Example of SUR estimation with panel data
. drop caar clar firmnr t1 t2 t3 t4 t5 t6
. reshape wide roe lev tobq cbeta, i(cusip) j(yearptr)
(note: j = 0 1 2 3 4 5 6)
Data wide -> long
-----------------------------------------------------------------------------
Number of obs. 350 -> 50
Number of variables 6 -> 29
j variable (7 values) yearptr -> (dropped)
xij variables:
roe -> roe0 roe1 ... roe6
lev -> lev0 lev1 ... lev6
tobq -> tobq0 tobq1 ... tobq6
cbeta -> cbeta0 cbeta1 ... cbeta6
-----------------------------------------------------------------------------
. summ
Variable | Obs Mean Std. Dev. Min Max
---------+-----------------------------------------------------
cusip | 50 469349 278445.4 1688 963320
cbeta0 | 50 1.0042 .2164471 .54 1.65
roe0 | 50 3.883854 7.862105 -20.0409 16.5186
tobq0 | 50 1.076708 .4774362 .569 3.1185
lev0 | 50 .35977 .4819179 .0026 3.2347
cbeta1 | 50 1.0278 .2903853 .29 2.27
roe1 | 50 6.196632 5.610777 -10.1931 22.1943
tobq1 | 50 1.007064 .4477677 .457 2.9761
lev1 | 50 .50814 .6496168 .0117 4.1957
cbeta2 | 50 1.0594 .3326051 .29 2.27
roe2 | 50 6.13169 5.589205 -8.0833 23.9925
tobq2 | 50 .953862 .3883063 .4298 2.3539
lev2 | 50 .615938 1.347538 .013 9.605
cbeta3 | 50 1.0098 .2935601 .29 2.27
roe3 | 50 5.526766 6.041315 -10.8963 22.5864
tobq3 | 50 .949924 .4558494 .4555 2.9094
lev3 | 50 .498612 .5469398 .0122 2.5907
cbeta4 | 50 1.022 .2492847 .29 2
roe4 | 50 3.744152 6.185379 -17.8136 19.2118
tobq4 | 50 .967758 .6017065 .4462 3.9244
lev4 | 50 .47525 .4761417 .015 2.407
cbeta5 | 50 .993 .230317 .29 1.7
roe5 | 50 4.291354 6.042261 -18.0329 13.7559
tobq5 | 50 .967456 .6110386 .4097 4.0775
lev5 | 50 .437304 .471578 .0041 2.3096
cbeta6 | 50 .9696 .2216079 .29 1.65
roe6 | 50 2.687956 7.497477 -13.8009 19.8513
tobq6 | 50 .933072 .4531542 .4336 2.6555
lev6 | 50 .520916 .6245689 .0034 3.6092
. eq roe0 lev0 tobq0 cbeta0
. eq roe1 lev1 tobq1 cbeta1
. eq roe2 lev2 tobq2 cbeta2
. eq roe3 lev3 tobq3 cbeta3
. eq roe4 lev4 tobq4 cbeta4
. eq roe5 lev5 tobq5 cbeta5
. eq roe6 lev6 tobq6 cbeta6
. sureg roe0 roe1 roe2 roe3 roe4 roe5 roe6
Equation Obs Parms RMSE "R-sq" F P
------------------------------------------------------------------
roe0 50 4 5.502964 0.5401 22.62 0.0000
roe1 50 4 4.099582 0.4988 15.62957 0.0000
roe2 50 4 3.816528 0.5623 19.84451 0.0000
roe3 50 4 4.969317 0.3648 9.090408 0.0000
roe4 50 4 4.760276 0.4440 14.49972 0.0000
roe5 50 4 5.024527 0.3508 8.718406 0.0000
roe6 50 4 3.868607 0.7501 61.73442 0.0000
------------------------------------------------------------------------------
| Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
roe0 |
lev0 | -5.200336 1.628849 -3.193 0.002 -8.404866 -1.995807
tobq0 | 10.33629 1.819211 5.682 0.000 6.757255 13.91533
cbeta0 | -9.901678 3.483853 -2.842 0.005 -16.75567 -3.047689
_cons | 4.568874 3.502497 1.304 0.193 -2.321793 11.45954
---------+--------------------------------------------------------------------
roe1 |
lev1 | -2.098479 .855281 -2.454 0.015 -3.781124 -.4158349
tobq1 | 6.806053 1.323821 5.141 0.000 4.201623 9.410484
cbeta1 | -.2608589 1.855424 -0.141 0.888 -3.911142 3.389425
_cons | .6769329 2.172655 0.312 0.756 -3.597457 4.951323
---------+--------------------------------------------------------------------
roe2 |
lev2 | -.5118847 .3442075 -1.487 0.138 -1.189064 .1652948
tobq2 | 9.397844 1.28108 7.336 0.000 6.8775 11.91819
cbeta2 | -1.317951 1.331242 -0.990 0.323 -3.936982 1.301079
_cons | -1.12103 1.764974 -0.635 0.526 -4.593367 2.351308
---------+--------------------------------------------------------------------
roe3 |
lev3 | -3.656251 1.053165 -3.472 0.001 -5.728204 -1.584297
tobq3 | 5.39683 1.78578 3.022 0.003 1.88356 8.9101
cbeta3 | -2.337329 2.679809 -0.872 0.384 -7.609474 2.934817
_cons | 4.583473 2.416172 1.897 0.059 -.1700047 9.33695
---------+--------------------------------------------------------------------
roe4 |
lev4 | -7.865786 1.376174 -5.716 0.000 -10.57321 -5.158359
tobq4 | 3.27522 1.318337 2.484 0.013 .6815774 5.868862
cbeta4 | -8.865709 3.125976 -2.836 0.005 -15.01563 -2.715793
_cons | 13.3735 3.122147 4.283 0.000 7.231118 19.51588
---------+--------------------------------------------------------------------
roe5 |
lev5 | -5.892689 1.375226 -4.285 0.000 -8.598252 -3.187125
tobq5 | 2.44463 1.305694 1.872 0.062 -.1241373 5.013398
cbeta5 | -4.739855 3.151931 -1.504 0.134 -10.94083 1.461122
_cons | 9.209854 3.033937 3.036 0.003 3.241012 15.1787
---------+--------------------------------------------------------------------
roe6 |
lev6 | -4.154991 .8099786 -5.130 0.000 -5.74851 -2.561473
tobq6 | 12.25611 1.284525 9.541 0.000 9.728983 14.78323
cbeta6 | -6.218179 2.213325 -2.809 0.005 -10.57258 -1.863774
_cons | -.5543249 2.279129 -0.243 0.808 -5.038189 3.92954
------------------------------------------------------------------------------
. which reg3
~:Stata:ado:reg3.ado
*! version 1.0.0 07Oct1997 Statalist distribution
. reg3 roe0 roe1 roe2 roe3 roe4 roe5 roe6
Three-stage regression results
------------------------------------------------------------------
Equation Obs Parms RMSE "R-sq" Chi2 P
------------------------------------------------------------------
roe0 50 3 5.305504 0.5353 73.76 0.0000
roe1 50 3 4.135927 0.4455 50.97 0.0000
roe2 50 3 3.989091 0.4802 64.71 0.0000
roe3 50 3 4.956471 0.3132 29.64 0.0000
roe4 50 3 4.607001 0.4339 47.28 0.0000
roe5 50 3 4.913361 0.3253 28.43 0.0000
roe6 50 3 3.726577 0.7479 201.31 0.0000
------------------------------------------------------------------
------------------------------------------------------------------------------
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
---------+--------------------------------------------------------------------
roe0 |
lev0 | -5.200336 1.562337 -3.329 0.001 -8.26246 -2.138212
tobq0 | 10.33629 1.744925 5.924 0.000 6.916303 13.75629
cbeta0 | -9.901678 3.341595 -2.963 0.003 -16.45108 -3.352273
_cons | 4.568874 3.359477 1.360 0.174 -2.01558 11.15333
---------+--------------------------------------------------------------------
roe1 |
lev1 | -2.098479 .8203567 -2.558 0.011 -3.706349 -.4906096
tobq1 | 6.806053 1.269764 5.360 0.000 4.317361 9.294746
cbeta1 | -.2608588 1.77966 -0.147 0.883 -3.748928 3.22721
_cons | .6769328 2.083937 0.325 0.745 -3.407509 4.761374
---------+--------------------------------------------------------------------
roe2 |
lev2 | -.5118847 .3301522 -1.550 0.121 -1.158971 .1352018
tobq2 | 9.397844 1.228769 7.648 0.000 6.989501 11.80619
cbeta2 | -1.317951 1.276883 -1.032 0.302 -3.820595 1.184693
_cons | -1.12103 1.692904 -0.662 0.508 -4.439061 2.197001
---------+--------------------------------------------------------------------
roe3 |
lev3 | -3.656251 1.010161 -3.619 0.000 -5.636129 -1.676372
tobq3 | 5.39683 1.71286 3.151 0.002 2.039686 8.753974
cbeta3 | -2.337329 2.570383 -0.909 0.363 -7.375186 2.700529
_cons | 4.583473 2.317511 1.978 0.048 .0412343 9.125711
---------+--------------------------------------------------------------------
roe4 |
lev4 | -7.865786 1.319979 -5.959 0.000 -10.4529 -5.278674
tobq4 | 3.27522 1.264505 2.590 0.010 .7968359 5.753603
cbeta4 | -8.865709 2.998331 -2.957 0.003 -14.74233 -2.989088
_cons | 13.3735 2.994658 4.466 0.000 7.504079 19.24292
---------+--------------------------------------------------------------------
roe5 |
lev5 | -5.892689 1.319071 -4.467 0.000 -8.47802 -3.307358
tobq5 | 2.44463 1.252377 1.952 0.051 -.0099843 4.899245
cbeta5 | -4.739855 3.023226 -1.568 0.117 -10.66527 1.185558
_cons | 9.209854 2.91005 3.165 0.002 3.506261 14.91345
---------+--------------------------------------------------------------------
roe6 |
lev6 | -4.154991 .7769042 -5.348 0.000 -5.677696 -2.632287
tobq6 | 12.25611 1.232074 9.948 0.000 9.841285 14.67093
cbeta6 | -6.218179 2.122947 -2.929 0.003 -10.37908 -2.057279
_cons | -.5543249 2.186064 -0.254 0.800 -4.838932 3.730282
------------------------------------------------------------------------------
. constraint define 1 [roe0]tobq0=[roe1]tobq1
. constraint define 2 [roe0]tobq0=[roe2]tobq2
. constraint define 3 [roe0]tobq0=[roe3]tobq3
. constraint define 4 [roe0]tobq0=[roe4]tobq4
. constraint define 5 [roe0]tobq0=[roe5]tobq5
. constraint define 6 [roe0]tobq0=[roe6]tobq6
. reg3 roe0 roe1 roe2 roe3 roe4 roe5 roe6, constr(1-6)
Three-stage regression results
------------------------------------------------------------------
Equation Obs Parms RMSE "R-sq" Chi2 P
------------------------------------------------------------------
roe0 50 3 5.378119 0.5225 137.65 0.0000
roe1 50 3 4.25828 0.4122 112.14 0.0000
roe2 50 3 4.129461 0.4430 104.88 0.0000
roe3 50 3 4.943927 0.3166 115.45 0.0000
roe4 50 3 5.202901 0.2780 145.29 0.0000
roe5 50 3 5.806511 0.0577 126.31 0.0000
roe6 50 3 3.987614 0.7114 204.44 0.0000
------------------------------------------------------------------
------------------------------------------------------------------------------
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
---------+--------------------------------------------------------------------
roe0 |
lev0 | -6.412792 1.449385 -4.424 0.000 -9.253535 -3.57205
tobq0 | 7.471666 .7462595 10.012 0.000 6.009024 8.934308
cbeta0 | -8.004176 3.122194 -2.564 0.010 -14.12357 -1.884788
_cons | 6.183976 3.267973 1.892 0.058 -.2211334 12.58909
---------+--------------------------------------------------------------------
roe1 |
lev1 | -1.339709 .7946672 -1.686 0.092 -2.897228 .2178104
tobq1 | 7.471666 .7462595 10.012 0.000 6.009024 8.934308
cbeta1 | -.0399838 1.664141 -0.024 0.981 -3.301641 3.221673
_cons | -.6059587 2.002758 -0.303 0.762 -4.531292 3.319375
---------+--------------------------------------------------------------------
roe2 |
lev2 | -.3827113 .3205957 -1.194 0.233 -1.011067 .2456446
tobq2 | 7.471666 .7462595 10.012 0.000 6.009024 8.934308
cbeta2 | -.712405 1.235687 -0.577 0.564 -3.134307 1.709497
_cons | -.0047998 1.583208 -0.003 0.998 -3.107831 3.098231
---------+--------------------------------------------------------------------
roe3 |
lev3 | -3.477603 .9914421 -3.508 0.000 -5.420794 -1.534412
tobq3 | 7.471666 .7462595 10.012 0.000 6.009024 8.934308
cbeta3 | -5.778826 1.908888 -3.027 0.002 -9.520178 -2.037474
_cons | 5.998685 2.289109 2.621 0.009 1.512113 10.48526
---------+--------------------------------------------------------------------
roe4 |
lev4 | -7.373291 1.310768 -5.625 0.000 -9.942348 -4.804233
tobq4 | 7.471666 .7462595 10.012 0.000 6.009024 8.934308
cbeta4 | -14.91344 2.641978 -5.645 0.000 -20.09163 -9.735262
_cons | 15.25908 2.949599 5.173 0.000 9.477977 21.04019
---------+--------------------------------------------------------------------
roe5 |
lev5 | -5.198221 1.296377 -4.010 0.000 -7.739073 -2.65737
tobq5 | 7.471666 .7462595 10.012 0.000 6.009024 8.934308
cbeta5 | -12.46723 2.750981 -4.532 0.000 -17.85905 -7.075405
_cons | 11.71601 2.892809 4.050 0.000 6.046206 17.38581
---------+--------------------------------------------------------------------
roe6 |
lev6 | -5.632286 .7275719 -7.741 0.000 -7.058301 -4.206271
tobq6 | 7.471666 .7462595 10.012 0.000 6.009024 8.934308
cbeta6 | -3.131417 2.020763 -1.550 0.121 -7.09204 .8292065
_cons | 1.686523 2.136525 0.789 0.430 -2.500988 5.874035
------------------------------------------------------------------------------
. log close
Example of fixed and random effects estimation and testing
. use 761panel
. iis cusip
. tis yearptr
. summ
Variable | Obs Mean Std. Dev. Min Max
---------+-----------------------------------------------------
cbeta | 350 1.012257 .2642095 .29 2.27
cusip | 350 469349 276041.5 1688 963320
roe | 350 4.637486 6.522068 -20.0409 23.9925
caar | 350 48.55116 12.19374 6.119 75.663
clar | 350 22.72243 8.557115 7.7771 52.4518
tobq | 350 .9794063 .4945858 .4097 4.0775
lev | 350 .48799 .7155065 .0026 9.605
yearptr | 350 3 2.002863 0 6
firmnr | 350 25.5 14.45153 1 50
. regress roe lev tobq cbeta
Source | SS df MS Number of obs = 350
---------+------------------------------ F( 3, 346) = 60.10
Model | 5085.68891 3 1695.22964 Prob > F = 0.0000
Residual | 9759.85575 346 28.2076756 R-squared = 0.3426
---------+------------------------------ Adj R-squared = 0.3369
Total | 14845.5447 349 42.5373773 Root MSE = 5.3111
------------------------------------------------------------------------------
roe | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
lev | -3.311485 .4175035 -7.932 0.000 -4.13265 -2.490321
tobq | 6.249819 .6699128 9.329 0.000 4.932205 7.567433
cbeta | -6.027554 1.258113 -4.791 0.000 -8.502067 -3.553042
_cons | 6.233781 1.239266 5.030 0.000 3.796339 8.671223
------------------------------------------------------------------------------
. xtreg roe lev tobq cbeta,fe
Fixed-effects (within) regression
sd(u_cusip) = 3.999577 Number of obs = 350
sd(e_cusip_t) = 4.303878 n = 50
sd(e_cusip_t + u_cusip) = 5.875371 T = 7
corr(u_cusip, Xb) = 0.3382 R-sq within = 0.0682
between = 0.4774
overall = 0.3021
F( 3, 297) = 7.24
Prob > F = 0.0001
------------------------------------------------------------------------------
roe | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
lev | -1.128466 .504682 -2.236 0.026 -2.121672 -.1352598
tobq | 4.195395 1.151747 3.643 0.000 1.928775 6.462015
cbeta | -1.410826 1.861015 -0.758 0.449 -5.073272 2.251621
_cons | 2.507288 2.285862 1.097 0.274 -1.99125 7.005826
------------------------------------------------------------------------------
cusip | F(49,297) = 4.692 0.000 (50 categories)
. gen t1=(yearptr==1)
. gen t2=(yearptr==2)
. gen t3=(yearptr==3)
. gen t4=(yearptr==4)
. gen t5=(yearptr==5)
. gen t6=(yearptr==6)
. xtreg roe lev tobq cbeta t1 t2 t3 t4 t5 t6,fe
Fixed-effects (within) regression
sd(u_cusip) = 3.888367 Number of obs = 350
sd(e_cusip_t) = 4.087506 n = 50
sd(e_cusip_t + u_cusip) = 5.641552 T = 7
corr(u_cusip, Xb) = 0.3630 R-sq within = 0.1765
between = 0.5601
overall = 0.3692
F( 9, 291) = 6.93
Prob > F = 0.0000
------------------------------------------------------------------------------
roe | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
lev | -1.422335 .4843476 -2.937 0.004 -2.375604 -.4690668
tobq | 4.302949 1.119553 3.843 0.000 2.099501 6.506398
cbeta | -3.302664 1.809873 -1.825 0.069 -6.864764 .2594367
t1 | 2.901427 .8245561 3.519 0.001 1.278578 4.524277
t2 | 3.3231 .8413604 3.950 0.000 1.667177 4.979023
t3 | 2.404432 .8310946 2.893 0.004 .7687135 4.04015
t4 | .552143 .8279086 0.667 0.505 -1.077305 2.181591
t5 | .9508953 .8271815 1.150 0.251 -.6771214 2.578912
t6 | -.4629081 .8378573 -0.552 0.581 -2.111937 1.18612
_cons | 3.079083 2.330518 1.321 0.187 -1.507725 7.66589
------------------------------------------------------------------------------
cusip | F(49,291) = 4.939 0.000 (50 categories)
. test t1 t2 t3 t4 t5 t6
( 1) t1 = 0.0
( 2) t2 = 0.0
( 3) t3 = 0.0
( 4) t4 = 0.0
( 5) t5 = 0.0
( 6) t6 = 0.0
F( 6, 291) = 6.38
Prob > F = 0.0000
. xtreg roe lev tobq cbeta,be
Between-CUSIP regression
Number of obs = 350
n = 50
T = 7
R-sq within = 0.0552
between = 0.6479
overall = 0.3296
sd(u_cusip + e_cusip) = 3.127082 F( 3, 46) = 28.21
where e_cusip = avg(e_cusip_t) Prob > F = 0.0000
------------------------------------------------------------------------------
roe | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
lev | -5.417003 .8862412 -6.112 0.000 -7.200914 -3.633092
tobq | 7.606025 1.266062 6.008 0.000 5.057575 10.15448
cbeta | -10.96147 2.528266 -4.336 0.000 -16.05061 -5.872337
_cons | 10.92737 2.34867 4.653 0.000 6.199742 15.655
------------------------------------------------------------------------------
. xtreg roe lev tobq cbeta t1 t2 t3 t4 t5 t6,re
Random-effects GLS regression
sd(u_cusip) = 2.718791 Number of obs = 350
sd(e_cusip_t) = 4.087506 n = 50
sd(e_cusip_t + u_cusip) = 4.909128 T = 7
corr(u_cusip, X) = 0 (assumed) R-sq within = 0.1708
between = 0.5834
overall = 0.3899
chi2( 9) = 118.22
(theta = 0.5060) Prob > chi2 = 0.0000
------------------------------------------------------------------------------
roe | Coef. Std. Err. z P>|z| [95% Conf. Interval]
---------+--------------------------------------------------------------------
lev | -2.275645 .4350806 -5.230 0.000 -3.128388 -1.422903
tobq | 5.522897 .8010853 6.894 0.000 3.952798 7.092995
cbeta | -4.34108 1.417614 -3.062 0.002 -7.119553 -1.562608
t1 | 3.137502 .8454078 3.711 0.000 1.480533 4.79447
t2 | 3.748877 .8584717 4.367 0.000 2.066303 5.431451
t3 | 2.683392 .8477208 3.165 0.002 1.02189 4.344894
t4 | .8020803 .8466725 0.947 0.343 -.8573672 2.461528
t5 | 1.138707 .8444958 1.348 0.178 -.5164742 2.793889
t6 | -.1861015 .8486201 -0.219 0.826 -1.849366 1.477163
_cons | 3.115329 1.645929 1.893 0.058 -.1106337 6.341291
------------------------------------------------------------------------------
. xttest0
Breusch and Pagan Lagrangian multiplier test for random effects:
roe[cusip,t] = Xb + u[cusip] + e[cusip,t]
Estimated results:
Var sd = sqrt(Var)
---------+-----------------------------
roe | 42.53738 6.522068
e | 16.70771 4.0875064
u | 7.391826 2.7187913
Test: Var(u) = 0
chi2(1) = 94.79
Prob>chi2 = 0.0000
. xthaus
Hausman specification test
---- Coefficients ----
| Fixed Random
roe | Effects Effects Difference
---------+-----------------------------------------
lev | -1.422335 -2.275645 .85331
tobq | 4.302949 5.522897 -1.219948
cbeta | -3.302664 -4.34108 1.038416
t1 | 2.901427 3.137502 -.2360742
t2 | 3.3231 3.748877 -.4257769
t3 | 2.404432 2.683392 -.2789602
t4 | .552143 .8020803 -.2499373
t5 | .9508953 1.138707 -.187812
t6 | -.4629081 -.1861015 -.2768067
Test: Ho: difference in coefficients not systematic
chi2( 9) = (b-B)'[S^(-1)](b-B), S = (S_fe - S_re)
= 27.73
Prob>chi2 = 0.0011
. xtreg roe lev tobq cbeta t1 t2 t3 t4 t5 t6,gee robust
Iteration 1: tolerance = .31924473
Iteration 2: tolerance = .05454121
Iteration 3: tolerance = .0068676
Iteration 4: tolerance = .00084529
Iteration 5: tolerance = .00010386
Iteration 6: tolerance = .00001276
Iteration 7: tolerance = 1.567e-06
Iteration 8: tolerance = 1.926e-07
General estimating equation for panel data Number of obs = 350
Group variable: cusip Number of groups = 50
Link: identity Obs/group, min = 7
Family: Gaussian avg = 7.00
Correlation: exchangeable max = 7
chi2(9) = 47.24
Scale parameter: 27.55153 Prob > chi2 = 0.0000
Pearson chi2(340): 9367.52 Deviance = 9367.52
Dispersion (Pearson): 27.55153 Dispersion = 27.55153
(standard errors adjusted for clustering on cusip)
------------------------------------------------------------------------------
| Robust
roe | Coef. Std. Err. z P>|z| [95% Conf. Interval]
---------+--------------------------------------------------------------------
lev | -2.103859 1.093423 -1.924 0.054 -4.246927 .0392101
tobq | 5.350733 2.129325 2.513 0.012 1.177332 9.524134
cbeta | -4.035968 1.293775 -3.120 0.002 -6.571719 -1.500216
t1 | 3.092823 .8840228 3.499 0.000 1.36017 4.825476
t2 | 3.666879 .886862 4.135 0.000 1.928661 5.405096
t3 | 2.636005 .9979949 2.641 0.008 .6799707 4.592039
t4 | .7580542 1.103556 0.687 0.492 -1.404875 2.920984
t5 | 1.109996 1.052563 1.055 0.292 -.9529891 3.172981
t6 | -.2279562 .7144659 -0.319 0.750 -1.628284 1.172371
_cons | 2.932501 3.082205 0.951 0.341 -3.108511 8.973512
------------------------------------------------------------------------------
. log close
Example of general estimating equation approach
. xtreg roe lev tobq cbeta,gee robust
Iteration 1: tolerance = .40395989
Iteration 2: tolerance = .10012121
Iteration 3: tolerance = .01515
Iteration 4: tolerance = .00208385
Iteration 5: tolerance = .00028282
Iteration 6: tolerance = .00003832
Iteration 7: tolerance = 5.189e-06
Iteration 8: tolerance = 7.028e-07
General estimating equation for panel data Number of obs = 350
Group variable: cusip Number of groups = 50
Link: identity Obs/group, min = 7
Family: Gaussian avg = 7.00
Correlation: exchangeable max = 7
chi2(3) = 10.20
Scale parameter: 29.7064 Prob > chi2 = 0.0169
Pearson chi2(346): 10278.41 Deviance = 10278.41
Dispersion (Pearson): 29.7064 Dispersion = 29.7064
(standard errors adjusted for clustering on cusip)
------------------------------------------------------------------------------
| Robust
roe | Coef. Std. Err. z P>|z| [95% Conf. Interval]
---------+--------------------------------------------------------------------
lev | -1.859506 1.204687 -1.544 0.123 -4.220649 .5016363
tobq | 5.110386 2.283293 2.238 0.025 .6352144 9.585558
cbeta | -2.703274 1.41072 -1.916 0.055 -5.468235 .0616876
_cons | 3.276171 2.804858 1.168 0.243 -2.22125 8.773591
------------------------------------------------------------------------------
. xtcorr
Estimated within-cusip correlation matrix R:
c1 c2 c3 c4 c5 c6 c7
r1 1.0000
r2 0.3679 1.0000
r3 0.3679 0.3679 1.0000
r4 0.3679 0.3679 0.3679 1.0000
r5 0.3679 0.3679 0.3679 0.3679 1.0000
r6 0.3679 0.3679 0.3679 0.3679 0.3679 1.0000
r7 0.3679 0.3679 0.3679 0.3679 0.3679 0.3679 1.0000
. xtgee roe lev tobq cbeta,i(cusip) robust corr(ar 1)
Iteration 1: tolerance = .47461104
Iteration 2: tolerance = .18630244
Iteration 3: tolerance = .04941979
Iteration 4: tolerance = .01135421
Iteration 5: tolerance = .00251905
Iteration 6: tolerance = .00055452
Iteration 7: tolerance = .00012186
Iteration 8: tolerance = .00002677
Iteration 9: tolerance = 5.880e-06
Iteration 10: tolerance = 1.291e-06
Iteration 11: tolerance = 2.837e-07
General estimating equation for panel data Number of obs = 350
Group and time vars: cusip yearptr Number of groups = 50
Link: identity Obs/group, min = 7
Family: Gaussian avg = 7.00
Correlation: AR(1) max = 7
chi2(3) = 11.75
Scale parameter: 30.26509 Prob > chi2 = 0.0083
Pearson chi2(346): 10471.72 Deviance = 10471.72
Dispersion (Pearson): 30.26509 Dispersion = 30.26509
(standard errors adjusted for clustering on cusip)
------------------------------------------------------------------------------
| Robust
roe | Coef. Std. Err. z P>|z| [95% Conf. Interval]
---------+--------------------------------------------------------------------
lev | -1.491783 1.143138 -1.305 0.192 -3.732291 .7487259
tobq | 5.841872 2.11482 2.762 0.006 1.696902 9.986842
cbeta | -2.64202 1.261292 -2.095 0.036 -5.114107 -.1699339
_cons | 1.896908 2.543048 0.746 0.456 -3.087375 6.881191
------------------------------------------------------------------------------
. xtcorr
Estimated within-cusip correlation matrix R:
c1 c2 c3 c4 c5 c6 c7
r1 1.0000
r2 0.5479 1.0000
r3 0.3002 0.5479 1.0000
r4 0.1644 0.3002 0.5479 1.0000
r5 0.0901 0.1644 0.3002 0.5479 1.0000
r6 0.0494 0.0901 0.1644 0.3002 0.5479 1.0000
r7 0.0270 0.0494 0.0901 0.1644 0.3002 0.5479 1.0000
. xtgee roe lev tobq cbeta,i(cusip) robust corr(unstr)
Iteration 1: tolerance = .51175757
Iteration 2: tolerance = 2.6738424
Iteration 3: tolerance = 2.3017692
Iteration 4: tolerance = 1.2167117
Iteration 5: tolerance = .35387164
Iteration 6: tolerance = .08978389
Iteration 7: tolerance = .02667489
Iteration 8: tolerance = .0081013
Iteration 9: tolerance = .00243384
Iteration 10: tolerance = .00086395
Iteration 11: tolerance = .0003479
Iteration 12: tolerance = .0001394
Iteration 13: tolerance = .00005563
Iteration 14: tolerance = .00002213
Iteration 15: tolerance = 8.776e-06
Iteration 16: tolerance = 3.473e-06
Iteration 17: tolerance = 1.372e-06
Iteration 18: tolerance = 5.409e-07
General estimating equation for panel data Number of obs = 350
Group and time vars: cusip yearptr Number of groups = 50
Link: identity Obs/group, min = 7
Family: Gaussian avg = 7.00
Correlation: unstructured max = 7
chi2(3) = 22.78
Scale parameter: 29.99862 Prob > chi2 = 0.0000
Pearson chi2(346): 10379.52 Deviance = 10379.52
Dispersion (Pearson): 29.99862 Dispersion = 29.99862
(standard errors adjusted for clustering on cusip)
------------------------------------------------------------------------------
| Robust
roe | Coef. Std. Err. z P>|z| [95% Conf. Interval]
---------+--------------------------------------------------------------------
lev | -1.418994 .9445 -1.502 0.133 -3.27018 .4321921
tobq | 6.714472 1.95538 3.434 0.001 2.881998 10.54695
cbeta | -3.824281 1.236249 -3.093 0.002 -6.247284 -1.401277
_cons | 2.705321 2.594746 1.043 0.297 -2.380288 7.790929
------------------------------------------------------------------------------
. xtcorr
Estimated within-cusip correlation matrix R:
c1 c2 c3 c4 c5 c6 c7
r1 1.0000
r2 0.2275 1.0000
r3 0.1898 0.5095 1.0000
r4 0.3641 0.4431 0.5111 1.0000
r5 0.3797 0.1068 0.1189 0.5607 1.0000
r6 0.5273 0.1861 0.1945 0.5300 0.9750 1.0000
r7 0.6698 0.0541 0.0662 0.2299 0.4149 0.4271 1.0000