landlock iron
Selected controls, CHS-PL (6):         edes1975 temp3 humid3 stepmid landlock
                                       iron
Partialled-out controls (1):           lat_abst
High-dim instruments (6):              logem4 euro1900 democ1 cons1 democ00a
                                       cons00a
Selected instruments (2):              euro1900 cons00a

Weak identification F stats (i.i.d.):
  Optimal Lasso IV(s):         3.64
  Optimal Post-Lasso IV(s):     2.47
  Full IV set:                 0.99
Weak identification F stats (robust):
  Optimal Lasso IV(s):         6.49
  Optimal Post-Lasso IV(s):     2.43
  Full IV set:                 1.94

Sup-score weak-identification-robust tests (method=abound)
H0: b(avexpr)=0   (10% significance level)
  Lasso-orthogonalized:      reject
  Post-lasso-orthogonalized: fail to reject
  No orthogonalization:      n.a.
90% confidence set (grid min=0.00, max=2.00, points=100):
  Lasso-orthogonalized:      [ .262626, 1.51515]
  Post-lasso-orthogonalized: entire grid
  No orthogonalization:      n.a.

Structural equation:

IV using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |    .6332145    .1796479      3.52    0.000       .281111      .985318
-------------+----------------------------------------------------------------

IV using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |    .6586291    .4053836      1.62    0.104     -.1359082     1.453166
-------------+----------------------------------------------------------------

IV with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
             |               Robust
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |    .5624004    .3646416      1.54    0.123      -.152284     1.277085
    edes1975 |    .0103874    .0054565      1.90    0.057     -.0003071      .021082
      humid3 |    .0082101     .008266      0.99    0.321     -.0079908     .0244111
    landlock |    .1949715    .4346825      0.45    0.654     -.6569904     1.046934
        iron |   -.0473915    .0771206     -0.61    0.539     -.1985451     .1037622
    lat_abst |    .1030756    .8598071      0.12    0.905     -1.582115     1.788267
       _cons |    3.769553    2.029699      1.86    0.063     -.2085838     7.747689
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    avexpr
------------------------------------------------------------------------------
r; t=3.45 21:48:02

.
.
. // Weights
.
. // make sure that the same sample is used throughout.
. cap drop touse
r; t=0.00 21:48:02

. gen touse=(democ1<.)
r; t=0.00 21:48:02

.
. cap drop one
r; t=0.00 21:48:02

. cap drop wt
r; t=0.00 21:48:02

. gen double one=1
r; t=0.00 21:48:02

. // use a non-integer weight
. global wtvar logpgp95
r; t=0.00 21:48:02

. gen double wt=$wtvar
r; t=0.00 21:48:02

. // assumes no missings for any regressors or dep var
. sum wt if touse

    Variable |        Obs        Mean    Std. Dev.       Min        Max
-------------+---------------------------------------------------------
          wt |         59    8.017272    .9988773   6.109248   10.21574
r; t=0.00 21:48:02

. replace wt = wt * 1/r(mean) if touse
(59 real changes made)
r; t=0.00 21:48:02

.
. * Basic estimation with constant and no partialling etc.
. * w_c_ vars are centered (demeaned using weighted means)
. * and then weighted by the sqrt of the weighting var.
.
. cap drop w_*
r; t=0.00 21:48:02

. * weighted centering (so no intercept)
. foreach var of varlist logpgp95 avexpr lat_abst logem4 edes1975 avelf           ///
>         temp* humid* steplow-oilres euro1900-cons00a {
  2.         qui sum `var' [aw=wt] if touse, meanonly
  3.         qui gen double w_c_`var' = (`var'-r(mean))*sqrt(wt) if touse
  4. }
r; t=0.00 21:48:02

.
. // basic PDS
. foreach opt in "" "rob" {
  2.         // cons automatically partialled out
.         pdslasso logpgp95 avexpr                                                                                                ///
>                 (lat_abst edes1975 avelf temp* humid*)                                                          ///
>                 [aw=logpgp95] if touse                                                                                          ///
>                 , lopt(tolzero(1e-10) tolups(1e-10) tolopt(1e-8)) `opt'
  3.         savedresults save pdslasso e()
  4.         mat b_pds=e(beta_pds)
  5.         mat V_pds=e(V_pds)
  6.         mat b_plasso=e(beta_plasso)
  7.         mat V_plasso=e(V_plasso)
  8.         mat b_lasso=e(beta_lasso)
  9.         mat V_lasso=e(V_lasso)
 10.         // prestd rlasso option
.         pdslasso logpgp95 avexpr                                                                                                ///
>                 (lat_abst edes1975 avelf temp* humid*)                                                          ///
>                 [aw=logpgp95] if touse                                                                                          ///
>                 , lopt(prestd tolzero(1e-10) tolups(1e-10) tolopt(1e-8)) `opt'
 11.         savedresults comp pdslasso e(), exclude(macros: loptions) tol(1e-9)
 12.         pdslasso w_c_logpgp95 w_c_avexpr                                                                                ///
>                 (w_c_lat_abst w_c_edes1975 w_c_avelf w_c_temp* w_c_humid*)                      ///
>                 if touse                                                                                                                        ///
>                 , nocons dm lopt(tolzero(1e-10) tolups(1e-10) tolopt(1e-8)) `opt'
 13.         // no constant to compare
.         mat b_pds=b_pds[1,1..colsof(b_pds)-1]
 14.         mat V_pds=V_pds[1..rowsof(V_pds),1..colsof(V_pds)-1]
 15.         mat V_pds=V_pds[1..rowsof(V_pds)-1,1..colsof(V_pds)]
 16.         assert mreldif(e(beta_pds),b_pds)<1e-8
 17.         assert mreldif(e(V_pds),V_pds)<1e-8
 18.         assert mreldif(e(beta_plasso),b_plasso)<1e-8
 19.         assert mreldif(e(V_plasso),V_plasso)<1e-8
 20.         assert mreldif(e(beta_lasso),b_lasso)<1e-8
 21.         assert mreldif(e(V_lasso),V_lasso)<1e-8
 22. }
(sum of wgt is     4.7302e+02)
Partialling out unpenalized controls...
1.  (PDS/CHS) Selecting HD controls for dep var logpgp95...
Selected:  edes1975 avelf
2.  (PDS/CHS) Selecting HD controls for exog regressor avexpr...
Selected:  edes1975


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      homoskedastic
Number of observations:                59
Exogenous (1):                         avexpr
High-dim controls (12):                lat_abst edes1975 avelf temp1 temp2
                                       temp3 temp4 temp5 humid1 humid2 humid3
                                       humid4
Selected controls (2):                 edes1975 avelf

Structural equation:

OLS using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |    .3842038    .0519129      7.40    0.000      .2824564     .4859511
-------------+----------------------------------------------------------------

OLS using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |    .3653392    .0527012      6.93    0.000      .2620468     .4686317
-------------+----------------------------------------------------------------

OLS with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |    .3657956    .0527073      6.94    0.000      .2624912     .4690999
    edes1975 |    .0096487    .0028559      3.38    0.001      .0040513     .0152461
       avelf |   -.7965314    .2411654     -3.30    0.001     -1.269207     -.323856
       _cons |    5.844511    .3469955     16.84    0.000      5.164412      6.52461
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    avexpr
------------------------------------------------------------------------------
(sum of wgt is     4.7302e+02)
Partialling out unpenalized controls...
1.  (PDS/CHS) Selecting HD controls for dep var logpgp95...
Selected:  edes1975 avelf
2.  (PDS/CHS) Selecting HD controls for exog regressor avexpr...
Selected:  edes1975


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      homoskedastic
Number of observations:                59
Exogenous (1):                         avexpr
High-dim controls (12):                lat_abst edes1975 avelf temp1 temp2
                                       temp3 temp4 temp5 humid1 humid2 humid3
                                       humid4
Selected controls (2):                 edes1975 avelf

Structural equation:

OLS using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |    .3842038    .0519129      7.40    0.000      .2824564     .4859511
-------------+----------------------------------------------------------------

OLS using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |    .3653392    .0527012      6.93    0.000      .2620468     .4686317
-------------+----------------------------------------------------------------

OLS with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |    .3657956    .0527073      6.94    0.000      .2624912     .4690999
    edes1975 |    .0096487    .0028559      3.38    0.001      .0040513     .0152461
       avelf |   -.7965314    .2411654     -3.30    0.001     -1.269207     -.323856
       _cons |    5.844511    .3469955     16.84    0.000      5.164412      6.52461
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    avexpr
------------------------------------------------------------------------------
1.  (PDS/CHS) Selecting HD controls for dep var w_c_logpgp95...
Selected:  w_c_edes1975 w_c_avelf
2.  (PDS/CHS) Selecting HD controls for exog regressor w_c_avexpr...
Selected:  w_c_edes1975


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      homoskedastic
Number of observations:                59
Exogenous (1):                         w_c_avexpr
High-dim controls (12):                w_c_lat_abst w_c_edes1975 w_c_avelf
                                       w_c_temp1 w_c_temp2 w_c_temp3 w_c_temp4
                                       w_c_temp5 w_c_humid1 w_c_humid2
                                       w_c_humid3 w_c_humid4
Selected controls (2):                 w_c_edes1975 w_c_avelf

Structural equation:

OLS using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
 w_c_logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
  w_c_avexpr |    .3842038    .0519129      7.40    0.000      .2824564     .4859511
-------------+----------------------------------------------------------------

OLS using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
 w_c_logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
  w_c_avexpr |    .3653392    .0527012      6.93    0.000      .2620468     .4686317
-------------+----------------------------------------------------------------

OLS with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
 w_c_logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
  w_c_avexpr |    .3657956    .0527073      6.94    0.000      .2624912     .4690999
w_c_edes1975 |    .0096487    .0028559      3.38    0.001      .0040513     .0152461
   w_c_avelf |   -.7965314    .2411654     -3.30    0.001     -1.269207     -.323856
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    w_c_avexpr
------------------------------------------------------------------------------
(sum of wgt is     4.7302e+02)
Partialling out unpenalized controls...
1.  (PDS/CHS) Selecting HD controls for dep var logpgp95...
Selected:  edes1975 avelf humid3
2.  (PDS/CHS) Selecting HD controls for exog regressor avexpr...
Selected:  edes1975


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      heteroskedastic
Number of observations:                59
Exogenous (1):                         avexpr
High-dim controls (12):                lat_abst edes1975 avelf temp1 temp2
                                       temp3 temp4 temp5 humid1 humid2 humid3
                                       humid4
Selected controls (3):                 edes1975 avelf humid3

Structural equation:

OLS using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |    .3739505    .0539022      6.94    0.000      .2683042     .4795969
-------------+----------------------------------------------------------------

OLS using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |    .3308952    .0590654      5.60    0.000      .2151292     .4466612
-------------+----------------------------------------------------------------

OLS with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
             |               Robust
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |    .3411153    .0599502      5.69    0.000      .2236151     .4586154
    edes1975 |    .0098944    .0027656      3.58    0.000      .0044739      .015315
       avelf |    -.787424    .2367708     -3.33    0.001     -1.251486    -.3233617
      humid3 |    .0109864    .0038349      2.86    0.004        .00347     .0185027
       _cons |    5.446995    .4084383     13.34    0.000      4.646471      6.24752
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    avexpr
------------------------------------------------------------------------------
(sum of wgt is     4.7302e+02)
Partialling out unpenalized controls...
1.  (PDS/CHS) Selecting HD controls for dep var logpgp95...
Selected:  edes1975 avelf humid3
2.  (PDS/CHS) Selecting HD controls for exog regressor avexpr...
Selected:  edes1975


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      heteroskedastic
Number of observations:                59
Exogenous (1):                         avexpr
High-dim controls (12):                lat_abst edes1975 avelf temp1 temp2
                                       temp3 temp4 temp5 humid1 humid2 humid3
                                       humid4
Selected controls (3):                 edes1975 avelf humid3

Structural equation:

OLS using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |    .3739505    .0539022      6.94    0.000      .2683042     .4795969
-------------+----------------------------------------------------------------

OLS using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |    .3308952    .0590654      5.60    0.000      .2151292     .4466612
-------------+----------------------------------------------------------------

OLS with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
             |               Robust
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |    .3411153    .0599502      5.69    0.000      .2236151     .4586154
    edes1975 |    .0098944    .0027656      3.58    0.000      .0044739      .015315
       avelf |    -.787424    .2367708     -3.33    0.001     -1.251486    -.3233617
      humid3 |    .0109864    .0038349      2.86    0.004        .00347     .0185027
       _cons |    5.446995    .4084383     13.34    0.000      4.646471      6.24752
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    avexpr
------------------------------------------------------------------------------
1.  (PDS/CHS) Selecting HD controls for dep var w_c_logpgp95...
Selected:  w_c_edes1975 w_c_avelf w_c_humid3
2.  (PDS/CHS) Selecting HD controls for exog regressor w_c_avexpr...
Selected:  w_c_edes1975


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      heteroskedastic
Number of observations:                59
Exogenous (1):                         w_c_avexpr
High-dim controls (12):                w_c_lat_abst w_c_edes1975 w_c_avelf
                                       w_c_temp1 w_c_temp2 w_c_temp3 w_c_temp4
                                       w_c_temp5 w_c_humid1 w_c_humid2
                                       w_c_humid3 w_c_humid4
Selected controls (3):                 w_c_edes1975 w_c_avelf w_c_humid3

Structural equation:

OLS using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
 w_c_logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
  w_c_avexpr |    .3739505    .0539022      6.94    0.000      .2683042     .4795969
-------------+----------------------------------------------------------------

OLS using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
 w_c_logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
  w_c_avexpr |    .3308952    .0590654      5.60    0.000      .2151292     .4466612
-------------+----------------------------------------------------------------

OLS with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
             |               Robust
 w_c_logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
  w_c_avexpr |    .3411153    .0599502      5.69    0.000      .2236151     .4586154
w_c_edes1975 |    .0098944    .0027656      3.58    0.000      .0044739      .015315
   w_c_avelf |    -.787424    .2367708     -3.33    0.001     -1.251486    -.3233617
  w_c_humid3 |    .0109864    .0038349      2.86    0.004        .00347     .0185027
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    w_c_avexpr
------------------------------------------------------------------------------
r; t=0.88 21:48:02

.
. // IV
. foreach opt in "" "rob" {
  2.         // cons automatically partialled out
.         ivlasso logpgp95 (avexpr=logem4 euro1900-cons00a)                                               ///
>                 (lat_abst edes1975 avelf temp* humid*)                                                          ///
>                 [aw=logpgp95]                                                                                                           ///
>                 , lopt(tolzero(1e-10) tolups(1e-10) tolopt(1e-8))                                       ///
>                 first `opt'
  3.         savedresults save ivlasso e()
  4.         mat b_pds=e(beta_pds)
  5.         mat V_pds=e(V_pds)
  6.         mat b_plasso=e(beta_plasso)
  7.         mat V_plasso=e(V_plasso)
  8.         mat b_lasso=e(beta_lasso)
  9.         mat V_lasso=e(V_lasso)
 10.         est restore _ivlasso_avexpr
 11.         mat b_avexpr = e(b)
 12.         // prestd rlasso option
.         ivlasso logpgp95 (avexpr=logem4 euro1900-cons00a)                                               ///
>                 (lat_abst edes1975 avelf temp* humid*)                                                          ///
>                 [aw=logpgp95]                                                                                                           ///
>                 , lopt(prestd tolzero(1e-10) tolups(1e-10) tolopt(1e-8))                        ///
>                 first `opt'
 13.         savedresults comp ivlasso e(), exclude(macros: loptions) tol(1e-7)
 14.         // preweighted data
.         ivlasso w_c_logpgp95 (w_c_avexpr=w_c_logem4 w_c_euro1900-w_c_cons00a)   ///
>                 (w_c_lat_abst w_c_edes1975 w_c_avelf w_c_temp* w_c_humid*)                      ///
>                 , nocons dm lopt(tolzero(1e-10) tolups(1e-10) tolopt(1e-8))                     ///
>                 first `opt'
 15.         // no constant to compare
.         mat b_pds=b_pds[1,1..colsof(b_pds)-1]
 16.         mat V_pds=V_pds[1..rowsof(V_pds),1..colsof(V_pds)-1]
 17.         mat V_pds=V_pds[1..rowsof(V_pds)-1,1..colsof(V_pds)]
 18.         assert mreldif(e(beta_pds),b_pds)<1e-8
 19.         assert mreldif(e(V_pds),V_pds)<1e-8
 20.         assert mreldif(e(beta_plasso),b_plasso)<1e-8
 21.         assert mreldif(e(V_plasso),V_plasso)<1e-8
 22.         assert mreldif(e(beta_lasso),b_lasso)<1e-8
 23.         assert mreldif(e(V_lasso),V_lasso)<1e-8
 24.         // compare first-stage regressions
.         est restore _ivlasso_w_c_avexpr
 25.         mat b_w_c_avexpr = e(b)
 26.         assert mreldif(b_avexpr,b_w_c_avexpr)<1e-10
 27. }
(sum of wgt is     4.7302e+02)
Partialling out unpenalized controls...
1.  (PDS/CHS) Selecting HD controls for dep var logpgp95...
Selected:  edes1975 avelf
3.  (PDS) Selecting HD controls for endog regressor avexpr...
Selected:  edes1975
5.  (PDS/CHS) Selecting HD controls/IVs for endog regressor avexpr...
Selected:  logem4 euro1900
6a. (CHS) Selecting lasso HD controls and creating optimal IV for endog regressor avexpr...
Selected:  edes1975 temp2 humid2
6b. (CHS) Selecting post-lasso HD controls and creating optimal IV for endog regressor avexpr...
Selected:  edes1975 temp2 humid2
7.  (CHS) Creating orthogonalized endogenous regressor avexpr...


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      homoskedastic
Number of observations:                59
Endogenous (1):                        avexpr
High-dim controls (12):                lat_abst edes1975 avelf temp1 temp2
                                       temp3 temp4 temp5 humid1 humid2 humid3
                                       humid4
Selected controls, PDS (2):            edes1975 avelf
Selected controls, CHS-L (4):          edes1975 avelf temp2 humid2
Selected controls, CHS-PL (4):         edes1975 avelf temp2 humid2
High-dim instruments (6):              logem4 euro1900 democ1 cons1 democ00a
                                       cons00a
Selected instruments (2):              logem4 euro1900

First-stage estimation(s):
-------------+----------------------------------------------------------------
       avexpr |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
    edes1975 |   -.0097348    .0238715     -0.41    0.683      -.056522     .0370525
       avelf |    .5143572    .5795852      0.89    0.375     -.6216088     1.650323
      logem4 |   -.4017744    .1617206     -2.48    0.013     -.7187409    -.0848078
    euro1900 |    .0344847    .0266322      1.29    0.195     -.0177135     .0866829
-------------+----------------------------------------------------------------

Structural equation:

IV using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |    .6941581    .1371803      5.06    0.000      .4252897     .9630266
-------------+----------------------------------------------------------------

IV using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |     .793109    .1932914      4.10    0.000      .4142647     1.171953
-------------+----------------------------------------------------------------

IV with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |    .6688488    .1607691      4.16    0.000      .3537472     .9839504
    edes1975 |    .0010034    .0054984      0.18    0.855     -.0097734     .0117801
       avelf |   -.8455103    .3021786     -2.80    0.005      -1.43777    -.2532511
       _cons |     4.02629     .980929      4.10    0.000      2.103704     5.948875
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    avexpr
------------------------------------------------------------------------------
(results _ivlasso_avexpr are active now)
(sum of wgt is     4.7302e+02)
Partialling out unpenalized controls...
1.  (PDS/CHS) Selecting HD controls for dep var logpgp95...
Selected:  edes1975 avelf
3.  (PDS) Selecting HD controls for endog regressor avexpr...
Selected:  edes1975
5.  (PDS/CHS) Selecting HD controls/IVs for endog regressor avexpr...
Selected:  logem4 euro1900
6a. (CHS) Selecting lasso HD controls and creating optimal IV for endog regressor avexpr...
Selected:  edes1975 temp2 humid2
6b. (CHS) Selecting post-lasso HD controls and creating optimal IV for endog regressor avexpr...
Selected:  edes1975 temp2 humid2
7.  (CHS) Creating orthogonalized endogenous regressor avexpr...


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      homoskedastic
Number of observations:                59
Endogenous (1):                        avexpr
High-dim controls (12):                lat_abst edes1975 avelf temp1 temp2
                                       temp3 temp4 temp5 humid1 humid2 humid3
                                       humid4
Selected controls, PDS (2):            edes1975 avelf
Selected controls, CHS-L (4):          edes1975 avelf temp2 humid2
Selected controls, CHS-PL (4):         edes1975 avelf temp2 humid2
High-dim instruments (6):              logem4 euro1900 democ1 cons1 democ00a
                                       cons00a
Selected instruments (2):              logem4 euro1900

First-stage estimation(s):
-------------+----------------------------------------------------------------
       avexpr |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
    edes1975 |   -.0097348    .0238715     -0.41    0.683      -.056522     .0370525
       avelf |    .5143572    .5795852      0.89    0.375     -.6216088     1.650323
      logem4 |   -.4017744    .1617206     -2.48    0.013     -.7187409    -.0848078
    euro1900 |    .0344847    .0266322      1.29    0.195     -.0177135     .0866829
-------------+----------------------------------------------------------------

Structural equation:

IV using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |    .6941581    .1371803      5.06    0.000      .4252897     .9630265
-------------+----------------------------------------------------------------

IV using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |     .793109    .1932914      4.10    0.000      .4142647     1.171953
-------------+----------------------------------------------------------------

IV with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |    .6688488    .1607691      4.16    0.000      .3537472     .9839504
    edes1975 |    .0010034    .0054984      0.18    0.855     -.0097734     .0117801
       avelf |   -.8455103    .3021786     -2.80    0.005      -1.43777    -.2532511
       _cons |     4.02629     .980929      4.10    0.000      2.103704     5.948875
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    avexpr
------------------------------------------------------------------------------
1.  (PDS/CHS) Selecting HD controls for dep var w_c_logpgp95...
Selected:  w_c_edes1975 w_c_avelf
3.  (PDS) Selecting HD controls for endog regressor w_c_avexpr...
Selected:  w_c_edes1975
5.  (PDS/CHS) Selecting HD controls/IVs for endog regressor w_c_avexpr...
Selected:  w_c_logem4 w_c_euro1900
6a. (CHS) Selecting lasso HD controls and creating optimal IV for endog regressor w_c_avexpr...
Selected:  w_c_edes1975 w_c_temp2 w_c_humid2
6b. (CHS) Selecting post-lasso HD controls and creating optimal IV for endog regressor w_c_avexpr...
Selected:  w_c_edes1975 w_c_temp2 w_c_humid2
7.  (CHS) Creating orthogonalized endogenous regressor w_c_avexpr...


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      homoskedastic
Number of observations:                59
Endogenous (1):                        w_c_avexpr
High-dim controls (12):                w_c_lat_abst w_c_edes1975 w_c_avelf
                                       w_c_temp1 w_c_temp2 w_c_temp3 w_c_temp4
                                       w_c_temp5 w_c_humid1 w_c_humid2
                                       w_c_humid3 w_c_humid4
Selected controls, PDS (2):            w_c_edes1975 w_c_avelf
Selected controls, CHS-L (4):          w_c_edes1975 w_c_avelf w_c_temp2
                                       w_c_humid2
Selected controls, CHS-PL (4):         w_c_edes1975 w_c_avelf w_c_temp2
                                       w_c_humid2
High-dim instruments (6):              w_c_logem4 w_c_euro1900 w_c_democ1
                                       w_c_cons1 w_c_democ00a w_c_cons00a
Selected instruments (2):              w_c_logem4 w_c_euro1900

First-stage estimation(s):
-------------+----------------------------------------------------------------
   w_c_avexpr |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
w_c_edes1975 |   -.0097348    .0238715     -0.41    0.683      -.056522     .0370525
   w_c_avelf |    .5143572    .5795852      0.89    0.375     -.6216088     1.650323
  w_c_logem4 |   -.4017744    .1617206     -2.48    0.013     -.7187409    -.0848078
w_c_euro1900 |    .0344847    .0266322      1.29    0.195     -.0177135     .0866829
-------------+----------------------------------------------------------------

Structural equation:

IV using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
 w_c_logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
  w_c_avexpr |    .6941581    .1371803      5.06    0.000      .4252897     .9630266
-------------+----------------------------------------------------------------

IV using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
 w_c_logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
  w_c_avexpr |     .793109    .1932914      4.10    0.000      .4142647     1.171953
-------------+----------------------------------------------------------------

IV with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
 w_c_logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
  w_c_avexpr |    .6688488    .1607691      4.16    0.000      .3537472     .9839504
w_c_edes1975 |    .0010034    .0054984      0.18    0.855     -.0097734     .0117801
   w_c_avelf |   -.8455103    .3021786     -2.80    0.005      -1.43777    -.2532511
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    w_c_avexpr
------------------------------------------------------------------------------
(results _ivlasso_w_c_avexpr are active now)
(sum of wgt is     4.7302e+02)
Partialling out unpenalized controls...
1.  (PDS/CHS) Selecting HD controls for dep var logpgp95...
Selected:  edes1975 avelf humid3
3.  (PDS) Selecting HD controls for endog regressor avexpr...
Selected:  edes1975
5.  (PDS/CHS) Selecting HD controls/IVs for endog regressor avexpr...
Selected:  logem4 euro1900 democ00a
6a. (CHS) Selecting lasso HD controls and creating optimal IV for endog regressor avexpr...
Selected:  lat_abst edes1975 temp1 temp2
6b. (CHS) Selecting post-lasso HD controls and creating optimal IV for endog regressor avexpr...
Selected:  edes1975 avelf temp2 humid2
7.  (CHS) Creating orthogonalized endogenous regressor avexpr...


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      heteroskedastic
Number of observations:                59
Endogenous (1):                        avexpr
High-dim controls (12):                lat_abst edes1975 avelf temp1 temp2
                                       temp3 temp4 temp5 humid1 humid2 humid3
                                       humid4
Selected controls, PDS (3):            edes1975 avelf humid3
Selected controls, CHS-L (6):          lat_abst edes1975 avelf temp1 temp2
                                       humid3
Selected controls, CHS-PL (5):         edes1975 avelf temp2 humid2 humid3
High-dim instruments (6):              logem4 euro1900 democ1 cons1 democ00a
                                       cons00a
Selected instruments (3):              logem4 euro1900 democ00a

First-stage estimation(s):
-------------+----------------------------------------------------------------
             |               Robust
       avexpr |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
    edes1975 |   -.0047598    .0203121     -0.23    0.815     -.0445709     .0350512
       avelf |    .5718258    .5177977      1.10    0.269      -.443039     1.586691
      humid3 |    .0149394    .0099258      1.51    0.132     -.0045148     .0343936
      logem4 |   -.3958138    .1945171     -2.03    0.042     -.7770603    -.0145673
    euro1900 |     .024264    .0239961      1.01    0.312     -.0227675     .0712956
    democ00a |    .0537519    .0563894      0.95    0.340     -.0567694     .1642731
-------------+----------------------------------------------------------------

Structural equation:

IV using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |    .5985071    .1258575      4.76    0.000      .3518309     .8451833
-------------+----------------------------------------------------------------

IV using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |    .6694489    .1573435      4.25    0.000      .3610614     .9778364
-------------+----------------------------------------------------------------

IV with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
             |               Robust
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |    .6296237    .1601387      3.93    0.000      .3157576     .9434899
    edes1975 |    .0018181    .0049349      0.37    0.713     -.0078542     .0114904
       avelf |   -.8357724    .2674623     -3.12    0.002     -1.359989     -.311556
      humid3 |    .0072942    .0057398      1.27    0.204     -.0039556     .0185439
       _cons |    3.899395    .9228124      4.23    0.000      2.090716     5.708074
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    avexpr
------------------------------------------------------------------------------
(results _ivlasso_avexpr are active now)
(sum of wgt is     4.7302e+02)
Partialling out unpenalized controls...
1.  (PDS/CHS) Selecting HD controls for dep var logpgp95...
Selected:  edes1975 avelf humid3
3.  (PDS) Selecting HD controls for endog regressor avexpr...
Selected:  edes1975
5.  (PDS/CHS) Selecting HD controls/IVs for endog regressor avexpr...
Selected:  logem4 euro1900 democ00a
6a. (CHS) Selecting lasso HD controls and creating optimal IV for endog regressor avexpr...
Selected:  lat_abst edes1975 temp1 temp2
6b. (CHS) Selecting post-lasso HD controls and creating optimal IV for endog regressor avexpr...
Selected:  edes1975 avelf temp2 humid2
7.  (CHS) Creating orthogonalized endogenous regressor avexpr...


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      heteroskedastic
Number of observations:                59
Endogenous (1):                        avexpr
High-dim controls (12):                lat_abst edes1975 avelf temp1 temp2
                                       temp3 temp4 temp5 humid1 humid2 humid3
                                       humid4
Selected controls, PDS (3):            edes1975 avelf humid3
Selected controls, CHS-L (6):          lat_abst edes1975 avelf temp1 temp2
                                       humid3
Selected controls, CHS-PL (5):         edes1975 avelf temp2 humid2 humid3
High-dim instruments (6):              logem4 euro1900 democ1 cons1 democ00a
                                       cons00a
Selected instruments (3):              logem4 euro1900 democ00a

First-stage estimation(s):
-------------+----------------------------------------------------------------
             |               Robust
       avexpr |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
    edes1975 |   -.0047598    .0203121     -0.23    0.815     -.0445709     .0350512
       avelf |    .5718258    .5177977      1.10    0.269      -.443039     1.586691
      humid3 |    .0149394    .0099258      1.51    0.132     -.0045148     .0343936
      logem4 |   -.3958138    .1945171     -2.03    0.042     -.7770603    -.0145673
    euro1900 |     .024264    .0239961      1.01    0.312     -.0227675     .0712956
    democ00a |    .0537519    .0563894      0.95    0.340     -.0567694     .1642731
-------------+----------------------------------------------------------------

Structural equation:

IV using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |    .5985071    .1258575      4.76    0.000      .3518309     .8451833
-------------+----------------------------------------------------------------

IV using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |    .6694489    .1573435      4.25    0.000      .3610614     .9778364
-------------+----------------------------------------------------------------

IV with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
             |               Robust
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |    .6296237    .1601387      3.93    0.000      .3157576     .9434899
    edes1975 |    .0018181    .0049349      0.37    0.713     -.0078542     .0114904
       avelf |   -.8357724    .2674623     -3.12    0.002     -1.359989     -.311556
      humid3 |    .0072942    .0057398      1.27    0.204     -.0039556     .0185439
       _cons |    3.899395    .9228124      4.23    0.000      2.090716     5.708074
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    avexpr
------------------------------------------------------------------------------
1.  (PDS/CHS) Selecting HD controls for dep var w_c_logpgp95...
Selected:  w_c_edes1975 w_c_avelf w_c_humid3
3.  (PDS) Selecting HD controls for endog regressor w_c_avexpr...
Selected:  w_c_edes1975
5.  (PDS/CHS) Selecting HD controls/IVs for endog regressor w_c_avexpr...
Selected:  w_c_logem4 w_c_euro1900 w_c_democ00a
6a. (CHS) Selecting lasso HD controls and creating optimal IV for endog regressor w_c_avexpr...
Selected:  w_c_lat_abst w_c_edes1975 w_c_temp1 w_c_temp2
6b. (CHS) Selecting post-lasso HD controls and creating optimal IV for endog regressor w_c_avexpr...
Selected:  w_c_edes1975 w_c_avelf w_c_temp2 w_c_humid2
7.  (CHS) Creating orthogonalized endogenous regressor w_c_avexpr...


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      heteroskedastic
Number of observations:                59
Endogenous (1):                        w_c_avexpr
High-dim controls (12):                w_c_lat_abst w_c_edes1975 w_c_avelf
                                       w_c_temp1 w_c_temp2 w_c_temp3 w_c_temp4
                                       w_c_temp5 w_c_humid1 w_c_humid2
                                       w_c_humid3 w_c_humid4
Selected controls, PDS (3):            w_c_edes1975 w_c_avelf w_c_humid3
Selected controls, CHS-L (6):          w_c_lat_abst w_c_edes1975 w_c_avelf
                                       w_c_temp1 w_c_temp2 w_c_humid3
Selected controls, CHS-PL (5):         w_c_edes1975 w_c_avelf w_c_temp2
                                       w_c_humid2 w_c_humid3
High-dim instruments (6):              w_c_logem4 w_c_euro1900 w_c_democ1
                                       w_c_cons1 w_c_democ00a w_c_cons00a
Selected instruments (3):              w_c_logem4 w_c_euro1900 w_c_democ00a

First-stage estimation(s):
-------------+----------------------------------------------------------------
             |               Robust
   w_c_avexpr |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
w_c_edes1975 |   -.0047598    .0203121     -0.23    0.815     -.0445709     .0350512
   w_c_avelf |    .5718258    .5177977      1.10    0.269      -.443039     1.586691
  w_c_humid3 |    .0149394    .0099258      1.51    0.132     -.0045148     .0343936
  w_c_logem4 |   -.3958138    .1945171     -2.03    0.042     -.7770603    -.0145673
w_c_euro1900 |     .024264    .0239961      1.01    0.312     -.0227675     .0712956
w_c_democ00a |    .0537519    .0563894      0.95    0.340     -.0567694     .1642731
-------------+----------------------------------------------------------------

Structural equation:

IV using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
 w_c_logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
  w_c_avexpr |    .5985071    .1258575      4.76    0.000      .3518309     .8451833
-------------+----------------------------------------------------------------

IV using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
 w_c_logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
  w_c_avexpr |    .6694489    .1573435      4.25    0.000      .3610614     .9778364
-------------+----------------------------------------------------------------

IV with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
             |               Robust
 w_c_logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
  w_c_avexpr |    .6296237    .1601387      3.93    0.000      .3157576     .9434899
w_c_edes1975 |    .0018181    .0049349      0.37    0.713     -.0078542     .0114904
   w_c_avelf |   -.8357724    .2674623     -3.12    0.002     -1.359989     -.311556
  w_c_humid3 |    .0072942    .0057398      1.27    0.204     -.0039556     .0185439
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    w_c_avexpr
------------------------------------------------------------------------------
(results _ivlasso_w_c_avexpr are active now)
r; t=1.50 21:48:04

.
. // IV + FEs + partialling out
. // make sure that the same sample is used throughout.
. cap drop touse
r; t=0.00 21:48:04

. gen touse=(democ1<.)
r; t=0.00 21:48:04

.
. cap drop one
r; t=0.00 21:48:04

. cap drop wt
r; t=0.00 21:48:04

. cap drop id
r; t=0.00 21:48:04

. gen double one=1
r; t=0.00 21:48:04

. // use a non-integer weight
. global wtvar logpgp95
r; t=0.00 21:48:04

. gen double wt=$wtvar
r; t=0.00 21:48:04

. // assumes no missings for any regressors or dep var
. sum wt if touse

    Variable |        Obs        Mean    Std. Dev.       Min        Max
-------------+---------------------------------------------------------
          wt |         59    8.017272    .9988773   6.109248   10.21574
r; t=0.00 21:48:04

. replace wt = wt * 1/r(mean) if touse
(59 real changes made)
r; t=0.00 21:48:04

. gen id=floor(_n/2)
r; t=0.00 21:48:04

.
. * Basic estimation with constant and no partialling etc.
. * w_c_ vars are centered (demeaned using weighted means)
. * and then weighted by the sqrt of the weighting var.
.
. cap drop w_*
r; t=0.00 21:48:04

. cap drop c_*
r; t=0.00 21:48:04

. * weighted centering (so no intercept)
. foreach var of varlist logpgp95 avexpr lat_abst logem4 edes1975 avelf           ///
>         temp* humid* euro1900-cons00a {
  2.         qui reg `var' steplow i.id [aw=wt] if touse
  3.         qui predict double c_`var' if touse, resid
  4.         qui gen double w_c_`var' = c_`var'*sqrt(wt) if touse
  5.         // don't need and get in the way
.         cap drop c_`var'
  6. }
r; t=0.27 21:48:04

.
. xtset id
       panel variable:  id (unbalanced)
r; t=0.00 21:48:04

.
. foreach opt in "" "rob" {
  2.         // cons automatically partialled out
.         ivlasso logpgp95 (avexpr=logem4 euro1900-cons00a)                                               ///
>                 (lat_abst edes1975 avelf temp* humid* steplow)                                          ///
>                 [aw=logpgp95]                                                                                                           ///
>                 , lopt(tolzero(1e-10) tolups(1e-10) tolopt(1e-8))                                       ///
>                 partial(steplow) fe                                                                                                     ///
>                 first `opt'
  3.         savedresults save ivlasso e()
  4.         mat b_pds=e(beta_pds)
  5.         mat V_pds=e(V_pds)
  6.         mat b_plasso=e(beta_plasso)
  7.         mat V_plasso=e(V_plasso)
  8.         mat b_lasso=e(beta_lasso)
  9.         mat V_lasso=e(V_lasso)
 10.         est restore _ivlasso_avexpr
 11.         mat b_avexpr = e(b)
 12.         // prestd rlasso option
.         ivlasso logpgp95 (avexpr=logem4 euro1900-cons00a)                                               ///
>                 (lat_abst edes1975 avelf temp* humid* steplow)                                          ///
>                 [aw=logpgp95]                                                                                                           ///
>                 , lopt(prestd tolzero(1e-10) tolups(1e-10) tolopt(1e-8))                        ///
>                 partial(steplow) fe                                                                                                     ///
>                 first `opt'
 13.         savedresults comp ivlasso e(), exclude(macros: loptions) tol(1e-7)
 14.         // preweighted data
.         ivlasso w_c_logpgp95 (w_c_avexpr=w_c_logem4 w_c_euro1900-w_c_cons00a)   ///
>                 (w_c_lat_abst w_c_edes1975 w_c_avelf w_c_temp* w_c_humid*)                      ///
>                 , nocons dm lopt(tolzero(1e-10) tolups(1e-10) tolopt(1e-8))                     ///
>                 first `opt'
 15.         // no constant to compare in either estimation but 1 var partialled out
.         // Can't compare Vs since dofs are different
.         mat b_pds=b_pds[1,1..colsof(b_pds)-1]
 16.         assert mreldif(e(beta_pds),b_pds)<1e-8
 17.         assert mreldif(e(beta_plasso),b_plasso)<1e-8
 18.         assert mreldif(e(beta_lasso),b_lasso)<1e-8
 19.         // compare first-stage regressions
.         est restore _ivlasso_w_c_avexpr
 20.         mat b_w_c_avexpr = e(b)
 21.         assert mreldif(b_avexpr,b_w_c_avexpr)<1e-10
 22. }
(sum of wgt is     4.7302e+02)
Fixed effects transformation...
1.  (PDS/CHS) Selecting HD controls for dep var logpgp95...
Selected:  edes1975 avelf
3.  (PDS) Selecting HD controls for endog regressor avexpr...
Selected:  edes1975
5.  (PDS/CHS) Selecting HD controls/IVs for endog regressor avexpr...
Selected:  euro1900
6a. (CHS) Selecting lasso HD controls and creating optimal IV for endog regressor avexpr...
Selected:  edes1975 temp2 temp5
6b. (CHS) Selecting post-lasso HD controls and creating optimal IV for endog regressor avexpr...
Selected:  edes1975 temp2 temp5
7.  (CHS) Creating orthogonalized endogenous regressor avexpr...


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      homoskedastic
Number of observations:                59
Number of fixed effects:               32
Endogenous (1):                        avexpr
High-dim controls (12):                lat_abst edes1975 avelf temp1 temp2
                                       temp3 temp4 temp5 humid1 humid2 humid3
                                       humid4
Selected controls, PDS (2):            edes1975 avelf
Selected controls, CHS-L (4):          edes1975 avelf temp2 temp5
Selected controls, CHS-PL (4):         edes1975 avelf temp2 temp5
Partialled-out controls (1):           steplow
High-dim instruments (6):              logem4 euro1900 democ1 cons1 democ00a
                                       cons00a
Selected instruments (1):              euro1900

First-stage estimation(s):
-------------+----------------------------------------------------------------
       avexpr |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
    edes1975 |   -.0240503    .0326894     -0.74    0.462     -.0881203     .0400197
       avelf |   -.2271345    .7647687     -0.30    0.766     -1.726054     1.271785
    euro1900 |    .0571654    .0319664      1.79    0.074     -.0054875     .1198184
-------------+----------------------------------------------------------------

Structural equation (fixed effects, #groups=32):

IV using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |    .5315286    .2597759      2.05    0.041      .0223772      1.04068
-------------+----------------------------------------------------------------

IV using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |    .5581536    .3710771      1.50    0.133     -.1691442     1.285451
-------------+----------------------------------------------------------------

IV with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |     .637265    .3461875      1.84    0.066       -.04125      1.31578
    edes1975 |    .0036458    .0125305      0.29    0.771     -.0209134     .0282051
       avelf |   -.8954397    .4567625     -1.96    0.050     -1.790678    -.0002016
     steplow |     .273186    .2891483      0.94    0.345     -.2935343     .8399063
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    avexpr
------------------------------------------------------------------------------
(results _ivlasso_avexpr are active now)
(sum of wgt is     4.7302e+02)
Fixed effects transformation...
1.  (PDS/CHS) Selecting HD controls for dep var logpgp95...
Selected:  edes1975 avelf
3.  (PDS) Selecting HD controls for endog regressor avexpr...
Selected:  edes1975
5.  (PDS/CHS) Selecting HD controls/IVs for endog regressor avexpr...
Selected:  euro1900
6a. (CHS) Selecting lasso HD controls and creating optimal IV for endog regressor avexpr...
Selected:  edes1975 temp2 temp5
6b. (CHS) Selecting post-lasso HD controls and creating optimal IV for endog regressor avexpr...
Selected:  edes1975 temp2 temp5
7.  (CHS) Creating orthogonalized endogenous regressor avexpr...


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      homoskedastic
Number of observations:                59
Number of fixed effects:               32
Endogenous (1):                        avexpr
High-dim controls (12):                lat_abst edes1975 avelf temp1 temp2
                                       temp3 temp4 temp5 humid1 humid2 humid3
                                       humid4
Selected controls, PDS (2):            edes1975 avelf
Selected controls, CHS-L (4):          edes1975 avelf temp2 temp5
Selected controls, CHS-PL (4):         edes1975 avelf temp2 temp5
Partialled-out controls (1):           steplow
High-dim instruments (6):              logem4 euro1900 democ1 cons1 democ00a
                                       cons00a
Selected instruments (1):              euro1900

First-stage estimation(s):
-------------+----------------------------------------------------------------
       avexpr |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
    edes1975 |   -.0240503    .0326894     -0.74    0.462     -.0881203     .0400197
       avelf |   -.2271345    .7647687     -0.30    0.766     -1.726054     1.271785
    euro1900 |    .0571654    .0319664      1.79    0.074     -.0054875     .1198184
-------------+----------------------------------------------------------------

Structural equation (fixed effects, #groups=32):

IV using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |    .5315287    .2597759      2.05    0.041      .0223772      1.04068
-------------+----------------------------------------------------------------

IV using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |    .5581536    .3710771      1.50    0.133     -.1691442     1.285451
-------------+----------------------------------------------------------------

IV with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |     .637265    .3461875      1.84    0.066       -.04125      1.31578
    edes1975 |    .0036458    .0125305      0.29    0.771     -.0209134     .0282051
       avelf |   -.8954397    .4567625     -1.96    0.050     -1.790678    -.0002016
     steplow |     .273186    .2891483      0.94    0.345     -.2935343     .8399063
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    avexpr
------------------------------------------------------------------------------
1.  (PDS/CHS) Selecting HD controls for dep var w_c_logpgp95...
Selected:  w_c_edes1975 w_c_avelf
3.  (PDS) Selecting HD controls for endog regressor w_c_avexpr...
Selected:  w_c_edes1975
5.  (PDS/CHS) Selecting HD controls/IVs for endog regressor w_c_avexpr...
Selected:  w_c_euro1900
6a. (CHS) Selecting lasso HD controls and creating optimal IV for endog regressor w_c_avexpr...
Selected:  w_c_edes1975 w_c_temp2 w_c_temp5
6b. (CHS) Selecting post-lasso HD controls and creating optimal IV for endog regressor w_c_avexpr...
Selected:  w_c_edes1975 w_c_temp2 w_c_temp5
7.  (CHS) Creating orthogonalized endogenous regressor w_c_avexpr...


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      homoskedastic
Number of observations:                59
Endogenous (1):                        w_c_avexpr
High-dim controls (12):                w_c_lat_abst w_c_edes1975 w_c_avelf
                                       w_c_temp1 w_c_temp2 w_c_temp3 w_c_temp4
                                       w_c_temp5 w_c_humid1 w_c_humid2
                                       w_c_humid3 w_c_humid4
Selected controls, PDS (2):            w_c_edes1975 w_c_avelf
Selected controls, CHS-L (4):          w_c_edes1975 w_c_avelf w_c_temp2
                                       w_c_temp5
Selected controls, CHS-PL (4):         w_c_edes1975 w_c_avelf w_c_temp2
                                       w_c_temp5
High-dim instruments (6):              w_c_logem4 w_c_euro1900 w_c_democ1
                                       w_c_cons1 w_c_democ00a w_c_cons00a
Selected instruments (1):              w_c_euro1900

First-stage estimation(s):
-------------+----------------------------------------------------------------
   w_c_avexpr |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
w_c_edes1975 |   -.0240503    .0221137     -1.09    0.277     -.0673925     .0192919
   w_c_avelf |   -.2271345    .5173518     -0.44    0.661     -1.241125     .7868564
w_c_euro1900 |    .0571654    .0216247      2.64    0.008      .0147819      .099549
-------------+----------------------------------------------------------------

Structural equation:

IV using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
 w_c_logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
  w_c_avexpr |    .5315286    .1757336      3.02    0.002      .1870972       .87596
-------------+----------------------------------------------------------------

IV using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
 w_c_logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
  w_c_avexpr |    .5581536    .2510268      2.22    0.026      .0661502     1.050157
-------------+----------------------------------------------------------------

IV with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
 w_c_logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
  w_c_avexpr |     .637265    .2341894      2.72    0.007      .1782622     1.096268
w_c_edes1975 |    .0036458    .0084766      0.43    0.667      -.012968     .0202597
   w_c_avelf |   -.8954397    .3089914     -2.90    0.004     -1.501052    -.2898278
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    w_c_avexpr
------------------------------------------------------------------------------
(results _ivlasso_w_c_avexpr are active now)
(sum of wgt is     4.7302e+02)
Fixed effects transformation...
1.  (PDS/CHS) Selecting HD controls for dep var logpgp95...
Selected:  edes1975
3.  (PDS) Selecting HD controls for endog regressor avexpr...
Selected:  edes1975
5.  (PDS/CHS) Selecting HD controls/IVs for endog regressor avexpr...
Selected:  euro1900 democ00a
6a. (CHS) Selecting lasso HD controls and creating optimal IV for endog regressor avexpr...
Selected:  edes1975 temp2 temp4 temp5
6b. (CHS) Selecting post-lasso HD controls and creating optimal IV for endog regressor avexpr...
Selected:  edes1975 temp2 temp4 temp5
7.  (CHS) Creating orthogonalized endogenous regressor avexpr...


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      heteroskedastic
Number of observations:                59
Number of fixed effects:               32
Endogenous (1):                        avexpr
High-dim controls (12):                lat_abst edes1975 avelf temp1 temp2
                                       temp3 temp4 temp5 humid1 humid2 humid3
                                       humid4
Selected controls, PDS (1):            edes1975
Selected controls, CHS-L (4):          edes1975 temp2 temp4 temp5
Selected controls, CHS-PL (4):         edes1975 temp2 temp4 temp5
Partialled-out controls (1):           steplow
High-dim instruments (6):              logem4 euro1900 democ1 cons1 democ00a
                                       cons00a
Selected instruments (2):              euro1900 democ00a

First-stage estimation(s):
-------------+----------------------------------------------------------------
             |               Robust
       avexpr |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
    edes1975 |   -.0172575    .0262522     -0.66    0.511     -.0687109      .034196
    euro1900 |    .0494105    .0321595      1.54    0.124     -.0136209      .112442
    democ00a |    .0213241    .0882034      0.24    0.809     -.1515515     .1941997
-------------+----------------------------------------------------------------

Structural equation (fixed effects, #groups=32):

IV using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |    .4104845    .1818244      2.26    0.024      .0541153     .7668537
-------------+----------------------------------------------------------------

IV using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |    .1559098     .216712      0.72    0.472      -.268838     .5806576
-------------+----------------------------------------------------------------

IV with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
             |               Robust
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |    .3644509     .195341      1.87    0.062     -.0184104     .7473122
    edes1975 |    .0164609    .0058448      2.82    0.005      .0050053     .0279164
     steplow |    .1779258    .2915146      0.61    0.542     -.3934323     .7492838
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    avexpr
------------------------------------------------------------------------------
(results _ivlasso_avexpr are active now)
(sum of wgt is     4.7302e+02)
Fixed effects transformation...
1.  (PDS/CHS) Selecting HD controls for dep var logpgp95...
Selected:  edes1975
3.  (PDS) Selecting HD controls for endog regressor avexpr...
Selected:  edes1975
5.  (PDS/CHS) Selecting HD controls/IVs for endog regressor avexpr...
Selected:  euro1900 democ00a
6a. (CHS) Selecting lasso HD controls and creating optimal IV for endog regressor avexpr...
Selected:  edes1975 temp2 temp4 temp5
6b. (CHS) Selecting post-lasso HD controls and creating optimal IV for endog regressor avexpr...
Selected:  edes1975 temp2 temp4 temp5
7.  (CHS) Creating orthogonalized endogenous regressor avexpr...


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      heteroskedastic
Number of observations:                59
Number of fixed effects:               32
Endogenous (1):                        avexpr
High-dim controls (12):                lat_abst edes1975 avelf temp1 temp2
                                       temp3 temp4 temp5 humid1 humid2 humid3
                                       humid4
Selected controls, PDS (1):            edes1975
Selected controls, CHS-L (4):          edes1975 temp2 temp4 temp5
Selected controls, CHS-PL (4):         edes1975 temp2 temp4 temp5
Partialled-out controls (1):           steplow
High-dim instruments (6):              logem4 euro1900 democ1 cons1 democ00a
                                       cons00a
Selected instruments (2):              euro1900 democ00a

First-stage estimation(s):
-------------+----------------------------------------------------------------
             |               Robust
       avexpr |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
    edes1975 |   -.0172575    .0262522     -0.66    0.511     -.0687109      .034196
    euro1900 |    .0494105    .0321595      1.54    0.124     -.0136209      .112442
    democ00a |    .0213241    .0882034      0.24    0.809     -.1515515     .1941997
-------------+----------------------------------------------------------------

Structural equation (fixed effects, #groups=32):

IV using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |    .4104846    .1818244      2.26    0.024      .0541154     .7668538
-------------+----------------------------------------------------------------

IV using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |    .1559098     .216712      0.72    0.472      -.268838     .5806576
-------------+----------------------------------------------------------------

IV with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
             |               Robust
     logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      avexpr |    .3644509     .195341      1.87    0.062     -.0184104     .7473122
    edes1975 |    .0164609    .0058448      2.82    0.005      .0050053     .0279164
     steplow |    .1779258    .2915146      0.61    0.542     -.3934323     .7492838
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    avexpr
------------------------------------------------------------------------------
1.  (PDS/CHS) Selecting HD controls for dep var w_c_logpgp95...
Selected:  w_c_edes1975
3.  (PDS) Selecting HD controls for endog regressor w_c_avexpr...
Selected:  w_c_edes1975
5.  (PDS/CHS) Selecting HD controls/IVs for endog regressor w_c_avexpr...
Selected:  w_c_euro1900 w_c_democ00a
6a. (CHS) Selecting lasso HD controls and creating optimal IV for endog regressor w_c_avexpr...
Selected:  w_c_edes1975 w_c_temp2 w_c_temp4 w_c_temp5
6b. (CHS) Selecting post-lasso HD controls and creating optimal IV for endog regressor w_c_avexpr...
Selected:  w_c_edes1975 w_c_temp2 w_c_temp4 w_c_temp5
7.  (CHS) Creating orthogonalized endogenous regressor w_c_avexpr...


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      heteroskedastic
Number of observations:                59
Endogenous (1):                        w_c_avexpr
High-dim controls (12):                w_c_lat_abst w_c_edes1975 w_c_avelf
                                       w_c_temp1 w_c_temp2 w_c_temp3 w_c_temp4
                                       w_c_temp5 w_c_humid1 w_c_humid2
                                       w_c_humid3 w_c_humid4
Selected controls, PDS (1):            w_c_edes1975
Selected controls, CHS-L (4):          w_c_edes1975 w_c_temp2 w_c_temp4
                                       w_c_temp5
Selected controls, CHS-PL (4):         w_c_edes1975 w_c_temp2 w_c_temp4
                                       w_c_temp5
High-dim instruments (6):              w_c_logem4 w_c_euro1900 w_c_democ1
                                       w_c_cons1 w_c_democ00a w_c_cons00a
Selected instruments (2):              w_c_euro1900 w_c_democ00a

First-stage estimation(s):
-------------+----------------------------------------------------------------
             |               Robust
   w_c_avexpr |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
w_c_edes1975 |   -.0172575    .0177591     -0.97    0.331     -.0520648     .0175498
w_c_euro1900 |    .0494105    .0217553      2.27    0.023      .0067709     .0920501
w_c_democ00a |    .0213241     .059668      0.36    0.721      -.095623     .1382712
-------------+----------------------------------------------------------------

Structural equation:

IV using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
 w_c_logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
  w_c_avexpr |    .4104845    .1230008      3.34    0.001      .1694074     .6515616
-------------+----------------------------------------------------------------

IV using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
             |               Robust
 w_c_logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
  w_c_avexpr |    .1559098    .1466017      1.06    0.288     -.1314242     .4432438
-------------+----------------------------------------------------------------

IV with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
             |               Robust
 w_c_logpgp95 |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
  w_c_avexpr |    .3644509    .1321446      2.76    0.006      .1054523     .6234495
w_c_edes1975 |    .0164609    .0039539      4.16    0.000      .0087114     .0242103
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    w_c_avexpr
------------------------------------------------------------------------------
(results _ivlasso_w_c_avexpr are active now)
r; t=1.63 21:48:06

.
.
. // ***************** END AJR DATASET ************************* //
.
. // ***************** ABDATA DATASET ************************** //
.
. webuse abdata, clear
r; t=1.06 21:48:07

.
. // FE and noftools options
. pdslasso ys L.k (L(1/3).w yr*), fe
Fixed effects transformation...
1.  (PDS/CHS) Selecting HD controls for dep var ys...
Selected:  L3.w yr1979 yr1980 yr1982 yr1983
2.  (PDS/CHS) Selecting HD controls for exog regressor L.k...
Selected:  yr1979 yr1980 yr1982 yr1983 yr1984


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      homoskedastic
Number of observations:                611
Number of fixed effects:               140
Exogenous (1):                         L.k
High-dim controls (12):                L.w L2.w L3.w yr1976 yr1977 yr1978
                                       yr1979 yr1980 yr1981 yr1982 yr1983
                                       yr1984
Selected controls (6):                 L3.w yr1979 yr1980 yr1982 yr1983 yr1984

Structural equation (fixed effects, #groups=140):

OLS using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
           ys |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
           k |
         L1. |    .0526222     .011746      4.48    0.000      .0296005     .0756439
-------------+----------------------------------------------------------------

OLS using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
           ys |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
           k |
         L1. |    .0418632    .0119694      3.50    0.000      .0184036     .0653227
-------------+----------------------------------------------------------------

OLS with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
           ys |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
           k |
         L1. |    .0420934    .0119536      3.52    0.000      .0186648      .065522
             |
           w |
         L3. |    .1454999    .0289107      5.03    0.000       .088836     .2021638
             |
      yr1979 |    .1395998    .0064184     21.75    0.000      .1270201     .1521796
      yr1980 |    .0749972     .004841     15.49    0.000      .0655089     .0844854
      yr1982 |   -.0165469    .0049087     -3.37    0.001     -.0261678     -.006926
      yr1983 |   -.0104521    .0063632     -1.64    0.100     -.0229238     .0020197
      yr1984 |    .0237791    .0088154      2.70    0.007      .0065012      .041057
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    L.k
------------------------------------------------------------------------------
r; t=0.19 21:48:07

. savedresults save ftools e()
r; t=0.00 21:48:07

. cap noi assert "`e(noftools)'"==""  // will be error if ftools not installed
r; t=0.00 21:48:07

. pdslasso ys L.k (L(1/3).w yr*), fe noftools
Fixed effects transformation...
1.  (PDS/CHS) Selecting HD controls for dep var ys...
Selected:  L3.w yr1979 yr1980 yr1982 yr1983
2.  (PDS/CHS) Selecting HD controls for exog regressor L.k...
Selected:  yr1979 yr1980 yr1982 yr1983 yr1984


Estimation results:

Specification:
Regularization method:                 lasso
Penalty loadings:                      homoskedastic
Number of observations:                611
Number of fixed effects:               140
Exogenous (1):                         L.k
High-dim controls (12):                L.w L2.w L3.w yr1976 yr1977 yr1978
                                       yr1979 yr1980 yr1981 yr1982 yr1983
                                       yr1984
Selected controls (6):                 L3.w yr1979 yr1980 yr1982 yr1983 yr1984

Structural equation (fixed effects, #groups=140):

OLS using CHS lasso-orthogonalized vars
-------------+----------------------------------------------------------------
           ys |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
           k |
         L1. |    .0526222     .011746      4.48    0.000      .0296005     .0756439
-------------+----------------------------------------------------------------

OLS using CHS post-lasso-orthogonalized vars
-------------+----------------------------------------------------------------
           ys |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
           k |
         L1. |    .0418632    .0119694      3.50    0.000      .0184036     .0653227
-------------+----------------------------------------------------------------

OLS with PDS-selected variables and full regressor set
-------------+----------------------------------------------------------------
           ys |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
           k |
         L1. |    .0420934    .0119536      3.52    0.000      .0186648      .065522
             |
           w |
         L3. |    .1454999    .0289107      5.03    0.000       .088836     .2021638
             |
      yr1979 |    .1395998    .0064184     21.75    0.000      .1270201     .1521796
      yr1980 |    .0749972     .004841     15.49    0.000      .0655089     .0844854
      yr1982 |   -.0165469    .0049087     -3.37    0.001     -.0261678     -.006926
      yr1983 |   -.0104521    .0063632     -1.64    0.100     -.0229238     .0020197
      yr1984 |    .0237791    .0088154      2.70    0.007      .0065012      .041057
-------------+----------------------------------------------------------------
Standard errors and test statistics valid for the following variables only:
    L.k
------------------------------------------------------------------------------
r; t=0.19 21:48:07

. assert "`e(noftools)'"=="noftools"
r; t=0.00 21:48:07

. savedresults comp ftools e()
r; t=0.00 21:48:07

.
.
. // *************** END ABDATA DATASET ************************ //
.
. cap log close