u panel_lecture sum Variable Obs Mean Std Dev Min Max datastre 639 9039644 6369418 900228 926665 year 639 1980 2584012 1976 1984 total_sa 639 9377839 3212313 682 441e+07 tot_fixe 639 5214385 1988422 642 270e+07 emp 639 1941808 3296682 141 208200 GENERATES NATURAL LOGS OF THE VARIABLES gen l_out=ln( total_sa) gen l_cap=ln( tot_fixe) gen l_emp=ln(emp) SIMPLE OLS MODEL FOR THE COBB-DOUGLAS PRODUCTION FUNCTION reg l_out l_cap l_emp Source SS df MS Number of obs = 639 ---------+------------------------------ F( 2, 636) = 679258 Model 263801202 2 131900601 Prob > F = 00000 Residual 123500583 636 194183307 R-squared = 09553 ---------+------------------------------ Adj R-squared = 09551 Total 27615126 638 432838966 Root MSE = 44066 l_out Coef Std Err t P> t [95% Conf Interval] l_cap 6651399 0213941 31090 0000 6231283 7071516 l_emp 3781565 0269705 14021 0000 3251946 4311185 _cons 1312989 0925374 14189 0000 1131273 1494705 COMMAND TO IDENTIFY ENTITIES (THE i PART) AND TIME (THE t PART) sort datastre year iis datastre tis year GENERATING LAGGED VARIABLES BY ENTITY: quietly by datastre: gen l_out_1= l_out[_n-1] sum l_out l_out_1 Variable Obs Mean Std Dev Min Max
l_out 639 1188205 2080478 652503 1760104 l_out_1 568 1184048 2075751 652503 1745204 quietly by datastre: gen l_cap_1= l_cap[_n-1] sum l_cap l_cap_1 Variable Obs Mean Std Dev Min Max l_cap 639 1096192 2141774 6464588 1710953 l_cap_1 568 1091742 2136717 6464588 1687525 quietly by datastre: gen l_emp_1= l_emp[_n-1] sum l_emp l_emp_1 Variable Obs Mean Std Dev Min Max l_emp 639 8667979 1698947 494876 1224625 l_emp_1 568 8674394 1694716 494876 1224625 CREATING THE FIRST-DIFFERENCE VARIABLES: ONE COLUMN SUBTRACTED FROM THE OTHER gen dl_out= l_out- l_out_1 (71 missing values generated) gen dl_cap= l_cap- l_cap_1 (71 missing values generated) gen dl_emp= l_emp- l_emp_1 (71 missing values generated) FIRST-DIFFERENCE REGRESSION (NOTE THE CODE ABOVE TO GENERATE THE FIRST- DIFFERENCED VARIABLES ON LOG OUTPUT, LOG CAPITAL AND LOG EMPLOYMENT reg dl_out dl_cap dl_emp Source SS df MS Number of obs = 568 ---------+------------------------------ F( 2, 565) = 13804 Model 551273048 2 275636524 Prob > F = 00000 Residual 112816065 565 019967445 R-squared = 03282 ---------+------------------------------ Adj R-squared = 03259 Total 16794337 567 029619642 Root MSE = 14131 dl_out Coef Std Err t P> t [95% Conf Interval] dl_cap 4488407 0345989 12973 0000 3808825 516799 dl_emp 1529615 0240827 6352 0000 105659 200264 _cons 0512393 0069031 7423 0000 0376805 0647981 COMMAND FOR GENERATING TIME DUMMIES tab year, gen(time)
INCLUDING TIME DUMMIES IN THE REGRESSION NOTE WE HAVE LOST (TIME1 = 1976 FROM THE FIRST DIFFERENCE reg dl_out dl_cap dl_emp time2- time9 Source SS df MS Number of obs = 568 ---------+------------------------------ F( 9, 558) = 3418 Model 596815824 9 663128694 Prob > F = 00000 Residual 108261787 558 019401754 R-squared = 03554 ---------+------------------------------ Adj R-squared = 03450 Total 16794337 567 029619642 Root MSE = 13929 dl_out Coef Std Err t P> t [95% Conf Interval] dl_cap 4471214 0346315 12911 0000 3790975 5151454 dl_emp 1301107 0250005 5204 0000 081004 1792173 time2 0212789 0234899 0906 0365-0248605 0674182 time3-0004267 0235301-0018 0986-046645 0457916 time4 0110023 0234443 0469 0639-0350476 0570522 time5-0467577 0234425-1995 0047-0928042 -0007113 time6-0674197 0236997-2845 0005-1139711 -0208682 time7-0312779 0234195-1336 0182-0772792 0147233 time8-0333793 0235603-1417 0157-079657 0128985 time9 (dropped) _cons 069794 0167845 4158 0000 0368256 1027625 COMMAND FOR GENERATING FIRM SPECIFIC DUMMY VARIABLES tab datastre, gen(fdum) FIXED EFFECTS REGRESSION (NOTE TO SAVE SPACE, THE FIRM SPECIFIC DUMMIES HAVE BEEN SUPPRESSED - ONLY FIRM2 AND FIRM71 ARE SHOWING OMITTED FIRM: FIRM1) reg l_out l_cap l_emp fdum2- fdum71 Source SS df MS Number of obs = 639 ---------+------------------------------ F( 72, 566) = 121306 Model 27437322 72 381073916 Prob > F = 00000 Residual 177804045 566 031414142 R-squared = 09936 ---------+------------------------------ Adj R-squared = 09927 Total 27615126 638 432838966 Root MSE = 17724 l_out Coef Std Err t P> t [95% Conf Interval] l_cap 7300485 020427 35739 0000 6899265 7701705 l_emp 1156112 0242128 4775 0000 0680533 1631691 fdum2-1821407 0933627-1951 0052-3655203 0012389
fdum71-6609142 1259654-5247 0000-9083309 -4134975 _cons 3203354 3131989 10228 0000 258818 3818528 FIXED EFFECTS REGRESSION WITH FIRM AND TIME DUMMIES reg l_out l_cap l_emp fdum2- fdum71 time2- time9 Source SS df MS Number of obs = 639 ---------+------------------------------ F( 80, 558) = 134360 Model 274725085 80 343406356 Prob > F = 00000 Residual 142617556 558 025558702 R-squared = 09948 ---------+------------------------------ Adj R-squared = 09941 Total 27615126 638 432838966 Root MSE = 15987 l_out Coef Std Err t P> t [95% Conf Interval] l_cap 4462243 0318839 13995 0000 3835972 5088515 l_emp 249869 0263928 9467 0000 1980276 3017105 fdum2-4969282 0885997-5609 0000-670958 -3228985 fdum71-1391584 1303745-10674 0000-1647669 -1135499 time2 0827797 027017 3064 0002 0297124 1358471 time9 4118378 037392 11014 0000 3383915 4852841 _cons 5204732 3329182 15634 0000 4550806 5858658 FIXED EFFECTS (WITHIN GROUPS) REGRESSION xtreg l_out l_cap l_emp, fe Fixed-effects (within) regression sd(u_datastre) = 5222397 Number of obs = 639 sd(e_datastre_t) = 1772404 n = 71 sd(e_datastre_t + u_datastre)= 5514966 T = 9 corr(u_datastre, Xb) = 05404 R-sq within = 07356 between = 09553 overall = 09495 F( 2, 566) = 78716 Prob > F = 00000 l_out Coef Std Err t P> t [95% Conf Interval] l_cap 7300485 020427 35739 0000 6899265 7701705 l_emp 1156112 0242128 4775 0000 0680533 1631691 _cons 2877204 252777 11382 0000 2380709 33737
datastre F(70,566) = 48077 0000 (71 categories) RANDOM EFFECTS REGRESSION xtreg l_out l_cap l_emp Random-effects GLS regression sd(u_datastre) = 4020154 Number of obs = 639 sd(e_datastre_t) = 1772404 n = 71 sd(e_datastre_t + u_datastre)= 4393524 T = 9 corr(u_datastre, X) = 0 (assumed) R-sq within = 07340 between = 09573 overall = 09515 chi2( 2) = 316393 (theta = 08546) Prob > chi2 = 00000 l_out Coef Std Err z P> z [95% Conf Interval] l_cap 7593242 0183558 41367 0000 7233475 7953009 l_emp 1698872 0223201 7611 0000 1261405 2136338 _cons 2085823 1892458 11022 0000 1714908 2456738 HAUSMAN TEST xthaus Hausman specification test ---- Coefficients ---- Fixed Random l_out Effects Effects Difference ---------+----------------------------------------- l_cap 7300485 7593242-0292757 l_emp 1156112 1698872-054276 Test: Ho: difference in coefficients not systematic chi2( 2) = (b-b)'[s^(-1)](b-b), S = (S_fe - S_re) = 4581 Prob>chi2 = 00000 SAME REGRESSIONS WITH TIME EFFECTS INCLUDED xtreg l_out l_cap l_emp time2- time9, fe Fixed-effects (within) regression sd(u_datastre) = 7875564 Number of obs = 639 sd(e_datastre_t) = 1598709 n = 71 sd(e_datastre_t + u_datastre)= 8036192 T = 9 corr(u_datastre, Xb) = 08403 R-sq within = 07879
between = 09621 overall = 09533 F( 10, 558) = 20727 Prob > F = 00000 l_out Coef Std Err t P> t [95% Conf Interval] l_cap 4462244 0318839 13995 0000 3835972 5088515 l_emp 249869 0263928 9467 0000 1980276 3017105 time2 0827797 027017 3064 0002 0297124 1358471 time3 1449522 0277687 5220 0000 0904083 1994961 time4 2219929 0288814 7686 0000 1652633 2787225 time5 2446083 030578 7999 0000 1845462 3046704 time6 2673673 0332876 8032 0000 201983 3327516 time7 3145015 0350334 8977 0000 245688 383315 time8 3397451 0354923 9572 0000 2700303 4094598 time9 4118378 037392 11014 0000 3383915 4852841 _cons 4599407 2740665 16782 0000 4061079 5137735 datastre F(70,558) = 59162 0000 (71 categories) xtreg l_out l_cap l_emp time2- time9 Random-effects GLS regression sd(u_datastre) = 4028238 Number of obs = 639 sd(e_datastre_t) = 1598709 n = 71 sd(e_datastre_t + u_datastre)= 4333886 T = 9 corr(u_datastre, X) = 0 (assumed) R-sq within = 07774 between = 09613 overall = 09553 chi2( 10) = 328291 (theta = 08689) Prob > chi2 = 00000 l_out Coef Std Err z P> z [95% Conf Interval] l_cap 6058734 0268102 22599 0000 5533264 6584205 l_emp 2733885 0269179 10156 0000 2206304 3261467 time2 0618169 0286912 2155 0031 0055832 1180506 time3 0987918 0290764 3398 0001 0418032 1557804 time4 1549524 0296922 5219 0000 0967567 2131481 time5 1564771 0307357 5091 0000 0962363 2167179 time6 1688645 0330574 5108 0000 1040733 2336557 time7 2093399 0345786 6054 0000 1415671 2771128 time8 2213377 0345578 6405 0000 1536056 2890697 time9 2812139 036013 7809 0000 2106297 3517981 _cons 272048 2010733 13530 0000 2326383 3114576 xthaus
Hausman specification test ---- Coefficients ---- Fixed Random l_out Effects Effects Difference ---------+----------------------------------------- l_cap 4462244 6058734-1596491 l_emp 249869 2733885-0235195 time2 0827797 0618169 0209629 time3 1449522 0987918 0461604 time4 2219929 1549524 0670404 time5 2446083 1564771 0881312 time6 2673673 1688645 0985028 time7 3145015 2093399 1051615 time8 3397451 2213377 1184074 time9 4118378 2812139 1306239 Test: Ho: difference in coefficients not systematic chi2( 10) = (b-b)'[s^(-1)](b-b), S = (S_fe - S_re) = 8559 Prob>chi2 = 00000