use TBL15-1, clear
Table 15.1, page 598, Least squares, OLS Standard errors.
regress i f c Source | SS df MS Number of obs = 100 -------------+------------------------------ F( 2, 97) = 170.81 Model | 5532554.18 2 2766277.09 Prob > F = 0.0000 Residual | 1570883.64 97 16194.6767 R-squared = 0.7789 -------------+------------------------------ Adj R-squared = 0.7743 Total | 7103437.82 99 71751.8972 Root MSE = 127.26 ------------------------------------------------------------------------------ i | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- f | .1050854 .0113778 9.24 0.000 .0825036 .1276673 c | .3053655 .0435078 7.02 0.000 .2190146 .3917165 _cons | -48.02974 21.48016 -2.24 0.028 -90.66192 -5.397556 ------------------------------------------------------------------------------ predict xb, xb . generate r2 = (i-xb)^2 . table firm, contents(mean r2) ---------------------- firm | mean(r2) ----------+----------- 1 | 9410.907 2 | 755.8508 3 | 34288.49 4 | 633.4236 5 | 33455.51 ----------------------
Table 15.1, page 598, Least squares, OLS Standard errors, using xtlgs.
xtgls i f c, i(firm) t(year) panels(iid) Cross-sectional time-series FGLS regression Coefficients: generalized least squares Panels: homoskedastic Correlation: no autocorrelation Estimated covariances = 1 Number of obs = 100 Estimated autocorrelations = 0 Number of groups = 5 Estimated coefficients = 3 No. of time periods= 20 Wald chi2(2) = 352.19 Log likelihood = -624.9928 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ i | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- f | .1050854 .0112059 9.38 0.000 .0831223 .1270485 c | .3053655 .0428502 7.13 0.000 .2213806 .3893504 _cons | -48.02974 21.15551 -2.27 0.023 -89.49377 -6.565701 ------------------------------------------------------------------------------ matrix list e(Sigma) symmetric e(Sigma)[5,5] c1 c2 c3 c4 c5 r1 15708.836 r2 0 15708.836 r3 0 0 15708.836 r4 0 0 0 15708.836 r5 0 0 0 0 15708.836
Table 15.1, page 598, White standard errors.
regress i f c, robust Regression with robust standard errors Number of obs = 100 F( 2, 97) = 205.34 Prob > F = 0.0000 R-squared = 0.7789 Root MSE = 127.26 ------------------------------------------------------------------------------ | Robust i | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- f | .1050854 .0092867 11.32 0.000 .0866538 .123517 c | .3053655 .0600123 5.09 0.000 .1862578 .4244733 _cons | -48.02974 15.24712 -3.15 0.002 -78.29105 -17.76842 ------------------------------------------------------------------------------ matrix d = vecdiag(e(V)) . matrix v = cholesky(diag(d)) . matrix s = sqrt((100-3)/100)*vecdiag(v) . matrix list s s[1,3] f c _cons r1 .00914637 .05910526 15.016673
Table 15.1, page 598, Correct standard errors.
tsset firm year panel variable: firm, 1 to 5 time variable: year, 1935 to 1954 xtpcse i f c, het Linear regression, heteroskedastic panels corrected standard errors Group variable: firm Number of obs = 100 Time variable: year Number of groups = 5 Panels: heteroskedastic (balanced) Obs per group: min = 20 Autocorrelation: no autocorrelation avg = 20 max = 20 Estimated covariances = 5 R-squared = 0.7789 Estimated autocorrelations = 0 Wald chi2(2) = 720.01 Estimated coefficients = 3 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ | Het-corrected | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- f | .1050854 .0090625 11.60 0.000 .0873232 .1228476 c | .3053655 .0409468 7.46 0.000 .2251113 .3856198 _cons | -48.02974 14.20367 -3.38 0.001 -75.86841 -20.19106 ------------------------------------------------------------------------------ matrix list e(Sigma) symmetric e(Sigma)[5,5] r1 r2 r3 r4 r5 r1 9410.9061 r2 0 755.85077 r3 0 0 34288.49 r4 0 0 0 633.42367 r5 0 0 0 0 33455.511
Table 15.1, page 598, FGLS.
xtgls i f c, i(firm) t(year) panels(het) Cross-sectional time-series FGLS regression Coefficients: generalized least squares Panels: heteroskedastic Correlation: no autocorrelation Estimated covariances = 5 Number of obs = 100 Estimated autocorrelations = 0 Number of groups = 5 Estimated coefficients = 3 No. of time periods= 20 Wald chi2(2) = 865.38 Log likelihood = -570.1305 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ i | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- f | .0949905 .007409 12.82 0.000 .0804692 .1095118 c | .3378129 .0302254 11.18 0.000 .2785722 .3970535 _cons | -36.2537 6.124363 -5.92 0.000 -48.25723 -24.25017 ------------------------------------------------------------------------------ predict xb, xb . generate r2 = (i-xb)^2 . tabstat r2, stat(mean semean) by(firm) Summary for variables: r2 by categories of: firm firm | mean se(mean) ---------+-------------------- 1 | 8612.145 2896.987 2 | 409.1902 136.7008 3 | 36563.24 5801.747 4 | 777.9749 323.5032 5 | 32902.83 7000.861 ---------+-------------------- Total | 15853.07 2449.648 ------------------------------
Table 15.1, page 598, ML.
xtgls i f c, i(firm) t(year) panel(het) igls Iteration 1: tolerance = .1603143 (output omitted) Iteration 15: tolerance = 2.892e-08 Cross-sectional time-series FGLS regression Coefficients: generalized least squares Panels: heteroskedastic Correlation: no autocorrelation Estimated covariances = 5 Number of obs = 100 Estimated autocorrelations = 0 Number of groups = 5 Estimated coefficients = 3 No. of time periods= 20 Wald chi2(2) = 1048.82 Log likelihood = -564.5355 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ i | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- f | .09435 .0062834 15.02 0.000 .0820347 .1066652 c | .3337015 .022039 15.14 0.000 .2905059 .376897 _cons | -23.25817 4.815172 -4.83 0.000 -32.69574 -13.82061 ------------------------------------------------------------------------------ matrix list e(Sigma) symmetric e(Sigma)[5,5] c1 c2 c3 c4 c5 r1 8657.8826 r2 0 175.7844 r3 0 0 40211.124 r4 0 0 0 1241.0108 r5 0 0 0 0 29824.904
Table 15.2, page 602, FGLS.
xtgls i f c, i(firm) t(year) panel(cor) xtgls i f c, i(firm) t(year) panel(cor) Cross-sectional time-series FGLS regression Coefficients: generalized least squares Panels: heteroskedastic with cross-sectional correlation Correlation: no autocorrelation Estimated covariances = 15 Number of obs = 100 Estimated autocorrelations = 0 Number of groups = 5 Estimated coefficients = 3 No. of time periods= 20 Wald chi2(2) = 1285.19 Log likelihood = -537.8045 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ i | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- f | .0961894 .0054752 17.57 0.000 .0854583 .1069206 c | .3095321 .0179851 17.21 0.000 .2742819 .3447822 _cons | -38.36128 5.344871 -7.18 0.000 -48.83703 -27.88552 ------------------------------------------------------------------------------
Table 15.2, page 602, MLE. The current version of Limdep produces these results which differ from those in the book (see Errata for book).
xtgls i f c, i(firm) t(year) panels(cor) igls xtgls i f c, i(firm) t(year) panel(cor) Cross-sectional time-series FGLS regression Coefficients: generalized least squares Panels: heteroskedastic with cross-sectional correlation Correlation: no autocorrelation Estimated covariances = 15 Number of obs = 100 Estimated autocorrelations = 0 Number of groups = 5 Estimated coefficients = 3 No. of time periods= 20 Wald chi2(2) = 558.51 Log likelihood = -515.4222 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ i | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- f | .023631 .004291 5.51 0.000 .0152207 .0320413 c | .1709472 .0152526 11.21 0.000 .1410526 .2008417 _cons | -2.216508 1.958845 -1.13 0.258 -6.055774 1.622759 ------------------------------------------------------------------------------
Table 15.3, page 607, Heteroscedastic.
tabulate t, gen(t) (output omitted) regress logc logq logf lf t1-t15, noconst Source | SS df MS Number of obs = 90 -------------+------------------------------ F( 18, 72) =59513.52 Model | 16190.5087 18 899.472708 Prob > F = 0.0000 Residual | 1.08819022 72 .015113753 R-squared = 0.9999 -------------+------------------------------ Adj R-squared = 0.9999 Total | 16191.5969 90 179.906633 Root MSE = .12294 ------------------------------------------------------------------------------ logc | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- logq | .8677268 .0154082 56.32 0.000 .8370111 .8984424 logf | -.4844835 .3641085 -1.33 0.188 -1.210321 .2413535 lf | -1.954404 .4423777 -4.42 0.000 -2.836268 -1.07254 t1 | 20.4958 4.209528 4.87 0.000 12.10426 28.88735 t2 | 20.57804 4.221526 4.87 0.000 12.16258 28.9935 t3 | 20.65573 4.224177 4.89 0.000 12.23499 29.07647 t4 | 20.74076 4.24575 4.89 0.000 12.27701 29.20451 t5 | 21.19983 4.440331 4.77 0.000 12.34819 30.05147 t6 | 21.41162 4.538621 4.72 0.000 12.36404 30.4592 t7 | 21.50335 4.571397 4.70 0.000 12.39044 30.61626 t8 | 21.65403 4.622886 4.68 0.000 12.43847 30.86958 t9 | 21.82957 4.656906 4.69 0.000 12.5462 31.11294 t10 | 22.1138 4.792648 4.61 0.000 12.55983 31.66777 t11 | 22.46533 4.949909 4.54 0.000 12.59786 32.33279 t12 | 22.65134 5.008592 4.52 0.000 12.66689 32.63578 t13 | 22.61656 4.986139 4.54 0.000 12.67687 32.55624 t14 | 22.55223 4.955942 4.55 0.000 12.67274 32.43172 t15 | 22.53677 4.940532 4.56 0.000 12.688 32.38554 ------------------------------------------------------------------------------
Table 14.2, Random effects, Firm effects.
xtreg logc logq logf lf, i(i) re Random-effects GLS regression Number of obs = 90 Group variable (i) : i Number of groups = 6 R-sq: within = 0.9925 Obs per group: min = 15 between = 0.9856 avg = 15.0 overall = 0.9876 max = 15 Random effects u_i ~ Gaussian Wald chi2(3) = 11091.33 corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ logc | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- logq | .9066805 .025625 35.38 0.000 .8564565 .9569045 logf | .4227784 .0140248 30.15 0.000 .3952904 .4502665 lf | -1.064499 .2000703 -5.32 0.000 -1.456629 -.672368 _cons | 9.627909 .210164 45.81 0.000 9.215995 10.03982 -------------+---------------------------------------------------------------- sigma_u | .12488859 sigma_e | .06010514 rho | .81193816 (fraction of variance due to u_i) ------------------------------------------------------------------------------
Table 14.2, Random effects with autocorrelation. Using xtregar we obtain slightly different values for the autocorrelation, coefficients and standard errors. It should be noted that the latest version of Greene’s Limdep program also computes different values from those found in the book.
tsset i t panel variable: i, 1 to 6 time variable: t, 1 to 15 xtregar logc logq logf lf, re Random-effects GLS regression Number of obs = 90 Group variable (i) : i Number of groups = 6 R-sq: within = 0.9925 Obs per group: min = 15 between = 0.9854 avg = 15.0 overall = 0.9866 max = 15 Wald chi2(4) = 3735.11 corr(u_i, Xb) = 0 (assumed) Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ logc | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- logq | .9276293 .0287051 32.32 0.000 .8713683 .9838904 logf | .3997841 .017633 22.67 0.000 .3652241 .4343442 lf | -.9870458 .198669 -4.97 0.000 -1.37643 -.5976618 _cons | 9.902918 .2626146 37.71 0.000 9.388203 10.41763 -------------+---------------------------------------------------------------- rho_ar | .69576607 (estimated autocorrelation coefficient) sigma_u | .10060015 sigma_e | .04720363 rho_fov | .81955952 (fraction of variance due to u_i) theta | .67082541 ------------------------------------------------------------------------------