Stata Code Companion to Baltagi’s Econometric Analysis of Panel Data, 6Ed
Solomon Negash
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name: <baltagipd>
log: ~\baltagi_panel_data_econometrics.smcl
log type: smcl
opened on: 3 Jun 2025, 01:41:53
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Chapter 02. The One-Way Error Component Regression Model
. clear all
Table 2.1 Grunfeld's data. One-way error component results
. import excel "grunfeld.xls", sheet("Sheet1") firstrow clear
(5 vars, 200 obs)
. xtset firm year
Panel variable: firm (strongly balanced)
Time variable: year, 1935 to 1954
Delta: 1 unit
. local y invest
. local xlist value cap
. eststo OLS: reg `y' `xlist'
Source | SS df MS Number of obs = 200
-------------+---------------------------------- F(2, 197) = 426.58
Model | 7604093.44 2 3802046.72 Prob > F = 0.0000
Residual | 1755850.48 197 8912.94662 R-squared = 0.8124
-------------+---------------------------------- Adj R-squared = 0.8105
Total | 9359943.93 199 47034.8941 Root MSE = 94.408
------------------------------------------------------------------------------
invest | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
value | .1155622 .0058357 19.80 0.000 .1040537 .1270706
cap | .2306785 .0254758 9.05 0.000 .1804382 .2809188
_cons | -42.71437 9.511676 -4.49 0.000 -61.47215 -23.95659
------------------------------------------------------------------------------
. eststo Between: xtreg `y' `xlist', be
Between regression (regression on group means) Number of obs = 200
Group variable: firm Number of groups = 10
R-squared: Obs per group:
Within = 0.4778 min = 20
Between = 0.8578 avg = 20.0
Overall = 0.7551 max = 20
F(2,7) = 21.11
sd(u_i + avg(e_i.)) = 85.02366 Prob > F = 0.0011
------------------------------------------------------------------------------
invest | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
value | .1346461 .0287455 4.68 0.002 .0666739 .2026183
cap | .0320315 .1909378 0.17 0.872 -.4194647 .4835276
_cons | -8.527114 47.51531 -0.18 0.863 -120.883 103.8287
------------------------------------------------------------------------------
. eststo Fixed: xtreg `y' `xlist', fe
Fixed-effects (within) regression Number of obs = 200
Group variable: firm Number of groups = 10
R-squared: Obs per group:
Within = 0.7668 min = 20
Between = 0.8194 avg = 20.0
Overall = 0.8060 max = 20
F(2, 188) = 309.01
corr(u_i, Xb) = -0.1517 Prob > F = 0.0000
------------------------------------------------------------------------------
invest | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
value | .1101238 .0118567 9.29 0.000 .0867345 .1335131
cap | .3100653 .0173545 17.87 0.000 .2758308 .3442999
_cons | -58.74394 12.45369 -4.72 0.000 -83.31087 -34.17701
-------------+----------------------------------------------------------------
sigma_u | 85.732502
sigma_e | 52.767966
rho | .72525011 (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(9, 188) = 49.18 Prob > F = 0.0000
. eststo Random: xtreg `y' `xlist', re theta
Random-effects GLS regression Number of obs = 200
Group variable: firm Number of groups = 10
R-squared: Obs per group:
Within = 0.7668 min = 20
Between = 0.8196 avg = 20.0
Overall = 0.8061 max = 20
Wald chi2(2) = 657.67
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000
theta = .86122362
------------------------------------------------------------------------------
invest | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
value | .1097812 .0104927 10.46 0.000 .0892159 .1303464
cap | .308113 .0171805 17.93 0.000 .2744399 .3417861
_cons | -57.83441 28.89894 -2.00 0.045 -114.4753 -1.193543
-------------+----------------------------------------------------------------
sigma_u | 84.200951
sigma_e | 52.767966
rho | .71800837 (fraction of variance due to u_i)
------------------------------------------------------------------------------
. eststo SWAR: xtreg `y' `xlist', sa
Random-effects GLS regression Number of obs = 200
Group variable: firm Number of groups = 10
R-squared: Obs per group:
Within = 0.7668 min = 20
Between = 0.8196 avg = 20.0
Overall = 0.8061 max = 20
Wald chi2(2) = 657.67
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000
------------------------------------------------------------------------------
invest | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
value | .1097812 .0104927 10.46 0.000 .0892159 .1303464
cap | .308113 .0171805 17.93 0.000 .2744399 .3417861
_cons | -57.83441 28.89894 -2.00 0.045 -114.4753 -1.193543
-------------+----------------------------------------------------------------
sigma_u | 84.200951
sigma_e | 52.767966
rho | .71800837 (fraction of variance due to u_i)
------------------------------------------------------------------------------
. eststo MLE: xtreg `y' `xlist', mle
Fitting constant-only model:
Iteration 0: Log likelihood = -1241.9899
Iteration 1: Log likelihood = -1241.9696
Iteration 2: Log likelihood = -1241.9696
Fitting full model:
Iteration 0: Log likelihood = -1105.6101
Iteration 1: Log likelihood = -1098.8418
Iteration 2: Log likelihood = -1095.4188
Iteration 3: Log likelihood = -1095.2576
Iteration 4: Log likelihood = -1095.257
Random-effects ML regression Number of obs = 200
Group variable: firm Number of groups = 10
Random effects u_i ~ Gaussian Obs per group:
min = 20
avg = 20.0
max = 20
LR chi2(2) = 293.43
Log likelihood = -1095.257 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
invest | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
value | .1097627 .0103389 10.62 0.000 .0894988 .1300265
cap | .307942 .0171006 18.01 0.000 .2744254 .3414585
_cons | -57.7672 27.70004 -2.09 0.037 -112.0583 -3.476119
-------------+----------------------------------------------------------------
/sigma_u | 80.29729 18.37811 51.27213 125.7536
/sigma_e | 52.49255 2.69306 47.47095 58.04535
rho | .7005943 .0985226 .4881266 .8603709
------------------------------------------------------------------------------
LR test of sigma_u=0: chibar2(01) = 193.09 Prob >= chibar2 = 0.000
. eststo PA: xtreg `y' `xlist', pa
Iteration 1: Tolerance = .3394649
Iteration 2: Tolerance = .00362672
Iteration 3: Tolerance = .00001665
Iteration 4: Tolerance = 7.455e-08
GEE population-averaged model Number of obs = 200
Group variable: firm Number of groups = 10
Family: Gaussian Obs per group:
Link: Identity min = 20
Correlation: exchangeable avg = 20.0
max = 20
Wald chi2(2) = 668.53
Scale parameter = 9203.122 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
invest | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
value | .1097627 .0103384 10.62 0.000 .0894997 .1300256
cap | .307942 .017072 18.04 0.000 .2744815 .3414025
_cons | -57.7672 27.69738 -2.09 0.037 -112.0531 -3.481346
------------------------------------------------------------------------------
. esttab OLS Between Fixed Random SWAR MLE, se
------------------------------------------------------------------------------------------------------------
(1) (2) (3) (4) (5) (6)
invest invest invest invest invest invest
------------------------------------------------------------------------------------------------------------
main
value 0.116*** 0.135** 0.110*** 0.110*** 0.110*** 0.110***
(0.00584) (0.0287) (0.0119) (0.0105) (0.0105) (0.0103)
cap 0.231*** 0.0320 0.310*** 0.308*** 0.308*** 0.308***
(0.0255) (0.191) (0.0174) (0.0172) (0.0172) (0.0171)
_cons -42.71*** -8.527 -58.74*** -57.83* -57.83* -57.77*
(9.512) (47.52) (12.45) (28.90) (28.90) (27.70)
------------------------------------------------------------------------------------------------------------
sigma_u
_cons 80.30***
(18.38)
------------------------------------------------------------------------------------------------------------
sigma_e
_cons 52.49***
(2.693)
------------------------------------------------------------------------------------------------------------
N 200 200 200 200 200 200
------------------------------------------------------------------------------------------------------------
Standard errors in parentheses
* p<0.05, ** p<0.01, *** p<0.001
. est clear
Table 2.5: Gasoline Demand Data. One-way Error Component Results
. import excel "gasoline.xls", sheet("Sheet1") firstrow clear
(6 vars, 342 obs)
. encode country, g(country2)
. xtset country2 year
Panel variable: country2 (strongly balanced)
Time variable: year, 1960 to 1978
Delta: 1 unit
. local y lgaspcar
. local xlist lincomep lrpmg lcarpcap
. eststo OLS: reg `y' `xlist'
Source | SS df MS Number of obs = 342
-------------+---------------------------------- F(3, 338) = 664.00
Model | 87.8386069 3 29.2795356 Prob > F = 0.0000
Residual | 14.9043574 338 .044095732 R-squared = 0.8549
-------------+---------------------------------- Adj R-squared = 0.8536
Total | 102.742964 341 .301299016 Root MSE = .20999
------------------------------------------------------------------------------
lgaspcar | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
lincomep | .8899617 .0358058 24.86 0.000 .8195314 .960392
lrpmg | -.8917979 .0303147 -29.42 0.000 -.9514272 -.8321686
lcarpcap | -.7633727 .0186083 -41.02 0.000 -.7999754 -.7267701
_cons | 2.391326 .1169343 20.45 0.000 2.161315 2.621336
------------------------------------------------------------------------------
. eststo Between: xtreg `y' `xlist', be
Between regression (regression on group means) Number of obs = 342
Group variable: country2 Number of groups = 18
R-squared: Obs per group:
Within = 0.7337 min = 19
Between = 0.8799 avg = 19.0
Overall = 0.8529 max = 19
F(3,14) = 34.19
sd(u_i + avg(e_i.)) = .1966886 Prob > F = 0.0000
------------------------------------------------------------------------------
lgaspcar | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
lincomep | .9675764 .1556662 6.22 0.000 .6337056 1.301447
lrpmg | -.9635504 .1329214 -7.25 0.000 -1.248639 -.6784623
lcarpcap | -.7952991 .0824742 -9.64 0.000 -.9721887 -.6184095
_cons | 2.54163 .5267844 4.82 0.000 1.41179 3.67147
------------------------------------------------------------------------------
. eststo Fixed: xtreg `y' `xlist', fe
Fixed-effects (within) regression Number of obs = 342
Group variable: country2 Number of groups = 18
R-squared: Obs per group:
Within = 0.8396 min = 19
Between = 0.5755 avg = 19.0
Overall = 0.6150 max = 19
F(3, 321) = 560.09
corr(u_i, Xb) = -0.2468 Prob > F = 0.0000
------------------------------------------------------------------------------
lgaspcar | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
lincomep | .6622497 .073386 9.02 0.000 .5178713 .806628
lrpmg | -.3217025 .0440993 -7.29 0.000 -.4084625 -.2349424
lcarpcap | -.6404829 .0296789 -21.58 0.000 -.6988725 -.5820933
_cons | 2.40267 .2253094 10.66 0.000 1.9594 2.845939
-------------+----------------------------------------------------------------
sigma_u | .34841288
sigma_e | .09233035
rho | .93438171 (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(17, 321) = 83.96 Prob > F = 0.0000
. eststo Random: xtreg `y' `xlist', re theta
Random-effects GLS regression Number of obs = 342
Group variable: country2 Number of groups = 18
R-squared: Obs per group:
Within = 0.8363 min = 19
Between = 0.7099 avg = 19.0
Overall = 0.7309 max = 19
Wald chi2(3) = 1642.20
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000
theta = .89230673
------------------------------------------------------------------------------
lgaspcar | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
lincomep | .5549857 .0591282 9.39 0.000 .4390966 .6708748
lrpmg | -.4203892 .0399781 -10.52 0.000 -.498745 -.3420335
lcarpcap | -.6068401 .025515 -23.78 0.000 -.6568487 -.5568316
_cons | 1.996698 .184326 10.83 0.000 1.635426 2.357971
-------------+----------------------------------------------------------------
sigma_u | .19554465
sigma_e | .09233035
rho | .81769849 (fraction of variance due to u_i)
------------------------------------------------------------------------------
. eststo SWAR: xtreg `y' `xlist', sa
Random-effects GLS regression Number of obs = 342
Group variable: country2 Number of groups = 18
R-squared: Obs per group:
Within = 0.8363 min = 19
Between = 0.7099 avg = 19.0
Overall = 0.7309 max = 19
Wald chi2(3) = 1642.20
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000
------------------------------------------------------------------------------
lgaspcar | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
lincomep | .5549857 .0591282 9.39 0.000 .4390966 .6708748
lrpmg | -.4203892 .0399781 -10.52 0.000 -.498745 -.3420335
lcarpcap | -.6068401 .025515 -23.78 0.000 -.6568487 -.5568316
_cons | 1.996698 .184326 10.83 0.000 1.635426 2.357971
-------------+----------------------------------------------------------------
sigma_u | .19554465
sigma_e | .09233035
rho | .81769849 (fraction of variance due to u_i)
------------------------------------------------------------------------------
. eststo MLE: xtreg `y' `xlist', mle
Fitting constant-only model:
Iteration 0: Log likelihood = -22.421495
Iteration 1: Log likelihood = -22.396827
Iteration 2: Log likelihood = -22.396815
Fitting full model:
Iteration 0: Log likelihood = 216.74303
Iteration 1: Log likelihood = 230.51818
Iteration 2: Log likelihood = 273.05803
Iteration 3: Log likelihood = 281.79283
Iteration 4: Log likelihood = 282.47029
Iteration 5: Log likelihood = 282.47693
Iteration 6: Log likelihood = 282.47694
Random-effects ML regression Number of obs = 342
Group variable: country2 Number of groups = 18
Random effects u_i ~ Gaussian Obs per group:
min = 19
avg = 19.0
max = 19
LR chi2(3) = 609.75
Log likelihood = 282.47694 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
lgaspcar | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
lincomep | .5881332 .0659581 8.92 0.000 .4588576 .7174088
lrpmg | -.3780466 .0440663 -8.58 0.000 -.464415 -.2916782
lcarpcap | -.6163722 .0272054 -22.66 0.000 -.6696938 -.5630506
_cons | 2.136168 .2156039 9.91 0.000 1.713592 2.558744
-------------+----------------------------------------------------------------
/sigma_u | .2922939 .0545496 .2027512 .4213821
/sigma_e | .0922537 .0036482 .0853734 .0996885
rho | .9094086 .0317608 .8303746 .9571561
------------------------------------------------------------------------------
LR test of sigma_u=0: chibar2(01) = 463.97 Prob >= chibar2 = 0.000
. eststo PA: xtreg `y' `xlist', pa
Iteration 1: Tolerance = .22237565
Iteration 2: Tolerance = .05813824
Iteration 3: Tolerance = .01578595
Iteration 4: Tolerance = .00328533
Iteration 5: Tolerance = .00066877
Iteration 6: Tolerance = .00013561
Iteration 7: Tolerance = .00002748
Iteration 8: Tolerance = 5.566e-06
Iteration 9: Tolerance = 1.128e-06
Iteration 10: Tolerance = 2.284e-07
GEE population-averaged model Number of obs = 342
Group variable: country2 Number of groups = 18
Family: Gaussian Obs per group:
Link: Identity min = 19
Correlation: exchangeable avg = 19.0
max = 19
Wald chi2(3) = 1715.11
Scale parameter = .0939464 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
lgaspcar | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
lincomep | .5881332 .0637347 9.23 0.000 .4632155 .7130509
lrpmg | -.3780466 .0408901 -9.25 0.000 -.4581897 -.2979036
lcarpcap | -.6163722 .0266907 -23.09 0.000 -.668685 -.5640593
_cons | 2.136168 .2055003 10.39 0.000 1.733394 2.538941
------------------------------------------------------------------------------
. esttab OLS Between Fixed Random SWAR MLE, se
------------------------------------------------------------------------------------------------------------
(1) (2) (3) (4) (5) (6)
lgaspcar lgaspcar lgaspcar lgaspcar lgaspcar lgaspcar
------------------------------------------------------------------------------------------------------------
main
lincomep 0.890*** 0.968*** 0.662*** 0.555*** 0.555*** 0.588***
(0.0358) (0.156) (0.0734) (0.0591) (0.0591) (0.0660)
lrpmg -0.892*** -0.964*** -0.322*** -0.420*** -0.420*** -0.378***
(0.0303) (0.133) (0.0441) (0.0400) (0.0400) (0.0441)
lcarpcap -0.763*** -0.795*** -0.640*** -0.607*** -0.607*** -0.616***
(0.0186) (0.0825) (0.0297) (0.0255) (0.0255) (0.0272)
_cons 2.391*** 2.542*** 2.403*** 1.997*** 1.997*** 2.136***
(0.117) (0.527) (0.225) (0.184) (0.184) (0.216)
------------------------------------------------------------------------------------------------------------
sigma_u
_cons 0.292***
(0.0545)
------------------------------------------------------------------------------------------------------------
sigma_e
_cons 0.0923***
(0.00365)
------------------------------------------------------------------------------------------------------------
N 342 342 342 342 342 342
------------------------------------------------------------------------------------------------------------
Standard errors in parentheses
* p<0.05, ** p<0.01, *** p<0.001
. est clear
Tables 2.6 - 2.10
. import excel "produc.xls", sheet("Sheet1") firstrow clear
(11 vars, 816 obs)
. g lny = ln(gsp)
. g lnk1 = ln(p_cap)
. g lnk2 = ln(pc)
. g lnl = ln(emp)
. g u = unemp
. encode(state), g(statenum)
. xtset statenum year
Panel variable: statenum (strongly balanced)
Time variable: year, 1970 to 1986
Delta: 1 unit
Table 2.7 Public capital productivity data: the Between estimator
. eststo be: xtreg lny lnk1 lnk2 lnl u, be
Between regression (regression on group means) Number of obs = 816
Group variable: statenum Number of groups = 48
R-squared: Obs per group:
Within = 0.9330 min = 17
Between = 0.9939 avg = 17.0
Overall = 0.9925 max = 17
F(4,43) = 1754.11
sd(u_i + avg(e_i.)) = .0832062 Prob > F = 0.0000
------------------------------------------------------------------------------
lny | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
lnk1 | .1793651 .0719719 2.49 0.017 .0342199 .3245104
lnk2 | .3019542 .0418215 7.22 0.000 .2176132 .3862953
lnl | .5761274 .0563746 10.22 0.000 .4624372 .6898176
u | -.0038903 .0099084 -0.39 0.697 -.0238724 .0160918
_cons | 1.589444 .2329795 6.82 0.000 1.119596 2.059292
------------------------------------------------------------------------------
Table 2.8 Public capital productivity data: the Within estimator
. eststo fe: xtreg lny lnk1 lnk2 lnl u, fe
Fixed-effects (within) regression Number of obs = 816
Group variable: statenum Number of groups = 48
R-squared: Obs per group:
Within = 0.9413 min = 17
Between = 0.9921 avg = 17.0
Overall = 0.9910 max = 17
F(4, 764) = 3064.81
corr(u_i, Xb) = 0.0608 Prob > F = 0.0000
------------------------------------------------------------------------------
lny | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
lnk1 | -.0261496 .0290016 -0.90 0.368 -.0830818 .0307826
lnk2 | .2920069 .0251197 11.62 0.000 .2426952 .3413187
lnl | .7681594 .0300917 25.53 0.000 .7090871 .8272317
u | -.0052977 .0009887 -5.36 0.000 -.0072387 -.0033568
_cons | 2.352899 .1748131 13.46 0.000 2.009728 2.69607
-------------+----------------------------------------------------------------
sigma_u | .09057293
sigma_e | .03813705
rho | .84940449 (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(47, 764) = 75.82 Prob > F = 0.0000
Table 2.9 Public capital productivity data: the Swamy and Arora estimator
. eststo re: xtreg lny lnk1 lnk2 lnl u, re theta
Random-effects GLS regression Number of obs = 816
Group variable: statenum Number of groups = 48
R-squared: Obs per group:
Within = 0.9412 min = 17
Between = 0.9928 avg = 17.0
Overall = 0.9917 max = 17
Wald chi2(4) = 19131.09
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000
theta = .88883529
------------------------------------------------------------------------------
lny | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
lnk1 | .0044387 .0234173 0.19 0.850 -.0414584 .0503357
lnk2 | .3105484 .0198047 15.68 0.000 .2717318 .349365
lnl | .7296705 .0249202 29.28 0.000 .6808278 .7785132
u | -.0061725 .0009073 -6.80 0.000 -.0079507 -.0043942
_cons | 2.135411 .1334615 16.00 0.000 1.873831 2.39699
-------------+----------------------------------------------------------------
sigma_u | .08269049
sigma_e | .03813705
rho | .82460105 (fraction of variance due to u_i)
------------------------------------------------------------------------------
Table 2.10 Public capital productivity data: the maximum likelihood estimator
. eststo mle: xtreg lny lnk1 lnk2 lnl u, mle
Fitting constant-only model:
Iteration 0: Log likelihood = 194.90992
Iteration 1: Log likelihood = 195.44872
Iteration 2: Log likelihood = 195.45155
Fitting full model:
Iteration 0: Log likelihood = 1374.1026
Iteration 1: Log likelihood = 1398.8952
Iteration 2: Log likelihood = 1401.8628
Iteration 3: Log likelihood = 1401.9041
Iteration 4: Log likelihood = 1401.9041
Random-effects ML regression Number of obs = 816
Group variable: statenum Number of groups = 48
Random effects u_i ~ Gaussian Obs per group:
min = 17
avg = 17.0
max = 17
LR chi2(4) = 2412.91
Log likelihood = 1401.9041 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
lny | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
lnk1 | .0031445 .0239185 0.13 0.895 -.043735 .0500239
lnk2 | .3098112 .020081 15.43 0.000 .2704531 .3491692
lnl | .7313372 .0256936 28.46 0.000 .6809787 .7816956
u | -.0061382 .0009143 -6.71 0.000 -.0079302 -.0043462
_cons | 2.143866 .1376582 15.57 0.000 1.87406 2.413671
-------------+----------------------------------------------------------------
/sigma_u | .085162 .0090452 .0691573 .1048706
/sigma_e | .0380836 .0009735 .0362226 .0400402
rho | .833348 .0304597 .7668537 .8861754
------------------------------------------------------------------------------
LR test of sigma_u=0: chibar2(01) = 1149.84 Prob >= chibar2 = 0.000
Table 2.6. Public capital productivity data. One-way error component results
. esttab be fe re mle, se
----------------------------------------------------------------------------
(1) (2) (3) (4)
lny lny lny lny
----------------------------------------------------------------------------
main
lnk1 0.179* -0.0261 0.00444 0.00314
(0.0720) (0.0290) (0.0234) (0.0239)
lnk2 0.302*** 0.292*** 0.311*** 0.310***
(0.0418) (0.0251) (0.0198) (0.0201)
lnl 0.576*** 0.768*** 0.730*** 0.731***
(0.0564) (0.0301) (0.0249) (0.0257)
u -0.00389 -0.00530*** -0.00617*** -0.00614***
(0.00991) (0.000989) (0.000907) (0.000914)
_cons 1.589*** 2.353*** 2.135*** 2.144***
(0.233) (0.175) (0.133) (0.138)
----------------------------------------------------------------------------
sigma_u
_cons 0.0852***
(0.00905)
----------------------------------------------------------------------------
sigma_e
_cons 0.0381***
(0.000973)
----------------------------------------------------------------------------
N 816 816 816 816
----------------------------------------------------------------------------
Standard errors in parentheses
* p<0.05, ** p<0.01, *** p<0.001
. est clear
Chapter 03. The Two-Way Error Component Regression Model
. import excel "grunfeld.xls", sheet("Sheet1") firstrow clear
(5 vars, 200 obs)
. xtset firm year
Panel variable: firm (strongly balanced)
Time variable: year, 1935 to 1954
Delta: 1 unit
. local y invest
. local xlist value cap
. eststo OLS: reg `y' `xlist'
Source | SS df MS Number of obs = 200
-------------+---------------------------------- F(2, 197) = 426.58
Model | 7604093.44 2 3802046.72 Prob > F = 0.0000
Residual | 1755850.48 197 8912.94662 R-squared = 0.8124
-------------+---------------------------------- Adj R-squared = 0.8105
Total | 9359943.93 199 47034.8941 Root MSE = 94.408
------------------------------------------------------------------------------
invest | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
value | .1155622 .0058357 19.80 0.000 .1040537 .1270706
cap | .2306785 .0254758 9.05 0.000 .1804382 .2809188
_cons | -42.71437 9.511676 -4.49 0.000 -61.47215 -23.95659
------------------------------------------------------------------------------
. eststo Fixed: xtreg `y' `xlist' i.year, fe
Fixed-effects (within) regression Number of obs = 200
Group variable: firm Number of groups = 10
R-squared: Obs per group:
Within = 0.7985 min = 20
Between = 0.8143 avg = 20.0
Overall = 0.8068 max = 20
F(21, 169) = 31.90
corr(u_i, Xb) = -0.3250 Prob > F = 0.0000
------------------------------------------------------------------------------
invest | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
value | .1177159 .0137513 8.56 0.000 .0905694 .1448623
cap | .3579163 .022719 15.75 0.000 .3130667 .4027659
|
year |
1936 | -19.19741 23.67586 -0.81 0.419 -65.93593 27.54112
1937 | -40.69001 24.69541 -1.65 0.101 -89.44123 8.061211
1938 | -39.2264 23.23594 -1.69 0.093 -85.09648 6.643668
1939 | -69.47029 23.65607 -2.94 0.004 -116.1698 -22.77082
1940 | -44.23508 23.80979 -1.86 0.065 -91.23801 2.767842
1941 | -18.80446 23.694 -0.79 0.429 -65.5788 27.96987
1942 | -21.13979 23.38163 -0.90 0.367 -67.29748 25.01789
1943 | -42.97762 23.55287 -1.82 0.070 -89.47335 3.5181
1944 | -43.09877 23.6102 -1.83 0.070 -89.70767 3.510128
1945 | -55.68304 23.89562 -2.33 0.021 -102.8554 -8.510695
1946 | -31.16928 24.11598 -1.29 0.198 -78.77666 16.43809
1947 | -39.39224 23.78368 -1.66 0.100 -86.34362 7.559135
1948 | -43.71651 23.96965 -1.82 0.070 -91.03502 3.601989
1949 | -73.4951 24.18292 -3.04 0.003 -121.2346 -25.75559
1950 | -75.89611 24.34553 -3.12 0.002 -123.9566 -27.8356
1951 | -62.48091 24.86425 -2.51 0.013 -111.5654 -13.39638
1952 | -64.63234 25.3495 -2.55 0.012 -114.6748 -14.58988
1953 | -67.71797 26.61108 -2.54 0.012 -120.2509 -15.18501
1954 | -93.52622 27.10786 -3.45 0.001 -147.0399 -40.01257
|
_cons | -32.83632 18.87533 -1.74 0.084 -70.09811 4.425477
-------------+----------------------------------------------------------------
sigma_u | 91.798272
sigma_e | 51.724525
rho | .75902159 (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(9, 169) = 52.36 Prob > F = 0.0000
*eststo Between: xtreg `y' `xlist', be
. eststo Random: xtreg `y' `xlist', re theta
Random-effects GLS regression Number of obs = 200
Group variable: firm Number of groups = 10
R-squared: Obs per group:
Within = 0.7668 min = 20
Between = 0.8196 avg = 20.0
Overall = 0.8061 max = 20
Wald chi2(2) = 657.67
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000
theta = .86122362
------------------------------------------------------------------------------
invest | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
value | .1097812 .0104927 10.46 0.000 .0892159 .1303464
cap | .308113 .0171805 17.93 0.000 .2744399 .3417861
_cons | -57.83441 28.89894 -2.00 0.045 -114.4753 -1.193543
-------------+----------------------------------------------------------------
sigma_u | 84.200951
sigma_e | 52.767966
rho | .71800837 (fraction of variance due to u_i)
------------------------------------------------------------------------------
. eststo SWAR: xtreg `y' `xlist', sa
Random-effects GLS regression Number of obs = 200
Group variable: firm Number of groups = 10
R-squared: Obs per group:
Within = 0.7668 min = 20
Between = 0.8196 avg = 20.0
Overall = 0.8061 max = 20
Wald chi2(2) = 657.67
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000
------------------------------------------------------------------------------
invest | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
value | .1097812 .0104927 10.46 0.000 .0892159 .1303464
cap | .308113 .0171805 17.93 0.000 .2744399 .3417861
_cons | -57.83441 28.89894 -2.00 0.045 -114.4753 -1.193543
-------------+----------------------------------------------------------------
sigma_u | 84.200951
sigma_e | 52.767966
rho | .71800837 (fraction of variance due to u_i)
------------------------------------------------------------------------------
. eststo MLE: xtreg `y' `xlist', mle
Fitting constant-only model:
Iteration 0: Log likelihood = -1241.9899
Iteration 1: Log likelihood = -1241.9696
Iteration 2: Log likelihood = -1241.9696
Fitting full model:
Iteration 0: Log likelihood = -1105.6101
Iteration 1: Log likelihood = -1098.8418
Iteration 2: Log likelihood = -1095.4188
Iteration 3: Log likelihood = -1095.2576
Iteration 4: Log likelihood = -1095.257
Random-effects ML regression Number of obs = 200
Group variable: firm Number of groups = 10
Random effects u_i ~ Gaussian Obs per group:
min = 20
avg = 20.0
max = 20
LR chi2(2) = 293.43
Log likelihood = -1095.257 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
invest | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
value | .1097627 .0103389 10.62 0.000 .0894988 .1300265
cap | .307942 .0171006 18.01 0.000 .2744254 .3414585
_cons | -57.7672 27.70004 -2.09 0.037 -112.0583 -3.476119
-------------+----------------------------------------------------------------
/sigma_u | 80.29729 18.37811 51.27213 125.7536
/sigma_e | 52.49255 2.69306 47.47095 58.04535
rho | .7005943 .0985226 .4881266 .8603709
------------------------------------------------------------------------------
LR test of sigma_u=0: chibar2(01) = 193.09 Prob >= chibar2 = 0.000
*eststo PA: xtreg `y' `xlist', pa
. esttab OLS Fixed Random SWAR MLE, keep(`xlist' _cons) se
--------------------------------------------------------------------------------------------
(1) (2) (3) (4) (5)
invest invest invest invest invest
--------------------------------------------------------------------------------------------
main
value 0.116*** 0.118*** 0.110*** 0.110*** 0.110***
(0.00584) (0.0138) (0.0105) (0.0105) (0.0103)
cap 0.231*** 0.358*** 0.308*** 0.308*** 0.308***
(0.0255) (0.0227) (0.0172) (0.0172) (0.0171)
_cons -42.71*** -32.84 -57.83* -57.83* -57.77*
(9.512) (18.88) (28.90) (28.90) (27.70)
--------------------------------------------------------------------------------------------
sigma_u
_cons 80.30***
(18.38)
--------------------------------------------------------------------------------------------
sigma_e
_cons 52.49***
(2.693)
--------------------------------------------------------------------------------------------
N 200 200 200 200 200
--------------------------------------------------------------------------------------------
Standard errors in parentheses
* p<0.05, ** p<0.01, *** p<0.001
. est clear
Chapter 04 Test of Hypotheses with Panel Data
. import excel "grunfeld.xls", sheet("Sheet1") firstrow clear
(5 vars, 200 obs)
. xtset firm year
Panel variable: firm (strongly balanced)
Time variable: year, 1935 to 1954
Delta: 1 unit
. xtregar invest value cap , re lbi
RE GLS regression with AR(1) disturbances Number of obs = 200
Group variable: firm Number of groups = 10
R-squared: Obs per group:
Within = 0.7649 min = 20
Between = 0.8068 avg = 20.0
Overall = 0.7967 max = 20
Wald chi2(3) = 360.31
corr(u_i, Xb) = 0 (assumed) Prob > chi2 = 0.0000
------------------------------------------------------------------------------
invest | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
value | .0949215 .0082168 11.55 0.000 .0788168 .1110262
cap | .3196589 .0258618 12.36 0.000 .2689707 .3703471
_cons | -44.38124 26.97525 -1.65 0.100 -97.25177 8.489277
-------------+----------------------------------------------------------------
rho_ar | .67210609 (estimated autocorrelation coefficient)
sigma_u | 74.517098
sigma_e | 41.482496
rho_fov | .76341859 (fraction of variance due to u_i)
theta | .67315697
------------------------------------------------------------------------------
Modified Bhargava et al. Durbin–Watson = .68447968
Baltagi–Wu LBI = .95635625
. xtregar invest value cap if year!=1951 & year!= 1952 , re lbi
RE GLS regression with AR(1) disturbances Number of obs = 180
Group variable: firm Number of groups = 10
R-squared: Obs per group:
Within = 0.7766 min = 18
Between = 0.8112 avg = 18.0
Overall = 0.8024 max = 18
Wald chi2(3) = 341.38
corr(u_i, Xb) = 0 (assumed) Prob > chi2 = 0.0000
------------------------------------------------------------------------------
invest | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
value | .0919986 .0083459 11.02 0.000 .0756409 .1083563
cap | .3243706 .0266376 12.18 0.000 .2721618 .3765793
_cons | -43.01925 27.05662 -1.59 0.112 -96.04925 10.01076
-------------+----------------------------------------------------------------
rho_ar | .68934342 (estimated autocorrelation coefficient)
sigma_u | 74.002134
sigma_e | 41.535676
rho_fov | .76043802 (fraction of variance due to u_i)
theta | .6551959
------------------------------------------------------------------------------
Modified Bhargava et al. Durbin–Watson = .80652307
Baltagi–Wu LBI = 1.1394027
. xtreg invest value cap, re
Random-effects GLS regression Number of obs = 200
Group variable: firm Number of groups = 10
R-squared: Obs per group:
Within = 0.7668 min = 20
Between = 0.8196 avg = 20.0
Overall = 0.8061 max = 20
Wald chi2(2) = 657.67
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000
------------------------------------------------------------------------------
invest | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
value | .1097812 .0104927 10.46 0.000 .0892159 .1303464
cap | .308113 .0171805 17.93 0.000 .2744399 .3417861
_cons | -57.83441 28.89894 -2.00 0.045 -114.4753 -1.193543
-------------+----------------------------------------------------------------
sigma_u | 84.200951
sigma_e | 52.767966
rho | .71800837 (fraction of variance due to u_i)
------------------------------------------------------------------------------
. xttest1, unadjusted
Tests for the error component model:
invest[firm,t] = Xb + u[firm] + v[firm,t]
v[firm,t] = lambda v[firm,(t-1)] + e[firm,t]
Estimated results:
| Var sd = sqrt(Var)
---------+-----------------------------
invest | 47034.89 216.8753
e | 2784.458 52.767966
u | 7089.8 84.200951
Tests:
Random Effects, Two Sided:
LM(Var(u)=0) = 798.16 Pr>chi2(1) = 0.0000
ALM(Var(u)=0) = 664.95 Pr>chi2(1) = 0.0000
Random Effects, One Sided:
LM(Var(u)=0) = 28.25 Pr>N(0,1) = 0.0000
ALM(Var(u)=0) = 25.79 Pr>N(0,1) = 0.0000
Serial Correlation:
LM(lambda=0) = 143.52 Pr>chi2(1) = 0.0000
ALM(lambda=0) = 10.31 Pr>chi2(1) = 0.0013
Joint Test:
LM(Var(u)=0,lambda=0) = 808.47 Pr>chi2(2) = 0.0000
. est clear
. xtgls invest value cap, corr(ar1) panels(heteroskedastic)
Cross-sectional time-series FGLS regression
Coefficients: generalized least squares
Panels: heteroskedastic
Correlation: common AR(1) coefficient for all panels (0.9261)
Estimated covariances = 10 Number of obs = 200
Estimated autocorrelations = 1 Number of groups = 10
Estimated coefficients = 3 Time periods = 20
Wald chi2(2) = 107.43
Prob > chi2 = 0.0000
------------------------------------------------------------------------------
invest | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
value | .0715306 .0087269 8.20 0.000 .0544262 .088635
cap | .1405652 .0314945 4.46 0.000 .0788371 .2022933
_cons | -1.979683 6.781351 -0.29 0.770 -15.27089 11.31152
------------------------------------------------------------------------------
. xtgls invest value cap, corr(psar1) panels(heteroskedastic)
Cross-sectional time-series FGLS regression
Coefficients: generalized least squares
Panels: heteroskedastic
Correlation: panel-specific AR(1)
Estimated covariances = 10 Number of obs = 200
Estimated autocorrelations = 10 Number of groups = 10
Estimated coefficients = 3 Time periods = 20
Wald chi2(2) = 100.13
Prob > chi2 = 0.0000
------------------------------------------------------------------------------
invest | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
value | .071577 .00818 8.75 0.000 .0555444 .0876096
cap | .165713 .0336642 4.92 0.000 .0997324 .2316935
_cons | 5.663741 9.870045 0.57 0.566 -13.68119 25.00867
------------------------------------------------------------------------------
. xtgls invest value cap, corr(psar1) panels(correlated)
Cross-sectional time-series FGLS regression
Coefficients: generalized least squares
Panels: heteroskedastic with cross-sectional correlation
Correlation: panel-specific AR(1)
Estimated covariances = 55 Number of obs = 200
Estimated autocorrelations = 10 Number of groups = 10
Estimated coefficients = 3 Time periods = 20
Wald chi2(2) = 326.73
Prob > chi2 = 0.0000
------------------------------------------------------------------------------
invest | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
value | .0846195 .0056835 14.89 0.000 .07348 .095759
cap | .245775 .0214979 11.43 0.000 .20364 .2879101
_cons | -8.819493 6.304894 -1.40 0.162 -21.17686 3.537871
------------------------------------------------------------------------------
Table 4.4 and Table 4.5
. eststo fe: qui xtreg invest value cap , fe
. eststo re: qui xtreg invest value cap , re
. eststo be: qui xtreg invest value cap , be
. hausman fe re
---- Coefficients ----
| (b) (B) (b-B) sqrt(diag(V_b-V_B))
| fe re Difference Std. err.
-------------+----------------------------------------------------------------
value | .1101238 .1097812 .0003427 .0055213
cap | .3100653 .308113 .0019524 .0024516
------------------------------------------------------------------------------
b = Consistent under H0 and Ha; obtained from xtreg.
B = Inconsistent under Ha, efficient under H0; obtained from xtreg.
Test of H0: Difference in coefficients not systematic
chi2(2) = (b-B)'[(V_b-V_B)^(-1)](b-B)
= 2.33
Prob > chi2 = 0.3119
. hausman be re
---- Coefficients ----
| (b) (B) (b-B) sqrt(diag(V_b-V_B))
| be re Difference Std. err.
-------------+----------------------------------------------------------------
value | .1346461 .1097812 .0248649 .026762
cap | .0320315 .308113 -.2760815 .1901633
------------------------------------------------------------------------------
b = Consistent under H0 and Ha; obtained from xtreg.
B = Inconsistent under Ha, efficient under H0; obtained from xtreg.
Test of H0: Difference in coefficients not systematic
chi2(2) = (b-B)'[(V_b-V_B)^(-1)](b-B)
= 2.13
Prob > chi2 = 0.3445
. est clear
Chapter 05. Heteroskedasticity and Serial Correlation
Table 2.1. Table 2.1 Grunfeld's data. One-way error component results
. import excel "grunfeld.xls", sheet("Sheet1") firstrow clear
(5 vars, 200 obs)
. xtset firm year
Panel variable: firm (strongly balanced)
Time variable: year, 1935 to 1954
Delta: 1 unit
Table 5.1 Grunfeld's data. Random effects and AR(1) remainder disturbances
. xtregar invest value cap , re lbi
RE GLS regression with AR(1) disturbances Number of obs = 200
Group variable: firm Number of groups = 10
R-squared: Obs per group:
Within = 0.7649 min = 20
Between = 0.8068 avg = 20.0
Overall = 0.7967 max = 20
Wald chi2(3) = 360.31
corr(u_i, Xb) = 0 (assumed) Prob > chi2 = 0.0000
------------------------------------------------------------------------------
invest | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
value | .0949215 .0082168 11.55 0.000 .0788168 .1110262
cap | .3196589 .0258618 12.36 0.000 .2689707 .3703471
_cons | -44.38124 26.97525 -1.65 0.100 -97.25177 8.489277
-------------+----------------------------------------------------------------
rho_ar | .67210609 (estimated autocorrelation coefficient)
sigma_u | 74.517098
sigma_e | 41.482496
rho_fov | .76341859 (fraction of variance due to u_i)
theta | .67315697
------------------------------------------------------------------------------
Modified Bhargava et al. Durbin–Watson = .68447968
Baltagi–Wu LBI = .95635625
Table 5.2 Grunfeld's data. Unequally spaced panel
. xtregar invest value cap if year!=1951 & year!= 1952 , re lbi
RE GLS regression with AR(1) disturbances Number of obs = 180
Group variable: firm Number of groups = 10
R-squared: Obs per group:
Within = 0.7766 min = 18
Between = 0.8112 avg = 18.0
Overall = 0.8024 max = 18
Wald chi2(3) = 341.38
corr(u_i, Xb) = 0 (assumed) Prob > chi2 = 0.0000
------------------------------------------------------------------------------
invest | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
value | .0919986 .0083459 11.02 0.000 .0756409 .1083563
cap | .3243706 .0266376 12.18 0.000 .2721618 .3765793
_cons | -43.01925 27.05662 -1.59 0.112 -96.04925 10.01076
-------------+----------------------------------------------------------------
rho_ar | .68934342 (estimated autocorrelation coefficient)
sigma_u | 74.002134
sigma_e | 41.535676
rho_fov | .76043802 (fraction of variance due to u_i)
theta | .6551959
------------------------------------------------------------------------------
Modified Bhargava et al. Durbin–Watson = .80652307
Baltagi–Wu LBI = 1.1394027
Table 5.3 Grunfeld's data. Joint test for random effects and AR(1) remainder disturbances
. xtreg invest value cap, re
Random-effects GLS regression Number of obs = 200
Group variable: firm Number of groups = 10
R-squared: Obs per group:
Within = 0.7668 min = 20
Between = 0.8196 avg = 20.0
Overall = 0.8061 max = 20
Wald chi2(2) = 657.67
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000
------------------------------------------------------------------------------
invest | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
value | .1097812 .0104927 10.46 0.000 .0892159 .1303464
cap | .308113 .0171805 17.93 0.000 .2744399 .3417861
_cons | -57.83441 28.89894 -2.00 0.045 -114.4753 -1.193543
-------------+----------------------------------------------------------------
sigma_u | 84.200951
sigma_e | 52.767966
rho | .71800837 (fraction of variance due to u_i)
------------------------------------------------------------------------------
. xttest1, unadjusted
Tests for the error component model:
invest[firm,t] = Xb + u[firm] + v[firm,t]
v[firm,t] = lambda v[firm,(t-1)] + e[firm,t]
Estimated results:
| Var sd = sqrt(Var)
---------+-----------------------------
invest | 47034.89 216.8753
e | 2784.458 52.767966
u | 7089.8 84.200951
Tests:
Random Effects, Two Sided:
LM(Var(u)=0) = 798.16 Pr>chi2(1) = 0.0000
ALM(Var(u)=0) = 664.95 Pr>chi2(1) = 0.0000
Random Effects, One Sided:
LM(Var(u)=0) = 28.25 Pr>N(0,1) = 0.0000
ALM(Var(u)=0) = 25.79 Pr>N(0,1) = 0.0000
Serial Correlation:
LM(lambda=0) = 143.52 Pr>chi2(1) = 0.0000
ALM(lambda=0) = 10.31 Pr>chi2(1) = 0.0013
Joint Test:
LM(Var(u)=0,lambda=0) = 808.47 Pr>chi2(2) = 0.0000
Table 5.5 Common rho and heteroskedastic AR(1) for Grunfeld data
. xtgls invest value cap, corr(ar1) panels(heteroskedastic)
Cross-sectional time-series FGLS regression
Coefficients: generalized least squares
Panels: heteroskedastic
Correlation: common AR(1) coefficient for all panels (0.9261)
Estimated covariances = 10 Number of obs = 200
Estimated autocorrelations = 1 Number of groups = 10
Estimated coefficients = 3 Time periods = 20
Wald chi2(2) = 107.43
Prob > chi2 = 0.0000
------------------------------------------------------------------------------
invest | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
value | .0715306 .0087269 8.20 0.000 .0544262 .088635
cap | .1405652 .0314945 4.46 0.000 .0788371 .2022933
_cons | -1.979683 6.781351 -0.29 0.770 -15.27089 11.31152
------------------------------------------------------------------------------
Table 5.6 Varying rhos and heteroskedastic AR(1) for Grunfeld data
. xtgls invest value cap, corr(psar1) panels(heteroskedastic)
Cross-sectional time-series FGLS regression
Coefficients: generalized least squares
Panels: heteroskedastic
Correlation: panel-specific AR(1)
Estimated covariances = 10 Number of obs = 200
Estimated autocorrelations = 10 Number of groups = 10
Estimated coefficients = 3 Time periods = 20
Wald chi2(2) = 100.13
Prob > chi2 = 0.0000
------------------------------------------------------------------------------
invest | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
value | .071577 .00818 8.75 0.000 .0555444 .0876096
cap | .165713 .0336642 4.92 0.000 .0997324 .2316935
_cons | 5.663741 9.870045 0.57 0.566 -13.68119 25.00867
------------------------------------------------------------------------------
Table 5.7 Varying rhos and cross-section dependence AR(1) for Grunfeld data
. xtgls invest value cap, corr(psar1) panels(correlated)
Cross-sectional time-series FGLS regression
Coefficients: generalized least squares
Panels: heteroskedastic with cross-sectional correlation
Correlation: panel-specific AR(1)
Estimated covariances = 55 Number of obs = 200
Estimated autocorrelations = 10 Number of groups = 10
Estimated coefficients = 3 Time periods = 20
Wald chi2(2) = 326.73
Prob > chi2 = 0.0000
------------------------------------------------------------------------------
invest | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
value | .0846195 .0056835 14.89 0.000 .07348 .095759
cap | .245775 .0214979 11.43 0.000 .20364 .2879101
_cons | -8.819493 6.304894 -1.40 0.162 -21.17686 3.537871
------------------------------------------------------------------------------
Table 5.8 Explaining OECD unemployment, 1961-95
. * Version 2 downloaded from https://cep.lse.ac.uk/_new/publications/abstract.asp?index=502
. import excel "Nickell et al\DATASET.xls", sheet("LMIDB") cellrange(A2:AA707) firstrow clear
(27 vars, 705 obs)
. encode country, g(ccode)
. xtset ccode year
Panel variable: ccode (unbalanced)
Time variable: year, 1960 to 1995
Delta: 1 unit
. g ur_1 = L.ur
(20 missing values generated)
. g c_ud = udnet
. *g c_ud = udnet-L.udnet
. foreach var of varlist bd br c_ud co tw{
2. egen `var'_mean = mean(`var')
3. }
. *"All variables in the interaction terms are expressed as deviations from the sample means." P.14
. g gd_bd_br = (bd - bd_mean) * (brr - brr_mean)
. g gd_co_ud = (c_ud - c_ud_mean) * (co - co_mean)
. g gd_co_tw = (co - co_mean) * (tw - tw_mean)
(43 missing values generated)
. xtgls ur ur_1 ep brr bd gd_bd_br c_ud co gd_co_ud tw gd_co_tw lds tfphpc tts d2ms rirl i.ccode c.year#i.ccode i.year ,
> p(hetero) corr(psar1) rhotype(theil) igls
note: 20.ccode#c.year omitted because of collinearity.
(note: 106 observations dropped because only 1 obs in group)
Iteration 1: Tolerance = 3.7255012
.
.
.
Iteration 53: Tolerance = 8.238e-08
Cross-sectional time-series FGLS regression
Coefficients: generalized least squares
Panels: heteroskedastic
Correlation: panel-specific AR(1)
Estimated covariances = 20 Number of obs = 599
Estimated autocorrelations = 20 Number of groups = 20
Estimated coefficients = 86 Obs per group:
min = 12
avg = 29.95
max = 33
Wald chi2(85) = 46915.28
Prob > chi2 = 0.0000
---------------------------------------------------------------------------------
ur | Coefficient Std. err. z P>|z| [95% conf. interval]
----------------+----------------------------------------------------------------
ur_1 | .8613531 .0182546 47.19 0.000 .8255748 .8971314
ep | .2746168 .174397 1.57 0.115 -.0671951 .6164287
brr | 2.460365 .4096456 6.01 0.000 1.657474 3.263256
bd | .5830818 .1994344 2.92 0.003 .1921975 .9739661
gd_bd_br | 3.974759 .9444889 4.21 0.000 2.123595 5.825924
c_ud | -.2064364 .9207731 -0.22 0.823 -2.011118 1.598246
co | -.9594787 .2789043 -3.44 0.001 -1.506121 -.4128363
gd_co_ud | -7.283085 1.198052 -6.08 0.000 -9.631224 -4.934945
tw | 1.493038 .8723322 1.71 0.087 -.2167016 3.202778
gd_co_tw | -3.636719 1.059612 -3.43 0.001 -5.713521 -1.559918
lds | -26.22182 2.326425 -11.27 0.000 -30.78153 -21.66211
tfphpc | -18.12906 1.283634 -14.12 0.000 -20.64494 -15.61318
tts | 5.899416 1.782549 3.31 0.001 2.405685 9.393147
d2ms | .3802618 .2637265 1.44 0.149 -.1366327 .8971562
rirl | 1.521738 1.174045 1.30 0.195 -.7793483 3.822824
---------------------------------------------------------------------------------
Time and country dummies as well as country specific time trends are not shown here.
Note also that the result presented here, which is based on version 2 of the data,
deviates slightly from the result in the original paper.
Table 5.9 Wooldridge test for serial correlation using Grunfeld's data
. * "net describe st0039, from(http://www.stata-journal.com/software/sj3-2)"
. import excel "grunfeld.xls", sheet("Sheet1") firstrow clear
(5 vars, 200 obs)
. xtset firm year
Panel variable: firm (strongly balanced)
Time variable: year, 1935 to 1954
Delta: 1 unit
. xtserial invest value cap, output
Linear regression Number of obs = 190
F(2, 9) = 47.80
Prob > F = 0.0000
R-squared = 0.4288
Root MSE = 42.896
(Std. err. adjusted for 10 clusters in firm)
------------------------------------------------------------------------------
| Robust
D.invest | Coefficient std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
value |
D1. | .0890628 .0145088 6.14 0.000 .0562416 .1218841
|
cap |
D1. | .278694 .138404 2.01 0.075 -.0343976 .5917857
------------------------------------------------------------------------------
Wooldridge test for autocorrelation in panel data
H0: no first-order autocorrelation
F( 1, 9) = 263.592
Prob > F = 0.0000
Chapter 06. Seemingly Unrelated Regressions
N/A
Chapter 07. Simultaneous Equations
* Example 7.2. Load fixed-format or delimited raw data
. infile ///
> county year crmrte prbarr prbconv prbpris avgsen polpc ///
> density taxpc west central urban pctmin80 wcon wtuc ///
> wtrd wfir wser wmfg wfed wsta wloc mix ///
> pctymle d82 d83 d84 d85 d86 d87 lcrmrte ///
> lprbarr lprbconv lprbpris lavgsen lpolpc ldensity ltaxpc lwcon ///
> lwtuc lwtrd lwfir lwser lwmfg lwfed lwsta lwloc ///
> lmix lpctymle lpctmin clcrmrte clprbarr clprbcon clprbpri clavgsen ///
> clpolpc cltaxpc clmix ///
> using "cornwell.raw", clear
(630 observations read)
. xtset county year
Panel variable: county (strongly balanced)
Time variable: year, 81 to 87
Delta: 1 unit
*export excel using "cornwell.xls", firstrow(variables) replace
Table 7.2 EC2SLS estimates for the crime data
. xtivreg lcrmrte lprbconv lprbpris lavgsen ldensity lwcon lwtuc lwtrd lwfir lwser lwmfg lwfed lwsta lwloc lpctymle lpct
> min west central urban d82 d83 d84 d85 d86 d87 ( lprbarr lpolpc= ltaxpc lmix), ec2sls
EC2SLS random-effects IV regression Number of obs = 630
Group variable: county Number of groups = 90
R-squared: Obs per group:
Within = 0.4521 min = 7
Between = 0.8158 avg = 7.0
Overall = 0.7840 max = 7
Wald chi2(26) = 575.74
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000
------------------------------------------------------------------------------
lcrmrte | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
lprbarr | -.4129261 .097402 -4.24 0.000 -.6038304 -.2220218
lpolpc | .4347492 .089695 4.85 0.000 .2589502 .6105482
lprbconv | -.3228872 .0535517 -6.03 0.000 -.4278465 -.2179279
lprbpris | -.1863195 .0419382 -4.44 0.000 -.2685169 -.1041222
lavgsen | -.0101765 .0270231 -0.38 0.706 -.0631408 .0427877
ldensity | .4290282 .0548483 7.82 0.000 .3215275 .536529
lwcon | -.0074751 .0395775 -0.19 0.850 -.0850455 .0700954
lwtuc | .045445 .0197926 2.30 0.022 .0066522 .0842379
lwtrd | -.0081412 .0413828 -0.20 0.844 -.0892499 .0729676
lwfir | -.0036395 .0289238 -0.13 0.900 -.0603292 .0530502
lwser | .0056098 .0201259 0.28 0.780 -.0338361 .0450557
lwmfg | -.2041398 .0804393 -2.54 0.011 -.361798 -.0464816
lwfed | -.1635108 .1594496 -1.03 0.305 -.4760263 .1490047
lwsta | -.0540503 .1056769 -0.51 0.609 -.2611732 .1530727
lwloc | .1630523 .119638 1.36 0.173 -.0714339 .3975384
lpctymle | -.1081057 .1396949 -0.77 0.439 -.3819026 .1656912
lpctmin | .189037 .0414988 4.56 0.000 .1077009 .2703731
west | -.2268433 .0995913 -2.28 0.023 -.4220387 -.0316479
central | -.1940428 .0598241 -3.24 0.001 -.3112958 -.0767898
urban | -.2251539 .1156302 -1.95 0.052 -.4517851 .0014772
d82 | .0107452 .0257969 0.42 0.677 -.0398158 .0613062
d83 | -.0837944 .0307088 -2.73 0.006 -.1439825 -.0236063
d84 | -.1034997 .0370885 -2.79 0.005 -.1761918 -.0308076
d85 | -.0957017 .0494502 -1.94 0.053 -.1926223 .0012189
d86 | -.0688982 .0595956 -1.16 0.248 -.1857036 .0479071
d87 | -.0314071 .0705197 -0.45 0.656 -.1696232 .1068091
_cons | -.9538033 1.283966 -0.74 0.458 -3.470331 1.562725
-------------+----------------------------------------------------------------
sigma_u | .21455964
sigma_e | .14923892
rho | .67394413 (fraction of variance due to u_i)
------------------------------------------------------------------------------
Endogenous: lprbarr lpolpc
Exogenous: lprbconv lprbpris lavgsen ldensity lwcon lwtuc lwtrd lwfir lwser
lwmfg lwfed lwsta lwloc lpctymle lpctmin west central urban d82
d83 d84 d85 d86 d87 ltaxpc lmix
Table 7.3 Random effects 2SLS for crime data (G2SLS)
. xtivreg lcrmrte lprbconv lprbpris lavgsen ldensity lwcon lwtuc lwtrd lwfir lwser lwmfg lwfed lwsta lwloc lpctymle lpct
> min west central urban d82 d83 d84 d85 d86 d87 ( lprbarr lpolpc= ltaxpc lmix), re
G2SLS random-effects IV regression Number of obs = 630
Group variable: county Number of groups = 90
R-squared: Obs per group:
Within = 0.4521 min = 7
Between = 0.8036 avg = 7.0
Overall = 0.7725 max = 7
Wald chi2(26) = 542.48
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000
------------------------------------------------------------------------------
lcrmrte | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
lprbarr | -.4141383 .2210496 -1.87 0.061 -.8473875 .0191109
lpolpc | .5049461 .2277778 2.22 0.027 .0585098 .9513824
lprbconv | -.3432506 .1324648 -2.59 0.010 -.6028768 -.0836244
lprbpris | -.1900467 .0733392 -2.59 0.010 -.333789 -.0463045
lavgsen | -.0064389 .0289407 -0.22 0.824 -.0631617 .0502838
ldensity | .4343449 .0711496 6.10 0.000 .2948943 .5737956
lwcon | -.0042958 .0414226 -0.10 0.917 -.0854826 .0768911
lwtuc | .0444589 .0215448 2.06 0.039 .0022318 .0866859
lwtrd | -.0085579 .0419829 -0.20 0.838 -.0908428 .073727
lwfir | -.0040305 .0294569 -0.14 0.891 -.0617649 .0537038
lwser | .0105602 .0215823 0.49 0.625 -.0317403 .0528608
lwmfg | -.201802 .0839373 -2.40 0.016 -.3663161 -.0372878
lwfed | -.2134579 .2151046 -0.99 0.321 -.6350551 .2081393
lwsta | -.0601232 .1203149 -0.50 0.617 -.295936 .1756896
lwloc | .1835363 .1396775 1.31 0.189 -.0902265 .4572992
lpctymle | -.1458703 .2268086 -0.64 0.520 -.5904071 .2986664
lpctmin | .1948763 .0459385 4.24 0.000 .1048384 .2849141
west | -.2281821 .101026 -2.26 0.024 -.4261894 -.0301747
central | -.1987703 .0607475 -3.27 0.001 -.3178332 -.0797075
urban | -.2595451 .1499718 -1.73 0.084 -.5534844 .0343942
d82 | .0132147 .0299924 0.44 0.660 -.0455692 .0719987
d83 | -.0847693 .032001 -2.65 0.008 -.1474901 -.0220485
d84 | -.1062027 .0387893 -2.74 0.006 -.1822284 -.0301769
d85 | -.0977457 .0511681 -1.91 0.056 -.1980334 .002542
d86 | -.0719451 .0605819 -1.19 0.235 -.1906835 .0467933
d87 | -.0396595 .0758531 -0.52 0.601 -.1883289 .1090099
_cons | -.4538501 1.702983 -0.27 0.790 -3.791636 2.883935
-------------+----------------------------------------------------------------
sigma_u | .21455964
sigma_e | .14923892
rho | .67394413 (fraction of variance due to u_i)
------------------------------------------------------------------------------
Endogenous: lprbarr lpolpc
Exogenous: lprbconv lprbpris lavgsen ldensity lwcon lwtuc lwtrd lwfir lwser
lwmfg lwfed lwsta lwloc lpctymle lpctmin west central urban d82
d83 d84 d85 d86 d87 ltaxpc lmix
Table 7.4 Fixed Effects 3SLS for Economic Growth and Foreign Aid
. u Bruckner2013/data-stata.dta, clear
. encode country, gen(Iccode)
*g lcru_l_sq = lcru_l^2
. keep if year >= 1960
(38 observations deleted)
. xtset Iccode year
Panel variable: Iccode (unbalanced)
Time variable: year, 1960 to 2000
Delta: 1 unit
. eststo su: qui reg3 (D.lgdp D.loda index_g_l D.lcru_l D.lcru_l_sq i.year i.Iccode) (D.loda D.lgdp D.polity2 war i.year
> i.Iccode)
. esttab su, drop(*.year *.Iccode) se
----------------------------
(1)
D.lgdp
----------------------------
D_lgdp
D.loda 0.120
(0.149)
index_g_l 0.476
(0.291)
D.lcru_l 0.273*
(0.125)
D.lcru_l_sq -0.0187*
(0.00865)
_cons -0.168
(0.156)
----------------------------
D_loda
D.lgdp -3.801*
(1.900)
D.polity2 0.0167*
(0.00832)
war -0.0736
(0.0779)
_cons 0.873***
(0.184)
----------------------------
N 1265
----------------------------
Standard errors in parentheses
* p<0.05, ** p<0.01, *** p<0.001
. est clear
Example 7.5. Empirical Example: Earnings Equation Using PSID Data
The data is missing ID and time variables. First, let's generate them.
Fortunately, the data is already sorted. N=595 and T= 7)
. import excel "wages.xls", sheet("Sheet1") firstrow clear
(12 vars, 4,165 obs)
. egen obs=seq()
. gen id = floor((_n - 1) / 7) + 1
. gen year = 1981 + mod(_n - 1, 7)
. rename *, lower // converts var-names to lower cases
*export excel using "wagesol.xls", firstrow(variables) replace
. xtset id year
Panel variable: id (strongly balanced)
Time variable: year, 1981 to 1987
Delta: 1 unit
Table 7.6 Hausman and Taylor estimates of a mincer wage equation
. g exp2 = exper^2
. xthtaylor lwage occ south smsa ind exper exp2 wks ms union fem blk ed, endog (exper exp2 wks ms union ed)
Hausman–Taylor estimation Number of obs = 4,165
Group variable: id Number of groups = 595
Obs per group:
min = 7
avg = 7
max = 7
Random effects u_i ~ i.i.d. Wald chi2(12) = 6891.87
Prob > chi2 = 0.0000
------------------------------------------------------------------------------
lwage | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
TVexogenous |
occ | -.0207047 .0137809 -1.50 0.133 -.0477149 .0063055
south | .0074398 .031955 0.23 0.816 -.0551908 .0700705
smsa | -.0418334 .0189581 -2.21 0.027 -.0789906 -.0046761
ind | .0136039 .0152374 0.89 0.372 -.0162608 .0434686
TVendogenous |
exper | .1131328 .002471 45.79 0.000 .1082898 .1179758
exp2 | -.0004189 .0000546 -7.67 0.000 -.0005259 -.0003119
wks | .0008374 .0005997 1.40 0.163 -.0003381 .0020129
ms | -.0298507 .01898 -1.57 0.116 -.0670508 .0073493
union | .0327714 .0149084 2.20 0.028 .0035514 .0619914
TIexogenous |
fem | -.1309236 .126659 -1.03 0.301 -.3791707 .1173234
blk | -.2857479 .1557019 -1.84 0.066 -.5909179 .0194222
TIendogenous |
ed | .137944 .0212485 6.49 0.000 .0962977 .1795902
|
_cons | 2.912726 .2836522 10.27 0.000 2.356778 3.468674
-------------+----------------------------------------------------------------
sigma_u | .941803
sigma_e | .15180272
rho | .97467788 (fraction of variance due to u_i)
------------------------------------------------------------------------------
Note: TV refers to time varying; TI refers to time invariant.
. eststo HT
Table 7.7 Amemiya and MaCurdy estimates of a mincer wage equation
. xthtaylor lwage occ south smsa ind exper exp2 wks ms union fem blk ed, endog (exper exp2 wks ms union ed) amacurdy
Amemiya–MaCurdy estimation Number of obs = 4,165
Group variable: id Number of groups = 595
Time variable: year Obs per group:
min = 7
avg = 7
max = 7
Random effects u_i ~ i.i.d. Wald chi2(12) = 6879.20
Prob > chi2 = 0.0000
------------------------------------------------------------------------------
lwage | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
TVexogenous |
occ | -.0208498 .0137653 -1.51 0.130 -.0478292 .0061297
south | .0072818 .0319365 0.23 0.820 -.0553126 .0698761
smsa | -.0419507 .0189471 -2.21 0.027 -.0790864 -.004815
ind | .0136289 .015229 0.89 0.371 -.0162194 .0434771
TVendogenous |
exper | .1129704 .0024688 45.76 0.000 .1081316 .1178093
exp2 | -.0004214 .0000546 -7.72 0.000 -.0005283 -.0003145
wks | .0008381 .0005995 1.40 0.162 -.0003368 .002013
ms | -.0300894 .0189674 -1.59 0.113 -.0672649 .0070861
union | .0324752 .0148939 2.18 0.029 .0032837 .0616667
TIexogenous |
fem | -.132008 .1266039 -1.04 0.297 -.380147 .1161311
blk | -.2859004 .1554857 -1.84 0.066 -.5906468 .0188459
TIendogenous |
ed | .1372049 .0205695 6.67 0.000 .0968894 .1775205
|
_cons | 2.927338 .2751274 10.64 0.000 2.388098 3.466578
-------------+----------------------------------------------------------------
sigma_u | .941803
sigma_e | .15180272
rho | .97467788 (fraction of variance due to u_i)
------------------------------------------------------------------------------
Note: TV refers to time varying; TI refers to time invariant.
. eststo AM
. xtreg lwage occ south smsa ind exper exp2 wks ms union fem blk ed, re
Random-effects GLS regression Number of obs = 4,165
Group variable: id Number of groups = 595
R-squared: Obs per group:
Within = 0.6124 min = 7
Between = 0.2539 avg = 7.0
Overall = 0.2512 max = 7
Wald chi2(12) = 2654.74
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000
------------------------------------------------------------------------------
lwage | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
occ | -.0500664 .0166469 -3.01 0.003 -.0826937 -.0174391
south | -.0166176 .0265265 -0.63 0.531 -.0686086 .0353734
smsa | -.0138231 .0199927 -0.69 0.489 -.0530081 .0253619
ind | .0037441 .0172618 0.22 0.828 -.0300883 .0375766
exper | .0820544 .0028478 28.81 0.000 .0764729 .0876359
exp2 | -.0008084 .0000628 -12.87 0.000 -.0009316 -.0006853
wks | .0010347 .0007734 1.34 0.181 -.0004811 .0025505
ms | -.0746283 .0230052 -3.24 0.001 -.1197178 -.0295389
union | .0632232 .01707 3.70 0.000 .0297666 .0966798
fem | -.3392101 .0513033 -6.61 0.000 -.4397627 -.2386574
blk | -.2102803 .0579888 -3.63 0.000 -.3239363 -.0966243
ed | .0996585 .0057475 17.34 0.000 .0883937 .1109234
_cons | 4.26367 .0977162 43.63 0.000 4.07215 4.45519
-------------+----------------------------------------------------------------
sigma_u | .26265815
sigma_e | .15199443
rho | .74913777 (fraction of variance due to u_i)
------------------------------------------------------------------------------
. eststo GLS
. xtreg lwage occ south smsa ind exper exp2 wks ms union fem blk ed, fe
note: fem omitted because of collinearity.
note: blk omitted because of collinearity.
note: ed omitted because of collinearity.
Fixed-effects (within) regression Number of obs = 4,165
Group variable: id Number of groups = 595
R-squared: Obs per group:
Within = 0.6581 min = 7
Between = 0.0261 avg = 7.0
Overall = 0.0461 max = 7
F(9, 3561) = 761.75
corr(u_i, Xb) = -0.9100 Prob > F = 0.0000
------------------------------------------------------------------------------
lwage | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
occ | -.0214765 .0137837 -1.56 0.119 -.0485012 .0055482
south | -.0018612 .0342993 -0.05 0.957 -.0691094 .065387
smsa | -.0424692 .0194284 -2.19 0.029 -.080561 -.0043773
ind | .0192101 .0154463 1.24 0.214 -.0110744 .0494946
exper | .1132083 .002471 45.81 0.000 .1083635 .1180531
exp2 | -.0004184 .0000546 -7.66 0.000 -.0005254 -.0003113
wks | .0008359 .0005997 1.39 0.163 -.0003398 .0020117
ms | -.0297258 .0189836 -1.57 0.117 -.0669456 .0074939
union | .0327849 .0149229 2.20 0.028 .0035266 .0620431
fem | 0 (omitted)
blk | 0 (omitted)
ed | 0 (omitted)
_cons | 4.648767 .046022 101.01 0.000 4.558535 4.738999
-------------+----------------------------------------------------------------
sigma_u | 1.0338102
sigma_e | .15199443
rho | .97884144 (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(594, 3561) = 38.25 Prob > F = 0.0000
. eststo Within
Table 7.5. Mincer Wage Equation. Dependent Variable: Log Wage
. esttab GLS Within HT AM, order(_cons wks south smsa ms exper exp2 occ ind union fem blk ed) se stats(N, fmt(%9.0g)) t
> label
------------------------------------------------------------------------------------
(1) (2) (3) (4)
LWAGE LWAGE LWAGE LWAGE
------------------------------------------------------------------------------------
Constant 4.264*** 4.649*** 2.913*** 2.927***
(0.0977) (0.0460) (0.284) (0.275)
WKS 0.00103 0.000836 0.000837 0.000838
(0.000773) (0.000600) (0.000600) (0.000599)
SOUTH -0.0166 -0.00186 0.00744 0.00728
(0.0265) (0.0343) (0.0320) (0.0319)
SMSA -0.0138 -0.0425* -0.0418* -0.0420*
(0.0200) (0.0194) (0.0190) (0.0189)
MS -0.0746** -0.0297 -0.0299 -0.0301
(0.0230) (0.0190) (0.0190) (0.0190)
EXPER 0.0821*** 0.113*** 0.113*** 0.113***
(0.00285) (0.00247) (0.00247) (0.00247)
exp2 -0.000808*** -0.000418*** -0.000419*** -0.000421***
(0.0000628) (0.0000546) (0.0000546) (0.0000546)
OCC -0.0501** -0.0215 -0.0207 -0.0208
(0.0166) (0.0138) (0.0138) (0.0138)
IND 0.00374 0.0192 0.0136 0.0136
(0.0173) (0.0154) (0.0152) (0.0152)
UNION 0.0632*** 0.0328* 0.0328* 0.0325*
(0.0171) (0.0149) (0.0149) (0.0149)
FEM -0.339*** 0 -0.131 -0.132
(0.0513) (.) (0.127) (0.127)
BLK -0.210*** 0 -0.286 -0.286
(0.0580) (.) (0.156) (0.155)
ED 0.0997*** 0 0.138*** 0.137***
(0.00575) (.) (0.0212) (0.0206)
------------------------------------------------------------------------------------
N 4165 4165 4165 4165
------------------------------------------------------------------------------------
Standard errors in parentheses
* p<0.05, ** p<0.01, *** p<0.001
. est clear
Chapter 08. Dynamic Panel Data Models
. import excel "cigar.xls", sheet("Sheet1") firstrow clear
(9 vars, 1,380 obs)
. forvalues year = 63(1)92 {
2. local id=`year'-62
3. gen dum`id' = (yr == `year' )
4. }
. g lnc = ln(c)
. g lnrp = ln(100*pric/cpi) // CPI in 1983 is base
. g lnrpn = ln(100*pimin/cpi)
. g lnrdi = ln(100*ndi/cpi)
. xtset state yr
Panel variable: state (strongly balanced)
Time variable: yr, 63 to 92
Delta: 1 unit
Table 8.2 Robust Arellano and Bond GMM estimates of cigarette demand
. xtabond2 lnc L.(lnc) lnrp lnrpn lnrdi dum3 dum8 dum10-dum29, gmm(L.(lnc),collapse) iv(lnrp lnrpn lnrdi dum3 dum8 dum10
> -dum29) noleveleq robust nomata twostep
Building GMM instruments..
Estimating.
Warning: Two-step estimated covariance matrix of moment conditions is singular.
Number of instruments may be large relative to number of groups.
Using a generalized inverse to calculate optimal weighting matrix for two-step estimation.
Computing Windmeijer finite-sample correction...............................................
Performing specification tests.
Dynamic panel-data estimation, two-step difference GMM
------------------------------------------------------------------------------
Group variable: state Number of obs = 1288
Time variable : yr Number of groups = 46
Number of instruments = 53 Obs per group: min = 28
Wald chi2(25) = 5514.80 avg = 28.00
Prob > chi2 = 0.000 max = 28
------------------------------------------------------------------------------
| Corrected
lnc | Coefficient std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
lnc |
L1. | .6229851 .0899459 6.93 0.000 .4466945 .7992758
|
lnrp | -.4037713 .0557992 -7.24 0.000 -.5131358 -.2944069
lnrpn | -.0860823 .0567726 -1.52 0.129 -.1973546 .02519
lnrdi | .1811735 .0296537 6.11 0.000 .1230533 .2392938
dum3 | .0130439 .0064342 2.03 0.043 .0004332 .0256546
dum8 | -.0229507 .0083476 -2.75 0.006 -.0393116 -.0065897
dum10 | .0265546 .0069401 3.83 0.000 .0129522 .040157
dum11 | -.0154596 .0093165 -1.66 0.097 -.0337197 .0028004
dum12 | -.0285942 .0100817 -2.84 0.005 -.0483539 -.0088345
dum13 | -.0414232 .0128014 -3.24 0.001 -.0665135 -.0163329
dum14 | -.0217906 .0141043 -1.54 0.122 -.0494345 .0058532
dum15 | -.0550672 .0156099 -3.53 0.000 -.0856621 -.0244724
dum16 | -.0455133 .015351 -2.96 0.003 -.0756007 -.0154259
dum17 | -.0894756 .0167478 -5.34 0.000 -.1223007 -.0566504
dum18 | -.1047575 .0189296 -5.53 0.000 -.1418588 -.0676562
dum19 | -.1280314 .0212807 -6.02 0.000 -.1697408 -.086322
dum20 | -.1210131 .0194657 -6.22 0.000 -.1591653 -.082861
dum21 | -.0942632 .0159669 -5.90 0.000 -.1255577 -.0629686
dum22 | -.0810146 .0126521 -6.40 0.000 -.1058123 -.056217
dum23 | -.0578651 .0105522 -5.48 0.000 -.078547 -.0371832
dum24 | -.0518459 .0110368 -4.70 0.000 -.0734776 -.0302141
dum25 | -.0585906 .0093694 -6.25 0.000 -.0769541 -.040227
dum26 | -.0615617 .0110503 -5.57 0.000 -.0832199 -.0399036
dum27 | -.0674198 .0076093 -8.86 0.000 -.0823336 -.0525059
dum28 | -.062461 .0096978 -6.44 0.000 -.0814683 -.0434537
dum29 | -.0557242 .0077968 -7.15 0.000 -.0710056 -.0404428
------------------------------------------------------------------------------
Instruments for first differences equation
Standard
D.(lnrp lnrpn lnrdi dum3 dum8 dum10 dum11 dum12 dum13 dum14 dum15 dum16
dum17 dum18 dum19 dum20 dum21 dum22 dum23 dum24 dum25 dum26 dum27 dum28
dum29)
GMM-type (missing=0, separate instruments for each period unless collapsed)
L(1/.).L.lnc collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z = -4.35 Pr > z = 0.000
Arellano-Bond test for AR(2) in first differences: z = 1.53 Pr > z = 0.127
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(27) = 67.91 Prob > chi2 = 0.000
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(27) = 27.16 Prob > chi2 = 0.455
(Robust, but weakened by many instruments.)
Table 8.3 System GMM estimates of cigarette demand
. xtabond2 lnc L.(lnc) lnrp lnrpn lnrdi dum3 dum8 dum10-dum29, gmm(L.(lnc),collapse) iv(lnrp lnrpn lnrdi dum3 dum8 dum10
> -dum29) robust nomata twostep
Building GMM instruments..
Estimating.
Warning: Two-step estimated covariance matrix of moment conditions is singular.
Number of instruments may be large relative to number of groups.
Using a generalized inverse to calculate optimal weighting matrix for two-step estimation.
Computing Windmeijer finite-sample correction...............................................
Performing specification tests.
Dynamic panel-data estimation, two-step system GMM
------------------------------------------------------------------------------
Group variable: state Number of obs = 1334
Time variable : yr Number of groups = 46
Number of instruments = 55 Obs per group: min = 29
Wald chi2(25) = 6025.77 avg = 29.00
Prob > chi2 = 0.000 max = 29
------------------------------------------------------------------------------
| Corrected
lnc | Coefficient std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
lnc |
L1. | .6097922 .1075885 5.67 0.000 .3989226 .8206619
|
lnrp | -.5135009 .1275413 -4.03 0.000 -.7634772 -.2635245
lnrpn | .0240955 .060918 0.40 0.692 -.0953015 .1434925
lnrdi | .1743783 .0474192 3.68 0.000 .0814383 .2673183
dum3 | .0111092 .0083385 1.33 0.183 -.005234 .0274524
dum8 | -.0193185 .0086728 -2.23 0.026 -.036317 -.0023201
dum10 | .0292373 .0076768 3.81 0.000 .0141911 .0442835
dum11 | -.0089089 .0101159 -0.88 0.378 -.0287356 .0109179
dum12 | -.0226511 .0147128 -1.54 0.124 -.0514877 .0061856
dum13 | -.0352768 .0172662 -2.04 0.041 -.0691178 -.0014357
dum14 | -.0166988 .0138771 -1.20 0.229 -.0438973 .0104998
dum15 | -.0506543 .0185271 -2.73 0.006 -.0869668 -.0143419
dum16 | -.0417593 .0160734 -2.60 0.009 -.0732627 -.010256
dum17 | -.0847489 .0235934 -3.59 0.000 -.1309911 -.0385067
dum18 | -.1038062 .0307475 -3.38 0.001 -.1640703 -.0435421
dum19 | -.1255405 .0377838 -3.32 0.001 -.1995953 -.0514857
dum20 | -.1199206 .0298965 -4.01 0.000 -.1785167 -.0613244
dum21 | -.094771 .0174418 -5.43 0.000 -.1289563 -.0605856
dum22 | -.0798828 .0127865 -6.25 0.000 -.104944 -.0548217
dum23 | -.0580374 .0133836 -4.34 0.000 -.0842687 -.0318061
dum24 | -.053246 .0120799 -4.41 0.000 -.0769221 -.0295699
dum25 | -.060592 .0103091 -5.88 0.000 -.0807975 -.0403865
dum26 | -.0576665 .0135268 -4.26 0.000 -.0841786 -.0311544
dum27 | -.066534 .0079063 -8.42 0.000 -.08203 -.051038
dum28 | -.0624675 .0091624 -6.82 0.000 -.0804256 -.0445095
dum29 | -.0547591 .0102868 -5.32 0.000 -.0749208 -.0345973
_cons | 2.51039 .8051728 3.12 0.002 .9322799 4.088499
------------------------------------------------------------------------------
Instruments for first differences equation
Standard
D.(lnrp lnrpn lnrdi dum3 dum8 dum10 dum11 dum12 dum13 dum14 dum15 dum16
dum17 dum18 dum19 dum20 dum21 dum22 dum23 dum24 dum25 dum26 dum27 dum28
dum29)
GMM-type (missing=0, separate instruments for each period unless collapsed)
L(1/.).L.lnc collapsed
Instruments for levels equation
Standard
_cons
lnrp lnrpn lnrdi dum3 dum8 dum10 dum11 dum12 dum13 dum14 dum15 dum16 dum17
dum18 dum19 dum20 dum21 dum22 dum23 dum24 dum25 dum26 dum27 dum28 dum29
GMM-type (missing=0, separate instruments for each period unless collapsed)
D.L.lnc collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z = -4.15 Pr > z = 0.000
Arellano-Bond test for AR(2) in first differences: z = 1.29 Pr > z = 0.196
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(28) = 85.97 Prob > chi2 = 0.000
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(28) = 28.79 Prob > chi2 = 0.423
(Robust, but weakened by many instruments.)
Table 8.4 Keane and Runkle estimates of cigarette demand in levels
. xtkr lnc lnrp lnrpn lnrdi (l.lnc=l.lnrp l.lnrpn l.lnrdi)
Keane-Runkle (1992) Regression
Number of Obs: 1334 Number of Panel Units: 46
------------------------------------------------------------------------------
lnc | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
lnrp | -.3872708 .0242384 -15.98 0.000 -.4347772 -.3397643
lnrpn | .0927905 .0271084 3.42 0.001 .0396591 .145922
lnrdi | .0773962 .0126045 6.14 0.000 .0526919 .1021006
|
lnc |
L1. | .6655751 .0284007 23.44 0.000 .6099108 .7212394
|
constant | 2.225425 .2024251 10.99 0.000 1.82868 2.622171
------------------------------------------------------------------------------
Instruments: lnrp lnrpn lnrdi constant L.lnrp L.lnrpn L.lnrdi
Table 8.5 Keane and Runkle estimates of cigarette demand in differences
. xtkr d.lnc d.lnrp d.lnrpn d.lnrdi (d.l.lnc=l(1/2).lnrp l(1/2).lnrpn l(1/2).lnrdi)
Keane-Runkle (1992) Regression
Number of Obs: 1288 Number of Panel Units: 46
------------------------------------------------------------------------------
D.lnc | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
lnrp |
D1. | -.3397847 .0184742 -18.39 0.000 -.3759936 -.3035759
|
lnrpn |
D1. | .0700778 .0185437 3.78 0.000 .0337328 .1064228
|
lnrdi |
D1. | .2267432 .0202211 11.21 0.000 .1871106 .2663758
|
lnc |
LD. | .4038734 .02775 14.55 0.000 .3494843 .4582624
|
constant | -.0051304 .0005255 -9.76 0.000 -.0061604 -.0041004
------------------------------------------------------------------------------
Instruments: D.lnrp D.lnrpn D.lnrdi constant L.lnrp L2.lnrp L.lnrpn L2.lnrpn L.lnrdi L2.lnrdi
Table 8.6 Robust Arellano and Bond estimates of the democracy equation
*xtabond2 dem L.(dem educ) yr* if year >=1960 & year <=2000 &
year>=(indyear+5), gmm(L.(dem)) iv(L.educ yr*) noleveleq > robust nomata
* Data Not Available
Table 8.7 System GMM estimates of the democracy equation
*xtabond2 dem L.(dem educ) yr* if year >=1960 & year <=2000 &
year>=(indyear+5), gmm(L.(dem)) iv(L.educ yr*) robust no > mata
* Data Not Available
Chapter 09. Unbalanced PanelData Models
. import excel "hedonic.xls", sheet("harris1") firstrow clear
(16 vars, 506 obs)
. xtset townid
Panel variable: townid (unbalanced)
Table 9.2
. xtreg mv crim zn indus chas nox rm age dis rad tax pt b lst, mle
Fitting constant-only model:
Iteration 0: Log likelihood = -70.952294
Iteration 1: Log likelihood = -67.800401
Iteration 2: Log likelihood = -65.887636
Iteration 3: Log likelihood = -65.787619
Iteration 4: Log likelihood = -65.787133
Fitting full model:
Iteration 0: Log likelihood = 213.22614
Iteration 1: Log likelihood = 229.23044
Iteration 2: Log likelihood = 235.97101
Iteration 3: Log likelihood = 236.26816
Iteration 4: Log likelihood = 236.26921
Random-effects ML regression Number of obs = 506
Group variable: townid Number of groups = 92
Random effects u_i ~ Gaussian Obs per group:
min = 1
avg = 5.5
max = 30
LR chi2(13) = 604.11
Log likelihood = 236.26921 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
mv | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
crim | -.0071948 .0010277 -7.00 0.000 -.009209 -.0051806
zn | .0000286 .0006894 0.04 0.967 -.0013226 .0013799
indus | .0022167 .0043906 0.50 0.614 -.0063887 .0108221
chas | -.0119739 .028971 -0.41 0.679 -.0687561 .0448083
nox | -.0058672 .0012282 -4.78 0.000 -.0082744 -.00346
rm | .0092024 .0011643 7.90 0.000 .0069204 .0114843
age | -.000943 .0004614 -2.04 0.041 -.0018473 -.0000387
dis | -.1298568 .0469261 -2.77 0.006 -.2218303 -.0378833
rad | .0971025 .0284233 3.42 0.001 .0413939 .152811
tax | -.0003741 .0001895 -1.97 0.048 -.0007456 -2.59e-06
ptratio | -.0297989 .0097987 -3.04 0.002 -.0490041 -.0105938
b | .5778527 .0999608 5.78 0.000 .381933 .7737723
lstat | -.2837923 .02405 -11.80 0.000 -.3309295 -.2366552
_cons | 9.675679 .2069417 46.76 0.000 9.270081 10.08128
-------------+----------------------------------------------------------------
/sigma_u | .1337509 .0132895 .1100833 .1625071
/sigma_e | .1304801 .0045557 .1218498 .1397217
rho | .5123767 .0546929 .4060176 .6178576
------------------------------------------------------------------------------
LR test of sigma_u=0: chibar2(01) = 172.71 Prob >= chibar2 = 0.000
. eststo mle
Table 9.3 Hedonic housing equation: Swamy and Arora estimator
. xtreg mv crim zn indus chas nox rm age dis rad tax pt b lst, sa
Random-effects GLS regression Number of obs = 506
Group variable: townid Number of groups = 92
R-squared: Obs per group:
Within = 0.6682 min = 1
Between = 0.8088 avg = 5.5
Overall = 0.7875 max = 30
Wald chi2(13) = 1169.62
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000
------------------------------------------------------------------------------
mv | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
crim | -.0072338 .0010346 -6.99 0.000 -.0092616 -.0052061
zn | .0000396 .0006878 0.06 0.954 -.0013084 .0013876
indus | .0020794 .0043403 0.48 0.632 -.0064273 .0105861
chas | -.0105913 .0289598 -0.37 0.715 -.0673515 .046169
nox | -.005863 .0012455 -4.71 0.000 -.0083041 -.0034219
rm | .0091773 .0011792 7.78 0.000 .0068662 .0114885
age | -.0009272 .0004647 -2.00 0.046 -.0018379 -.0000164
dis | -.1328824 .0456826 -2.91 0.004 -.2224185 -.0433462
rad | .0968634 .0283495 3.42 0.001 .0412994 .1524274
tax | -.0003747 .000189 -1.98 0.047 -.0007452 -4.25e-06
ptratio | -.029723 .0097538 -3.05 0.002 -.0488402 -.0106059
b | .5750649 .101031 5.69 0.000 .3770479 .773082
lstat | -.28514 .0238546 -11.95 0.000 -.3318942 -.2383859
_cons | 9.677802 .2071417 46.72 0.000 9.271811 10.08379
-------------+----------------------------------------------------------------
sigma_u | .12973801
sigma_e | .13024875
rho | .49803552 (fraction of variance due to u_i)
------------------------------------------------------------------------------
. eststo sa
Table 9.1. Incompelete table
. qui eststo ols: reg mv crim zn indus chas nox rm age dis rad tax pt b lst,
. qui eststo re: xtreg mv crim zn indus chas nox rm age dis rad tax pt b lst, re
. qui eststo fe: xtreg mv crim zn indus chas nox rm age dis rad tax pt b lst, fe
. esttab ols fe sa re mle, se stats(N, fmt(%9.0g))
--------------------------------------------------------------------------------------------
(1) (2) (3) (4) (5)
mv mv mv mv mv
--------------------------------------------------------------------------------------------
main
crim -0.0119*** -0.00625*** -0.00723*** -0.00762*** -0.00719***
(0.00124) (0.00104) (0.00103) (0.00106) (0.00103)
zn 0.0000803 0 0.0000396 0.000108 0.0000286
(0.000506) (.) (0.000688) (0.000618) (0.000689)
indus 0.000241 0 0.00208 0.00111 0.00222
(0.00236) (.) (0.00434) (0.00377) (0.00439)
chas 0.0914** -0.0452 -0.0106 0.00239 -0.0120
(0.0332) (0.0299) (0.0290) (0.0295) (0.0290)
nox -0.00638*** -0.00559*** -0.00586*** -0.00582*** -0.00587***
(0.00113) (0.00135) (0.00125) (0.00124) (0.00123)
rm 0.00633*** 0.00927*** 0.00918*** 0.00890*** 0.00920***
(0.00131) (0.00122) (0.00118) (0.00120) (0.00116)
age 0.0000898 -0.00141** -0.000927* -0.000784 -0.000943*
(0.000526) (0.000486) (0.000465) (0.000472) (0.000461)
dis -0.191*** 0.0801 -0.133** -0.154*** -0.130**
(0.0334) (0.0712) (0.0457) (0.0426) (0.0469)
rad 0.0957*** 0 0.0969*** 0.0953*** 0.0971***
(0.0191) (.) (0.0283) (0.0251) (0.0284)
tax -0.000420*** 0 -0.000375* -0.000380* -0.000374*
(0.000123) (.) (0.000189) (0.000167) (0.000190)
ptratio -0.0311*** 0 -0.0297** -0.0293*** -0.0298**
(0.00501) (.) (0.00975) (0.00847) (0.00980)
b 0.364*** 0.663*** 0.575*** 0.549*** 0.578***
(0.103) (0.103) (0.101) (0.103) (0.1000)
lstat -0.371*** -0.245*** -0.285*** -0.298*** -0.284***
(0.0250) (0.0256) (0.0239) (0.0240) (0.0241)
_cons 9.756*** 8.993*** 9.678*** 9.693*** 9.676***
(0.150) (0.135) (0.207) (0.189) (0.207)
--------------------------------------------------------------------------------------------
sigma_u
_cons 0.134***
(0.0133)
--------------------------------------------------------------------------------------------
sigma_e
_cons 0.130***
(0.00456)
--------------------------------------------------------------------------------------------
N 506 506 506 506 506
--------------------------------------------------------------------------------------------
Standard errors in parentheses
* p<0.05, ** p<0.01, *** p<0.001
. est clear
Table 9.5 Nested Public Capital Equation: MLE Estimator
. u productivity, clear
(Public Capital Productivity)
. xtset state year
Panel variable: state (strongly balanced)
Time variable: year, 1970 to 1986
Delta: 1 unit
. xtmixed gsp private emp hwy water other unemp || region: || state:, mle
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: Log likelihood = 1430.5017
Iteration 1: Log likelihood = 1430.5017
Computing standard errors:
Mixed-effects ML regression Number of obs = 816
Grouping information
-------------------------------------------------------------
| No. of Observations per group
Group variable | groups Minimum Average Maximum
----------------+--------------------------------------------
region | 9 51 90.7 136
state | 48 17 17.0 17
-------------------------------------------------------------
Wald chi2(6) = 18829.06
Log likelihood = 1430.5017 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
gsp | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
private | .2671484 .0212591 12.57 0.000 .2254814 .3088154
emp | .754072 .0261868 28.80 0.000 .7027468 .8053973
hwy | .0709767 .023041 3.08 0.002 .0258172 .1161363
water | .0761187 .0139248 5.47 0.000 .0488266 .1034109
other | -.0999955 .0169366 -5.90 0.000 -.1331906 -.0668004
unemp | -.0058983 .0009031 -6.53 0.000 -.0076684 -.0041282
_cons | 2.128823 .1543854 13.79 0.000 1.826233 2.431413
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects parameters | Estimate Std. err. [95% conf. interval]
-----------------------------+------------------------------------------------
region: Identity |
sd(_cons) | .038087 .0170591 .0158316 .091628
-----------------------------+------------------------------------------------
state: Identity |
sd(_cons) | .0792193 .0093861 .0628027 .0999273
-----------------------------+------------------------------------------------
sd(Residual) | .0366893 .000939 .0348944 .0385766
------------------------------------------------------------------------------
LR test vs. linear model: chi2(2) = 1154.73 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
Table 9.6 Nested Public Capital Equation: REML Estimator
. xtmixed gsp private emp hwy water other unemp || region: || state:, reml
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: Log restricted-likelihood = 1404.7101
Iteration 1: Log restricted-likelihood = 1404.7101
Computing standard errors:
Mixed-effects REML regression Number of obs = 816
Grouping information
-------------------------------------------------------------
| No. of Observations per group
Group variable | groups Minimum Average Maximum
----------------+--------------------------------------------
region | 9 51 90.7 136
state | 48 17 17.0 17
-------------------------------------------------------------
Wald chi2(6) = 18382.38
Log restricted-likelihood = 1404.7101 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
gsp | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
private | .2660308 .0215471 12.35 0.000 .2237993 .3082623
emp | .7555059 .0264556 28.56 0.000 .7036539 .807358
hwy | .0718857 .0233478 3.08 0.002 .0261249 .1176465
water | .0761552 .0139952 5.44 0.000 .0487251 .1035853
other | -.1005396 .0170173 -5.91 0.000 -.1338929 -.0671863
unemp | -.0058815 .0009093 -6.47 0.000 -.0076636 -.0040994
_cons | 2.126995 .1574865 13.51 0.000 1.818327 2.435663
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects parameters | Estimate Std. err. [95% conf. interval]
-----------------------------+------------------------------------------------
region: Identity |
sd(_cons) | .0435474 .0186293 .0188289 .1007164
-----------------------------+------------------------------------------------
state: Identity |
sd(_cons) | .0802738 .0095512 .0635762 .1013567
-----------------------------+------------------------------------------------
sd(Residual) | .0368008 .0009442 .034996 .0386986
------------------------------------------------------------------------------
LR test vs. linear model: chi2(2) = 1162.40 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
Chapter 10. SpecialTopics
. infile ///
> OBSNO YEAR CUSIP ARDSSIC SCISECT LOGK SUMPAT PAT PAT1 ///
> PAT2 PAT3 PAT4 LOGR LOGR1 LOGR2 LOGR3 LOGR4 LOGR5 ///
> using patentdata.asc, clear
(1,730 observations read)
. forvalues yr = 1(1)5 {
2. gen dyear`yr' = (YEAR == `yr' )
3. }
. xtset OBSNO YEAR
Panel variable: OBSNO (strongly balanced)
Time variable: YEAR, 1 to 5
Delta: 1 unit
Table 10.1 Poisson fixed effects for the R & D data
. xtpois PAT LOGR LOGR1 LOGR2 LOGR3 LOGR4 LOGR5 dyear2 dyear3 dyear4 dyear5,fe
note: 22 groups (110 obs) dropped because of all zero outcomes
Iteration 0: Log likelihood = -3660.2656
Iteration 1: Log likelihood = -3536.3518
Iteration 2: Log likelihood = -3536.3086
Iteration 3: Log likelihood = -3536.3086
Conditional fixed-effects Poisson regression Number of obs = 1,620
Group variable: OBSNO Number of groups = 324
Obs per group:
min = 5
avg = 5.0
max = 5
Wald chi2(10) = 245.39
Log likelihood = -3536.3086 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
PAT | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
LOGR | .3222105 .0459412 7.01 0.000 .2321674 .4122535
LOGR1 | -.0871295 .0486887 -1.79 0.074 -.1825576 .0082986
LOGR2 | .0785816 .044784 1.75 0.079 -.0091934 .1663567
LOGR3 | .00106 .0414151 0.03 0.980 -.0801122 .0822322
LOGR4 | -.0046414 .0378489 -0.12 0.902 -.0788238 .0695411
LOGR5 | .0026068 .0322596 0.08 0.936 -.0606209 .0658346
dyear2 | -.0426076 .013132 -3.24 0.001 -.0683458 -.0168695
dyear3 | -.0400462 .0134677 -2.97 0.003 -.0664423 -.01365
dyear4 | -.1571185 .0142281 -11.04 0.000 -.1850051 -.1292319
dyear5 | -.1980306 .0152946 -12.95 0.000 -.2280074 -.1680538
------------------------------------------------------------------------------
Table 10.2 Negative binomial fixed effects for the R & D data
. xtnbreg PAT LOGR LOGR1 LOGR2 LOGR3 LOGR4 LOGR5 dyear2 dyear3 dyear4 dyear5,fe
note: 22 groups (110 obs) dropped because of all zero outcomes
Iteration 0: Log likelihood = -3281.3343
Iteration 1: Log likelihood = -3210.112
Iteration 2: Log likelihood = -3206.8772
Iteration 3: Log likelihood = -3206.867
Iteration 4: Log likelihood = -3206.867
Conditional FE negative binomial regression Number of obs = 1,620
Group variable: OBSNO Number of groups = 324
Obs per group:
min = 5
avg = 5.0
max = 5
Wald chi2(10) = 117.12
Log likelihood = -3206.867 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
PAT | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
LOGR | .3188563 .0673654 4.73 0.000 .1868225 .4508902
LOGR1 | -.080442 .0773311 -1.04 0.298 -.2320082 .0711241
LOGR2 | .0559045 .0710929 0.79 0.432 -.0834351 .1952441
LOGR3 | -.0128025 .0659707 -0.19 0.846 -.1421028 .1164978
LOGR4 | .0355272 .0620031 0.57 0.567 -.0859966 .1570511
LOGR5 | .0094533 .0516237 0.18 0.855 -.0917273 .1106338
dyear2 | -.0422643 .0249051 -1.70 0.090 -.0910773 .0065488
dyear3 | -.0488698 .0253965 -1.92 0.054 -.098646 .0009063
dyear4 | -.1606011 .0262724 -6.11 0.000 -.2120941 -.1091081
dyear5 | -.2154138 .0265014 -8.13 0.000 -.2673556 -.163472
_cons | 2.423638 .1749545 13.85 0.000 2.080734 2.766543
------------------------------------------------------------------------------
Table 10.3 Poisson random effects for the R & D data
. xtpois PAT LOGR LOGR1 LOGR2 LOGR3 LOGR4 LOGR5 dyear2 dyear3 dyear4 dyear5 LOGK SCISECT, re
Fitting Poisson model:
Iteration 0: Log likelihood = -17836.658
Iteration 1: Log likelihood = -17834.138
Iteration 2: Log likelihood = -17834.138
Fitting full model:
Iteration 0: Log likelihood = -5303.2636
Iteration 1: Log likelihood = -5241.765
Iteration 2: Log likelihood = -5234.9526
Iteration 3: Log likelihood = -5234.9265
Iteration 4: Log likelihood = -5234.9265
Random-effects Poisson regression Number of obs = 1,730
Group variable: OBSNO Number of groups = 346
Random effects u_i ~ Gamma Obs per group:
min = 5
avg = 5.0
max = 5
Wald chi2(12) = 1272.14
Log likelihood = -5234.9265 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
PAT | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
LOGR | .4034537 .0435022 9.27 0.000 .318191 .4887165
LOGR1 | -.0461765 .0482224 -0.96 0.338 -.1406906 .0483376
LOGR2 | .1079235 .0447115 2.41 0.016 .0202905 .1955565
LOGR3 | .0297733 .0413235 0.72 0.471 -.0512193 .110766
LOGR4 | .0106957 .0377074 0.28 0.777 -.0632094 .0846008
LOGR5 | .0406111 .0315738 1.29 0.198 -.0212724 .1024946
dyear2 | -.0449624 .0131291 -3.42 0.001 -.070695 -.0192298
dyear3 | -.0483864 .0134018 -3.61 0.000 -.0746534 -.0221193
dyear4 | -.1741619 .0139702 -12.47 0.000 -.201543 -.1467809
dyear5 | -.2258977 .0146645 -15.40 0.000 -.2546396 -.1971557
LOGK | .2916932 .0393368 7.42 0.000 .2145945 .368792
SCISECT | .2570001 .1122716 2.29 0.022 .0369517 .4770484
_cons | .4107881 .1467443 2.80 0.005 .1231746 .6984016
-------------+----------------------------------------------------------------
/lnalpha | -.156739 .0809735 -.3154441 .0019661
-------------+----------------------------------------------------------------
alpha | .8549271 .0692264 .7294648 1.001968
------------------------------------------------------------------------------
LR test of alpha=0: chibar2(01) = 2.5e+04 Prob >= chibar2 = 0.000
Table 10.4 Negative binomial random effects for the R & D data
. xtnbreg PAT LOGR LOGR1 LOGR2 LOGR3 LOGR4 LOGR5 dyear2 dyear3 dyear4 dyear5 LOGK SCISECT, re
Fitting negative binomial (constant dispersion) model:
Iteration 0: Log likelihood = -17836.658
Iteration 1: Log likelihood = -17834.138
Iteration 2: Log likelihood = -17834.138
Iteration 0: Log likelihood = -37163.276
Iteration 1: Log likelihood = -17331.718
Iteration 2: Log likelihood = -8376.139 (backed up)
Iteration 3: Log likelihood = -6999.1967
Iteration 4: Log likelihood = -6948.0162
Iteration 5: Log likelihood = -6948.0022
Iteration 6: Log likelihood = -6948.0022
Iteration 0: Log likelihood = -6948.0022
Iteration 1: Log likelihood = -6484.3647 (not concave)
Iteration 2: Log likelihood = -6063.4801
Iteration 3: Log likelihood = -5996.6042
Iteration 4: Log likelihood = -5954.4866
Iteration 5: Log likelihood = -5954.1073
Iteration 6: Log likelihood = -5954.1071
Fitting full model:
Iteration 0: Log likelihood = -5074.487
Iteration 1: Log likelihood = -4961.2657
Iteration 2: Log likelihood = -4948.6428
Iteration 3: Log likelihood = -4948.4945
Iteration 4: Log likelihood = -4948.4944
Random-effects negative binomial regression Number of obs = 1,730
Group variable: OBSNO Number of groups = 346
Random effects u_i ~ Beta Obs per group:
min = 5
avg = 5.0
max = 5
Wald chi2(12) = 944.21
Log likelihood = -4948.4944 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
PAT | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
LOGR | .3503119 .0652818 5.37 0.000 .2223619 .4782619
LOGR1 | -.0030317 .0750916 -0.04 0.968 -.1502085 .1441452
LOGR2 | .1049876 .0688488 1.52 0.127 -.0299537 .2399289
LOGR3 | .0163523 .0636376 0.26 0.797 -.1083752 .1410797
LOGR4 | .0359425 .0587161 0.61 0.540 -.0791389 .1510239
LOGR5 | .0718323 .0482887 1.49 0.137 -.0228119 .1664764
dyear2 | -.0436736 .0213435 -2.05 0.041 -.085506 -.0018411
dyear3 | -.0556597 .0218572 -2.55 0.011 -.098499 -.0128203
dyear4 | -.1831055 .0227183 -8.06 0.000 -.2276326 -.1385784
dyear5 | -.2300438 .0231525 -9.94 0.000 -.2754219 -.1846658
LOGK | .161937 .0417874 3.88 0.000 .0800351 .2438388
SCISECT | .1176419 .1066164 1.10 0.270 -.0913224 .3266063
_cons | .8995618 .1681113 5.35 0.000 .5700698 1.229054
-------------+----------------------------------------------------------------
/ln_r | .9877591 .0961426 .7993231 1.176195
/ln_s | .7009608 .1079684 .4893467 .9125748
-------------+----------------------------------------------------------------
r | 2.68521 .2581631 2.224035 3.242015
s | 2.015688 .2176306 1.63125 2.490728
------------------------------------------------------------------------------
LR test vs. pooled: chibar2(01) = 2011.23 Prob >= chibar2 = 0.000
Chapter 11. Limited Dependent Variables and PanelData
* Fernandez-Val (2009) downloaded from Open ICPSR
. infile ///
> id year lfp lfp_1 kids0_2 kids3_5 kids6_17 loghusbandincome ///
> age age2 dy1-dy8 using "Fernandez-Val-2009\lfp_psid_fs.txt", clear
(13,149 observations read)
. xtset id year
Panel variable: id (strongly balanced)
Time variable: year, 1980 to 1988
Delta: 1 unit
Table 11.1 Conditional Logit: Female Labor Force Participation
. xtlogit lfp kids0_2 kids3_5 kids6_17 loghusbandincome age age2, fe
note: multiple positive outcomes within groups encountered.
note: 797 groups (7,173 obs) omitted because of all positive or
all negative outcomes.
Iteration 0: Log likelihood = -2306.0175
Iteration 1: Log likelihood = -2267.9125
Iteration 2: Log likelihood = -2267.8037
Iteration 3: Log likelihood = -2267.8037
Conditional fixed-effects logistic regression Number of obs = 5,976
Group variable: id Number of groups = 664
Obs per group:
min = 9
avg = 9.0
max = 9
LR chi2(6) = 272.67
Log likelihood = -2267.8037 Prob > chi2 = 0.0000
----------------------------------------------------------------------------------
lfp | Coefficient Std. err. z P>|z| [95% conf. interval]
-----------------+----------------------------------------------------------------
kids0_2 | -1.086185 .0912304 -11.91 0.000 -1.264993 -.9073763
kids3_5 | -.6265956 .0835397 -7.50 0.000 -.7903304 -.4628607
kids6_17 | -.206979 .0672433 -3.08 0.002 -.3387734 -.0751847
loghusbandincome | -.3662394 .0880333 -4.16 0.000 -.5387814 -.1936974
age | 3.641422 .6080303 5.99 0.000 2.449705 4.83314
age2 | -.4520102 .0807705 -5.60 0.000 -.6103174 -.2937029
----------------------------------------------------------------------------------
Table 11.2 Probit Random Effects: Female Labor Force Participatio
. xtprobit lfp kids0_2 kids3_5 kids6_17 loghusbandincome age age2, re
Fitting comparison model:
Iteration 0: Log likelihood = -7750.2801
Iteration 1: Log likelihood = -7473.199
Iteration 2: Log likelihood = -7472.7313
Iteration 3: Log likelihood = -7472.7313
Fitting full model:
rho = 0.0 Log likelihood = -7472.7313
rho = 0.1 Log likelihood = -6451.8464
rho = 0.2 Log likelihood = -5922.2083
rho = 0.3 Log likelihood = -5592.5289
rho = 0.4 Log likelihood = -5369.9071
rho = 0.5 Log likelihood = -5215.1801
rho = 0.6 Log likelihood = -5112.0359
rho = 0.7 Log likelihood = -5062.9248
rho = 0.8 Log likelihood = -5106.2435
Iteration 0: Log likelihood = -5049.2731
Iteration 1: Log likelihood = -4938.4733
Iteration 2: Log likelihood = -4928.4508
Iteration 3: Log likelihood = -4928.4235
Iteration 4: Log likelihood = -4928.4235 (backed up)
Iteration 5: Log likelihood = -4928.3851
Iteration 6: Log likelihood = -4928.3851
Random-effects probit regression Number of obs = 13,149
Group variable: id Number of groups = 1,461
Random effects u_i ~ Gaussian Obs per group:
min = 9
avg = 9.0
max = 9
Integration method: mvaghermite Integration pts. = 12
Wald chi2(6) = 330.65
Log likelihood = -4928.3851 Prob > chi2 = 0.0000
----------------------------------------------------------------------------------
lfp | Coefficient Std. err. z P>|z| [95% conf. interval]
-----------------+----------------------------------------------------------------
kids0_2 | -.6865494 .0489026 -14.04 0.000 -.7823968 -.5907021
kids3_5 | -.4050329 .0441319 -9.18 0.000 -.4915299 -.318536
kids6_17 | -.1290886 .0320563 -4.03 0.000 -.1919179 -.0662594
loghusbandincome | -.2538797 .0440499 -5.76 0.000 -.340216 -.1675435
age | 2.119458 .2901562 7.30 0.000 1.550763 2.688154
age2 | -.2832263 .037195 -7.61 0.000 -.3561272 -.2103254
_cons | .6753673 .6574111 1.03 0.304 -.6131348 1.963869
-----------------+----------------------------------------------------------------
/lnsig2u | 1.296086 .0686458 1.161543 1.43063
-----------------+----------------------------------------------------------------
sigma_u | 1.911796 .0656184 1.787417 2.04483
rho | .7851756 .0115788 .761613 .8069994
----------------------------------------------------------------------------------
LR test of rho=0: chibar2(01) = 5088.69 Prob >= chibar2 = 0.000
Table 11.3 Union Membership: Random-effects probit
. infile ///
> nr year black married educ union d81 d82 d83 d84 d85 d86 d87 ///
> union80 union_1 marravg educu80 marr81 marr82 marr83 marr84 ///
> marr85 marr86 marr87 using jmw-data/union.raw, clear
(4,360 observations read)
. u jmw-data/union.dta, clear
. xtset nr year
Panel variable: nr (strongly balanced)
Time variable: year, 1980 to 1987
Delta: 1 unit
. xtprobit union married union_1 union80 marr81 marr82 marr83 marr84 marr85 marr86 marr87 d81 d82 d83 d84 d85 d86, re
Fitting comparison model:
Iteration 0: Log likelihood = -2115.4174
Iteration 1: Log likelihood = -1370.5301
Iteration 2: Log likelihood = -1366.0556
Iteration 3: Log likelihood = -1366.0497
Iteration 4: Log likelihood = -1366.0497
Fitting full model:
rho = 0.0 Log likelihood = -1366.0497
rho = 0.1 Log likelihood = -1346.9419
rho = 0.2 Log likelihood = -1342.4578
rho = 0.3 Log likelihood = -1345.9175
Iteration 0: Log likelihood = -1342.4578
Iteration 1: Log likelihood = -1315.5077
Iteration 2: Log likelihood = -1306.5529
Iteration 3: Log likelihood = -1288.3926
Iteration 4: Log likelihood = -1288.0839
Iteration 5: Log likelihood = -1288.0834
Iteration 6: Log likelihood = -1288.0834
Random-effects probit regression Number of obs = 3,815
Group variable: nr Number of groups = 545
Random effects u_i ~ Gaussian Obs per group:
min = 7
avg = 7.0
max = 7
Integration method: mvaghermite Integration pts. = 12
Wald chi2(16) = 348.98
Log likelihood = -1288.0834 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
union | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
married | .1672066 .1106776 1.51 0.131 -.0497176 .3841307
union_1 | .8929075 .0924593 9.66 0.000 .7116907 1.074124
union80 | 1.490334 .1661415 8.97 0.000 1.164702 1.815965
marr81 | .0631461 .2160679 0.29 0.770 -.3603392 .4866315
marr82 | -.1229025 .2552495 -0.48 0.630 -.6231824 .3773774
marr83 | -.0719672 .2582289 -0.28 0.780 -.5780866 .4341522
marr84 | -.0001787 .2781883 -0.00 0.999 -.5454177 .5450603
marr85 | .3825586 .2623512 1.46 0.145 -.1316403 .8967576
marr86 | .1210022 .263442 0.46 0.646 -.3953346 .637339
marr87 | -.4209373 .2064262 -2.04 0.041 -.8255251 -.0163494
d81 | -.0739664 .118948 -0.62 0.534 -.3071002 .1591675
d82 | -.0464172 .1172915 -0.40 0.692 -.2763044 .1834699
d83 | -.1629567 .1178112 -1.38 0.167 -.3938625 .0679491
d84 | -.1235878 .1170587 -1.06 0.291 -.3530187 .1058431
d85 | -.3403144 .1196731 -2.84 0.004 -.5748693 -.1057595
d86 | -.3897729 .1198515 -3.25 0.001 -.6246776 -.1548683
_cons | -1.727352 .144532 -11.95 0.000 -2.010629 -1.444074
-------------+----------------------------------------------------------------
/lnsig2u | .1778768 .1659054 -.1472918 .5030454
-------------+----------------------------------------------------------------
sigma_u | 1.093013 .0906684 .9290006 1.285982
rho | .5443523 .04115 .4632435 .6231747
------------------------------------------------------------------------------
LR test of rho=0: chibar2(01) = 155.93 Prob >= chibar2 = 0.000
*********************************************************
*********** Chapter 12. Nonstationary Panels ************
*********************************************************
* Data Not Available
*********************************************************
******** Chapter 13. Spatial Panel Data Models **********
*********************************************************
* Data Not Available
. log close
name: <baltagipd>
log: ~\baltagi_panel_data_econometrics.smcl
log type: smcl
closed on: 3 Jun 2025, 01:42:57
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