-------------------------------------------------------------------------------
name: <unnamed>
log: D:\home\stephenj\MYProjects\DWP_SDP\kyado\Clean_Ados\ky_example.lo
> g
log type: text
opened on: 24 May 2021, 10:51:56
.
.
. /////////////////////////////////////////////////////////////////////////////
> ///
> /// This file provides a working example that uses ky_fit
> /// to simulate data used in Kapteyn-Ypma (Journal of Labor Economics, 2007)
> = "KY"
> /// , estimate those models, and provide relevant summary statistics
> ///
> /// The code replicates some of the tables in KY as well as the
> /// reliability reports in Meijer, Rohwedder & Wansbeek (Journal of Business
> /// and Economic Statistics, 2012) = "MRW"
> /////////////////////////////////////////////////////////////////////////////
> ///
>
. /// SET UP: Storing model parameters reported in KY, Table C2
>
. global mean_e 12.283
. global mean_t 9.187
. global mean_w (-0.304)
. global mean_n (-0.048)
.
. global sig_e 0.717
. global sig_t 1.807
. global sig_w 1.239
. global sig_n 0.099
.
. global pi_r 0.959
. global pi_s 0.152
. global pi_w 0.156
.
. global rho_s (-0.013)
.
. /// Step 1: Simulating data using -ky_fit-
>
. /// Notice that this includes option "clear" to replace any data in memory
>
. // First, declare the model to be used for simulation
. // Second, declare values of model parameters
. ky_sim, nobs(400) model(4) seed(101) ///
> mean_e($mean_e) mean_t($mean_t) mean_w($mean_w) mean_n($mean_
> n) ///
> sig_e($sig_e) sig_t($sig_t) sig_w($sig_w) sig_n($sig_n)
> ///
> pi_r($pi_r) pi_s($pi_s) pi_w($pi_w) rho_s($rho_s)
> clear
.
. /// This also stores all coefficients in equation form:
>
. ereturn display
------------------------------------------------------------------------------
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
mu_e |
_cons | 12.283 . . . . .
-------------+----------------------------------------------------------------
mu_n |
_cons | -.048 . . . . .
-------------+----------------------------------------------------------------
mu_t |
_cons | 9.187 . . . . .
-------------+----------------------------------------------------------------
mu_w |
_cons | -.304 . . . . .
-------------+----------------------------------------------------------------
ln_sig_e |
_cons | -.3326794 . . . . .
-------------+----------------------------------------------------------------
ln_sig_n |
_cons | -2.312635 . . . . .
-------------+----------------------------------------------------------------
ln_sig_t |
_cons | .591668 . . . . .
-------------+----------------------------------------------------------------
ln_sig_w |
_cons | .2143046 . . . . .
-------------+----------------------------------------------------------------
arho_s |
_cons | -.0130007 . . . . .
-------------+----------------------------------------------------------------
lpi_r |
_cons | 3.152319 . . . . .
-------------+----------------------------------------------------------------
lpi_s |
_cons | -1.719 . . . . .
-------------+----------------------------------------------------------------
lpi_w |
_cons | -1.688296 . . . . .
------------------------------------------------------------------------------
.
. /// which are stored for later use
>
. estimates store model0
.
. /// some summary statistics and data description
>
. describe *
storage display value
variable name type format label variable label
-------------------------------------------------------------------------------
e_var double %10.0g True Latent log(earnings)
n_var double %10.0g Noise in RTM survey data
w_var double %10.0g Contamination error in survey
t_var double %10.0g Mismatched values to admin data
pi_si byte %8.0g =1 if data reported correctly
pi_wi byte %8.0g =1 if data have additional
contamination in survey data
pi_ri byte %8.0g =1 if data are matched correctly
r_var double %10.0g Administrative log(earnings)
s_var double %10.0g Survey log(earnings)
l_var double %10.0g =1 if r_i and s_i are error free
rclass byte %8.0g Data type for R
sclass byte %8.0g Data type for S
class byte %8.0g Data type for (R,S)
. summarize *, sep(0)
Variable | Obs Mean Std. Dev. Min Max
-------------+---------------------------------------------------------
e_var | 400 12.34898 .665869 10.4206 14.51099
n_var | 400 -.0513431 .1030404 -.3312704 .2292065
w_var | 400 -.3139371 1.128783 -3.336294 2.629267
t_var | 400 9.012969 1.753307 4.315567 13.78396
pi_si | 400 .135 .3421515 0 1
pi_wi | 400 .1525 .3599551 0 1
pi_ri | 400 .9725 .16374 0 1
r_var | 400 12.23967 .9549137 5.839129 14.51099
s_var | 400 12.25409 .7501207 9.732128 15.20382
l_var | 400 .1325 .3394581 0 1
rclass | 400 1.0275 .16374 1 2
sclass | 400 1.985 .5053845 1 3
class | 400 2.0675 .6958119 1 5
.
. /// We first show how -ky_fit- can be used to estimate KY models using simula
> ted data
> /// For simplicity, we replicate all models shown in KY, Table 2C:
>
. // Basic model (using contraint)
. constraint 1 [mu_n]_cons = 0
. ky_fit r_var s_var l_var, model(1) technique(nr bhhh) constraint(1)
initial: log likelihood = -1511.7161
rescale: log likelihood = -1511.7161
rescale eq: log likelihood = -1268.2513
(setting technique to nr)
Iteration 0: log likelihood = -1268.3086
Iteration 1: log likelihood = -1218.582
Iteration 2: log likelihood = -1047.3117
Iteration 3: log likelihood = -1041.8053
Iteration 4: log likelihood = -1041.7489
(switching technique to bhhh)
Iteration 5: log likelihood = -1041.7489
Number of obs = 400
Wald chi2(0) = .
Log likelihood = -1041.7489 Prob > chi2 = .
( 1) [mu_n]_cons = 0
------------------------------------------------------------------------------
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
mu_e |
_cons | 12.24605 .0368206 332.59 0.000 12.17389 12.31822
-------------+----------------------------------------------------------------
mu_n |
_cons | 0 (omitted)
-------------+----------------------------------------------------------------
ln_sig_e |
_cons | -.0473635 .0353563 -1.34 0.180 -.1166605 .0219336
-------------+----------------------------------------------------------------
ln_sig_n |
_cons | -.4486958 .0379606 -11.82 0.000 -.5230973 -.3742943
-------------+----------------------------------------------------------------
arho_s |
_cons | -.6801724 .0535134 -12.71 0.000 -.7850567 -.5752882
-------------+----------------------------------------------------------------
lpi_s |
_cons | -1.879033 .1474781 -12.74 0.000 -2.168085 -1.589982
------------------------------------------------------------------------------
. estimates store model1
.
. // No mismatch
. ky_fit r_var s_var l_var, model(2)
Estimating Basic model
initial: log likelihood = -1284.7239
rescale: log likelihood = -1284.7239
rescale eq: log likelihood = -1269.0608
Iteration 0: log likelihood = -1269.0608
Iteration 1: log likelihood = -1213.0075
Iteration 2: log likelihood = -1044.7601
Iteration 3: log likelihood = -1041.7521
Iteration 4: log likelihood = -1041.7267
Iteration 5: log likelihood = -1041.7267
Estimating KY model with no mismatching: pi_r = 0
initial: log likelihood = -1059.9817
rescale: log likelihood = -1059.9817
rescale eq: log likelihood = -848.34996
Iteration 0: log likelihood = -848.34996
Iteration 1: log likelihood = -743.20061
Iteration 2: log likelihood = -699.6481
Iteration 3: log likelihood = -695.56593
Iteration 4: log likelihood = -695.4982
Iteration 5: log likelihood = -695.4981
Iteration 6: log likelihood = -695.4981
Number of obs = 400
Wald chi2(0) = .
Log likelihood = -695.4981 Prob > chi2 = .
------------------------------------------------------------------------------
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
mu_e |
_cons | 12.23967 .047686 256.67 0.000 12.14621 12.33313
-------------+----------------------------------------------------------------
mu_n |
_cons | -.0588547 .0064924 -9.07 0.000 -.0715796 -.0461298
-------------+----------------------------------------------------------------
mu_w |
_cons | .4794169 .2837865 1.69 0.091 -.0767945 1.035628
-------------+----------------------------------------------------------------
ln_sig_e |
_cons | -.0473859 .0353553 -1.34 0.180 -.1166811 .0219093
-------------+----------------------------------------------------------------
ln_sig_n |
_cons | -2.268464 .0464964 -48.79 0.000 -2.359595 -2.177333
-------------+----------------------------------------------------------------
ln_sig_w |
_cons | .7312065 .0996814 7.34 0.000 .5358346 .9265784
-------------+----------------------------------------------------------------
arho_s |
_cons | -.0263245 .0096821 -2.72 0.007 -.0453011 -.007348
-------------+----------------------------------------------------------------
lpi_s |
_cons | -1.879033 .147478 -12.74 0.000 -2.168085 -1.589981
-------------+----------------------------------------------------------------
lpi_w |
_cons | -1.682576 .1612965 -10.43 0.000 -1.998711 -1.36644
------------------------------------------------------------------------------
. estimates store model2
.
. // No contamination
. ky_fit r_var s_var l_var, model(3)
Estimating Basic KY model
initial: log likelihood = -1284.7239
rescale: log likelihood = -1284.7239
rescale eq: log likelihood = -1269.0608
Iteration 0: log likelihood = -1269.0608
Iteration 1: log likelihood = -1213.0075
Iteration 2: log likelihood = -1044.7601
Iteration 3: log likelihood = -1041.7521
Iteration 4: log likelihood = -1041.7267
Iteration 5: log likelihood = -1041.7267
Estimating KY model with no contamination: pi_w = 0
initial: log likelihood = -1055.2145
rescale: log likelihood = -1055.2145
rescale eq: log likelihood = -774.99588
Iteration 0: log likelihood = -774.99588
Iteration 1: log likelihood = -667.12499
Iteration 2: log likelihood = -629.02496
Iteration 3: log likelihood = -608.03708
Iteration 4: log likelihood = -595.73316
Iteration 5: log likelihood = -595.52803
Iteration 6: log likelihood = -595.52796
Iteration 7: log likelihood = -595.52796
Number of obs = 400
Wald chi2(0) = .
Log likelihood = -595.52796 Prob > chi2 = .
------------------------------------------------------------------------------
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
mu_e |
_cons | 12.30638 .0376808 326.60 0.000 12.23252 12.38023
-------------+----------------------------------------------------------------
mu_n |
_cons | -.0617516 .0063582 -9.71 0.000 -.0742135 -.0492898
-------------+----------------------------------------------------------------
mu_t |
_cons | 11.62244 .2556069 45.47 0.000 11.12146 12.12342
-------------+----------------------------------------------------------------
ln_sig_e |
_cons | -.2851316 .0357302 -7.98 0.000 -.3551615 -.2151016
-------------+----------------------------------------------------------------
ln_sig_n |
_cons | -2.269749 .0467776 -48.52 0.000 -2.361432 -2.178067
-------------+----------------------------------------------------------------
ln_sig_t |
_cons | .6219186 .0978989 6.35 0.000 .4300402 .8137969
-------------+----------------------------------------------------------------
arho_s |
_cons | -.014559 .0096932 -1.50 0.133 -.0335572 .0044393
-------------+----------------------------------------------------------------
lpi_r |
_cons | 1.83766 .1587687 11.57 0.000 1.526479 2.148841
-------------+----------------------------------------------------------------
lpi_s |
_cons | -1.708419 .1496447 -11.42 0.000 -2.001717 -1.415121
------------------------------------------------------------------------------
. estimates store model3
.
. // Full model
. ky_fit r_var s_var l_var, model(4)
Estimating Basic KY model
initial: log likelihood = -1284.7239
rescale: log likelihood = -1284.7239
rescale eq: log likelihood = -1269.0608
Iteration 0: log likelihood = -1269.0608
Iteration 1: log likelihood = -1213.0075
Iteration 2: log likelihood = -1044.7601
Iteration 3: log likelihood = -1041.7521
Iteration 4: log likelihood = -1041.7267
Iteration 5: log likelihood = -1041.7267
Estimating KY model with no contamination: pi_w = 0
initial: log likelihood = -1055.2145
rescale: log likelihood = -1055.2145
rescale eq: log likelihood = -774.99588
Iteration 0: log likelihood = -774.99588
Iteration 1: log likelihood = -667.12499
Iteration 2: log likelihood = -629.02496
Iteration 3: log likelihood = -608.03708
Iteration 4: log likelihood = -595.73316
Iteration 5: log likelihood = -595.52803
Iteration 6: log likelihood = -595.52796
Iteration 7: log likelihood = -595.52796
Estimating full KY full model with contamination and mismatch
initial: log likelihood = -651.19502
rescale: log likelihood = -651.19502
rescale eq: log likelihood = -625.46355
Iteration 0: log likelihood = -625.46355 (not concave)
Iteration 1: log likelihood = -558.04591
Iteration 2: log likelihood = -557.50002
Iteration 3: log likelihood = -549.53031
Iteration 4: log likelihood = -543.43433
Iteration 5: log likelihood = -543.43383
Iteration 6: log likelihood = -543.03672
Iteration 7: log likelihood = -543.02821
Iteration 8: log likelihood = -543.0282
Number of obs = 400
Wald chi2(0) = .
Log likelihood = -543.0282 Prob > chi2 = .
------------------------------------------------------------------------------
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
mu_e |
_cons | 12.34936 .0335341 368.26 0.000 12.28364 12.41509
-------------+----------------------------------------------------------------
mu_n |
_cons | -.0608566 .0063531 -9.58 0.000 -.0733084 -.0484048
-------------+----------------------------------------------------------------
mu_w |
_cons | -.3435238 .1479331 -2.32 0.020 -.6334672 -.0535803
-------------+----------------------------------------------------------------
mu_t |
_cons | 8.586232 .6782988 12.66 0.000 7.256791 9.915673
-------------+----------------------------------------------------------------
ln_sig_e |
_cons | -.4064735 .0356129 -11.41 0.000 -.4762735 -.3366734
-------------+----------------------------------------------------------------
ln_sig_n |
_cons | -2.294618 .048419 -47.39 0.000 -2.389518 -2.199719
-------------+----------------------------------------------------------------
ln_sig_w |
_cons | -.0255898 .1117823 -0.23 0.819 -.2446791 .1934995
-------------+----------------------------------------------------------------
ln_sig_t |
_cons | .5011476 .3145946 1.59 0.111 -.1154465 1.117742
-------------+----------------------------------------------------------------
arho_s |
_cons | -.0220849 .0097251 -2.27 0.023 -.0411458 -.003024
-------------+----------------------------------------------------------------
lpi_r |
_cons | 3.519683 .33491 10.51 0.000 2.863271 4.176094
-------------+----------------------------------------------------------------
lpi_s |
_cons | -1.843984 .1478913 -12.47 0.000 -2.133845 -1.554122
-------------+----------------------------------------------------------------
lpi_w |
_cons | -1.784123 .1893322 -9.42 0.000 -2.155207 -1.413039
------------------------------------------------------------------------------
. estimates store model4
.
. // all models can be also be estimated allowing for covariates.
. // For illustrative purposes, create a covariate as a random var
> iable
.
. generate x = rnormal()
.
. ky_fit r_var s_var l_var, model(4) mu_e(x) ln_sig_e(x)
Estimating Basic KY model
initial: log likelihood = -1284.7239
rescale: log likelihood = -1284.7239
rescale eq: log likelihood = -1269.0608
Iteration 0: log likelihood = -1269.0608
Iteration 1: log likelihood = -1247.8509
Iteration 2: log likelihood = -1082.0976
Iteration 3: log likelihood = -1024.9697
Iteration 4: log likelihood = -1023.068
Iteration 5: log likelihood = -1023.0497
Iteration 6: log likelihood = -1023.0497
Estimating KY model with no contamination: pi_w = 0
initial: log likelihood = -1053.1999
rescale: log likelihood = -1053.1999
rescale eq: log likelihood = -791.87357
Iteration 0: log likelihood = -791.87357
Iteration 1: log likelihood = -633.86529
Iteration 2: log likelihood = -596.50958
Iteration 3: log likelihood = -594.15902
Iteration 4: log likelihood = -594.11425
Iteration 5: log likelihood = -594.11424
Estimating full KY full model with contamination and mismatch
initial: log likelihood = -649.48691
rescale: log likelihood = -649.48691
rescale eq: log likelihood = -623.85271
Iteration 0: log likelihood = -623.85271 (not concave)
Iteration 1: log likelihood = -556.21099
Iteration 2: log likelihood = -547.09786
Iteration 3: log likelihood = -540.9457
Iteration 4: log likelihood = -540.78075
Iteration 5: log likelihood = -540.77843
Iteration 6: log likelihood = -540.77843
Number of obs = 400
Wald chi2(1) = 4.14
Log likelihood = -540.77843 Prob > chi2 = 0.0418
------------------------------------------------------------------------------
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
mu_e |
x | .069709 .0342444 2.04 0.042 .0025913 .1368267
_cons | 12.35256 .0333898 369.95 0.000 12.28712 12.41801
-------------+----------------------------------------------------------------
mu_n |
_cons | -.0607139 .0063489 -9.56 0.000 -.0731575 -.0482703
-------------+----------------------------------------------------------------
mu_w |
_cons | -.3523141 .147634 -2.39 0.017 -.6416715 -.0629568
-------------+----------------------------------------------------------------
mu_t |
_cons | 8.659894 .7223845 11.99 0.000 7.244046 10.07574
-------------+----------------------------------------------------------------
ln_sig_e |
x | .0076999 .0323136 0.24 0.812 -.0556337 .0710335
_cons | -.4118867 .0356516 -11.55 0.000 -.4817626 -.3420107
-------------+----------------------------------------------------------------
ln_sig_n |
_cons | -2.295698 .0484046 -47.43 0.000 -2.390569 -2.200827
-------------+----------------------------------------------------------------
ln_sig_w |
_cons | -.031389 .1116725 -0.28 0.779 -.2502631 .1874852
-------------+----------------------------------------------------------------
ln_sig_t |
_cons | .5317966 .3223551 1.65 0.099 -.1000079 1.163601
-------------+----------------------------------------------------------------
arho_s |
_cons | -.0229143 .0097737 -2.34 0.019 -.0420704 -.0037582
-------------+----------------------------------------------------------------
lpi_r |
_cons | 3.494761 .3382142 10.33 0.000 2.831873 4.157649
-------------+----------------------------------------------------------------
lpi_s |
_cons | -1.843337 .1479197 -12.46 0.000 -2.133254 -1.553419
-------------+----------------------------------------------------------------
lpi_w |
_cons | -1.789573 .1905939 -9.39 0.000 -2.16313 -1.416016
------------------------------------------------------------------------------
.
. // For reporting, we use Ben Jann's "estout"
.
. capture ssc install estout
. esttab model0 model4 model3 model2 model1 , se wide compress b(3) ///
> nostar scalars(ll) nogaps ///
> mtitle(Original "Full model" "No contamination" "No mismatch" "Basic
> Model") ///
> noeqline
-------------------------------------------------------------------------------
> -------------------------------
(1) (2) (3) (4
> ) (5)
Original Full mo~l No cont~n No mism~
> h Basic M~l
-------------------------------------------------------------------------------
> -------------------------------
mu_e
>
_cons 12.283 (.) 12.349 (0.034) 12.306 (0.038) 12.24
> 0 (0.048) 12.246 (0.037)
mu_n
>
_cons -0.048 (.) -0.061 (0.006) -0.062 (0.006) -0.05
> 9 (0.006) 0.000 (.)
mu_t
>
_cons 9.187 (.) 8.586 (0.678) 11.622 (0.256)
>
mu_w
>
_cons -0.304 (.) -0.344 (0.148) 0.47
> 9 (0.284)
ln_sig_e
>
_cons -0.333 (.) -0.406 (0.036) -0.285 (0.036) -0.04
> 7 (0.035) -0.047 (0.035)
ln_sig_n
>
_cons -2.313 (.) -2.295 (0.048) -2.270 (0.047) -2.26
> 8 (0.046) -0.449 (0.038)
ln_sig_t
>
_cons 0.592 (.) 0.501 (0.315) 0.622 (0.098)
>
ln_sig_w
>
_cons 0.214 (.) -0.026 (0.112) 0.73
> 1 (0.100)
arho_s
>
_cons -0.013 (.) -0.022 (0.010) -0.015 (0.010) -0.02
> 6 (0.010) -0.680 (0.054)
lpi_r
>
_cons 3.152 (.) 3.520 (0.335) 1.838 (0.159)
>
lpi_s
>
_cons -1.719 (.) -1.844 (0.148) -1.708 (0.150) -1.87
> 9 (0.147) -1.879 (0.147)
lpi_w
>
_cons -1.688 (.) -1.784 (0.189) -1.68
> 3 (0.161)
-------------------------------------------------------------------------------
> -------------------------------
N 400 400 40
> 0 400
ll -543.028 -595.528 -695.49
> 8 -1041.749
-------------------------------------------------------------------------------
> -------------------------------
Standard errors in parentheses
.
. // The results reported are very similar to those reported by KY
.
. /////////////////////////////////////////////////////////////////////////////
> /////////////////////////
> // Post estimation:
.
. quietly: ky_fit r_var s_var l_var, model(4)
Estimating Basic KY model
Estimating KY model with no contamination: pi_w = 0
Estimating full KY full model with contamination and mismatch
.
. // We can request the full report of probabilities and reliability from this
> data:
.
. estat reliability,
Model structure:
Survey with RTM error and contamination and Admin data with Mismatch
Pr of correctly reporting data pi_s: 0.1366
Pr of contamination pi_w: 0.1438
Pr of correctly match pi_r: 0.9712
Data TYPE for R
Type I : r_i = e_i
with p = pi_r : 0.9712
Type II : r_i = t_i
with p = (1- pi_r) : 0.0288
Data TYPE for S
Type I : s_i = e_i
with p = pi_s : 0.1366
Type II : s_i = e_i+rho_s*[e_i-E(e_i|X)]+n_i
with pr (1- pi_s)*(1-pi_w): 0.7393
Type III: s_i = e_i+rho_s*[e_i-E(e_i|X)]+n_i+w_i
with pr (1- pi_s)* pi_w : 0.1242
Class probabilities
Pr R type I & S Type I : 0.1327
Pr R type I & S Type II : 0.7180
Pr R type I & S Type III: 0.1206
Pr R type II & S Type I : 0.0039
Pr R type II & S Type II : 0.0213
Pr R type II & S Type III: 0.0036
Summary Moments Statistics
E(x_i) V(x_i)= V(E(x_i|X)) Sig_x^2
e_i 12.3494 0.4435 0.0000 0.4435
n_i -0.0609 0.0102 0.0000 0.0102
w_i -0.3435 0.9501 0.0000 0.9501
t_i 8.5862 2.7245 0.0000 2.7245
Reliability Statistics: R
Var(r_i) 0.9047
Cov(r_i,e_i) 0.4308
Reliability 0.4762
Reliability 2 0.4625
Reliability Statistics: S
Var(s_i) 0.5675
Cov(s_i,e_i) 0.4351
Reliability 0.7666
Reliability 2 0.7520
.
. // and we can also obtain the simulation based reliabilities
.
. estat reliability, sim seed(10)
Reliability Statistics: R
Var(r_i) 0.8980
Cov(r_i,e_i) 0.4207
Reliability 0.4684
Reliability 2 0.4512
Reliability Statistics: S
Var(s_i) 0.5578
Cov(s_i,e_i) 0.4292
Reliability 0.7694
Reliability 2 0.7561
.
. // More interestingly, we can also report the coefficients in their original
> scales
. // as well as estimating marginal effects via -margins-
. // Here is an example for predicted means, which could be extended
. // to marginal effects, or means by groups defined by covariate levels and
> combinations
.
. margins , predict(mean_e) predict(sig_e) ///
> predict(mean_t) predict(sig_t) ///
> predict(mean_w) predict(sig_w) ///
> predict(mean_n) predict(sig_n) ///
> predict(pi_r) predict(pi_s) predict(pi_w) ///
> predict(rho_s)
Warning: prediction constant over observations.
Warning: prediction constant over observations.
Warning: prediction constant over observations.
Warning: prediction constant over observations.
Warning: prediction constant over observations.
Warning: prediction constant over observations.
Warning: prediction constant over observations.
Warning: prediction constant over observations.
Warning: prediction constant over observations.
Warning: prediction constant over observations.
Warning: prediction constant over observations.
Warning: prediction constant over observations.
Predictive margins Number of obs = 400
Model VCE : OIM
1._predict : Conditional mean for component e, predict(mean_e)
2._predict : Conditional stdev for component e, predict(sig_e)
3._predict : Conditional mean for component t, predict(mean_t)
4._predict : Conditional stdev for component t, predict(sig_t)
5._predict : Conditional mean for component w, predict(mean_w)
6._predict : Conditional stdev for component w, predict(sig_w)
7._predict : Conditional mean for component n, predict(mean_n)
8._predict : Conditional stdev for component n, predict(sig_n)
9._predict : A priori Pi_r, predict(pi_r)
10._predict : A priori Pi_s, predict(pi_s)
11._predict : A priori Pi_r, predict(pi_w)
12._predict : Rho s: RTM Survey data, predict(rho_s)
------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_predict |
1 | 12.34936 .0335341 368.26 0.000 12.28364 12.41509
2 | .6659948 .023718 28.08 0.000 .6195083 .7124812
3 | 8.586232 .6782988 12.66 0.000 7.256791 9.915673
4 | 1.650614 .5192744 3.18 0.001 .6328553 2.668374
5 | -.3435238 .1479331 -2.32 0.020 -.6334672 -.0535803
6 | .9747348 .1089581 8.95 0.000 .7611809 1.188289
7 | -.0608566 .0063531 -9.58 0.000 -.0733084 -.0484048
8 | .1007999 .0048806 20.65 0.000 .091234 .1103657
9 | .9712426 .0093542 103.83 0.000 .9529088 .9895765
10 | .1365808 .0174403 7.83 0.000 .1023985 .1707632
11 | .1437948 .0233102 6.17 0.000 .0981077 .1894819
12 | -.0220813 .0097204 -2.27 0.023 -.041133 -.0030297
------------------------------------------------------------------------------
.
. /////////////////////////////////////////////////////////////////////
> /// The last exercise uses -predict-'s "star" option to obtain
> /// hybrid earnings predictors, combining information from the survey and
> admin data
> /// For this we simulate the data again, using KY's parameters for the excerc
> ise
>
. // First, declare the model to be used for simulation
. // Second, declare values of model parameters
. ky_sim, nobs(400) model(4) seed(101) ///
> mean_e($mean_e) mean_t($mean_t) mean_w($mean_w) mean_n($mean_n) ///
> sig_e($sig_e) sig_t($sig_t) sig_w($sig_w) sig_n($sig_n) ///
> pi_r($pi_r) pi_s($pi_s) pi_w($pi_w) rho_s($rho_s) clear
.
. predict xi_, star
. // we can compare the true value of the latent data (simulated) with estimato
> rs
. // proposed by MRW(12)
. sum e_var xi_*, sep(0)
Variable | Obs Mean Std. Dev. Min Max
-------------+---------------------------------------------------------
e_var | 400 12.34898 .665869 10.4206 14.51099
xi_1 | 400 12.24331 .8960243 6.575324 14.48422
xi_2 | 400 12.24466 .8982783 6.576832 14.4954
xi_3 | 400 12.3475 .6613628 10.44586 14.51076
xi_4 | 400 12.34792 .663123 10.43073 14.51101
xi_5 | 400 12.3493 .6660313 10.4206 14.51099
xi_6 | 400 12.34937 .6662144 10.4206 14.51099
xi_7 | 400 12.33033 .5635707 10.61069 14.25576
.
. corr e_var xi_*,
(obs=400)
| e_var xi_1 xi_2 xi_3 xi_4 xi_5 xi_6
-------------+---------------------------------------------------------------
e_var | 1.0000
xi_1 | 0.7160 1.0000
xi_2 | 0.7177 1.0000 1.0000
xi_3 | 0.9989 0.7213 0.7230 1.0000
xi_4 | 0.9990 0.7157 0.7173 0.9999 1.0000
xi_5 | 0.9998 0.7147 0.7163 0.9986 0.9987 1.0000
xi_6 | 0.9998 0.7140 0.7156 0.9985 0.9987 1.0000 1.0000
xi_7 | 0.8911 0.8436 0.8452 0.8970 0.8957 0.8906 0.8904
| xi_7
-------------+---------
xi_7 | 1.0000
. // The following provides simple plots for the true e_var and the predictions
> based on MRW
. plot e_var xi_1
14.511 +
T | *
r |
u |
e | **
| **
L | *** *
a | * ***
t | ***
e | ***
n | * * ***
t | * * ****
| * * * ***
l | * * ***
o | ****
g | ****
( | * ***
e | ***
a | ***
r | ***
10.4206 + **
+----------------------------------------------------------------+
6.57532 Weighted unconditional prediction for e 14.4842
. plot e_var xi_2
14.511 +
T | *
r |
u |
e | **
| **
L | *** *
a | * ***
t | ***
e | ***
n | * * ***
t | * * ****
| * * * ****
l | * * ****
o | * ***
g | ****
( | * ***
e | ***
a | ***
r | ***
10.4206 + **
+----------------------------------------------------------------+
6.57683 Weighted unconditional, unbiased predict 14.4954
. plot e_var xi_7
14.511 +
T | *
r |
u |
e | *** *
| ****
L | ** * * ** * *
a | * *****
t | * ******
e | * ***** * *
n | * * * * ********
t | * * ** ***** *
| * * * * * * * ******
l | ** * * * ***** **
o | * * *******
g | ******* *
( | * * * ***
e | **** *
a | * ***
r | * **
10.4206 + * *
+----------------------------------------------------------------+
10.6107 System-wide, linear prediction for e 14.2558
.
. // we could even produce the predictions assuming we only have access to surv
> ey data:
. predict xis_, star surv_only
. corr e_var xis_*,
(obs=400)
| e_var xis_1 xis_2 xis_3 xis_4 xis_5 xis_6
-------------+---------------------------------------------------------------
e_var | 1.0000
xis_1 | 0.8920 1.0000
xis_2 | 0.8907 0.9998 1.0000
xis_3 | 0.9008 0.9728 0.9711 1.0000
xis_4 | 0.8834 0.9986 0.9987 0.9653 1.0000
xis_5 | 0.8748 0.9247 0.9270 0.9606 0.9163 1.0000
xis_6 | 0.8700 0.9821 0.9856 0.9436 0.9853 0.9310 1.0000
xis_7 | 0.8677 0.9833 0.9870 0.9439 0.9846 0.9310 0.9978
| xis_7
-------------+---------
xis_7 | 1.0000
.
. // finally, we prepare some summary statistics that show
. // the reliability of the data as suggested by MRW
. // This replicates MRW reliability (rel2) for survey and admin data exactly.
. quietly: estat reliability
. matrix rel_analytical = r(rel)
. quietly: estat reliability, sim reps(100) seed(10)
. matrix rel_simulation = r(rel)
. matrix roweq rel_analytical = Analytical
. matrix roweq rel_simulation = Simulation
. matrix result = rel_analytical \ rel_simulation
. matrix list result, format(%5.4f)
result[4,4]
Var Cov Rel1 Rel2
Analytical:R 1.0038 0.4930 0.4912 0.4710
Analytical:S 0.7257 0.5084 0.7006 0.6929
Simulation:R 0.9947 0.4866 0.4892 0.4662
Simulation:S 0.7169 0.5055 0.7051 0.6981
.
. // We can report the Reliability for all 7 hybrid earnings predictors
. // following MRW's methodology.
. // This replicates MRW's Table 6:
. estat xirel, seed(10) reps(100)
Rel Statistics for 'e' predictions
Rel1 Rel2 MSE E(Bias) Var(Bias)
r_var 0.5005 0.4786 0.5480 -0.1267 0.5321
s_var 0.7097 0.7021 0.2227 -0.0783 0.2165
e_1 0.5605 0.5353 0.4344 -0.1189 0.4204
e_2 0.5600 0.5375 0.4342 -0.1178 0.4204
e_3 1.0020 0.9795 0.0105 0.0009 0.0105
e_4 0.9879 0.9738 0.0137 0.0013 0.0136
e_5 0.9892 0.9758 0.0125 -0.0002 0.0125
e_6 0.9805 0.9714 0.0150 -0.0003 0.0150
e_7 1.0068 0.7627 0.1216 0.0018 0.1217
.
. ****
. log close
name: <unnamed>
log: D:\home\stephenj\MYProjects\DWP_SDP\kyado\Clean_Ados\ky_example.lo
> g
log type: text
closed on: 24 May 2021, 10:54:21
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