---------------------------------------------------------------------- name: log: analysis.log log type: text opened on: 01 Dec 2023, 10:00:00 . **************************************************** . * Spatial Panel Regression in Stata: . * Cigarette Demand Across US States . **************************************************** . clear all . macro drop _all . set more off . version 12 . . *--------------------------------------------------- . * Section 3: Setup and data loading . *--------------------------------------------------- . * 3.1 Spatial weight matrix . use "https://github.com/quarcs-lab/data-open/raw/master/cigar/Wct_bin.dta", replace . spmat dta Wst m1-m46, norm(row) replace . . * 3.2 Panel data setup . use "https://github.com/quarcs-lab/data-open/raw/master/cigar/baltagi_cigar.dta", clear . sort year state . xtset state year Panel variable: state (strongly balanced) Time variable: year, 1963 to 1992 Delta: 1 unit . . * 3.3 Panel summary statistics . xtsum Variable | Mean Std. dev. Min Max | Observations -----------------+--------------------------------------------+---------------- logc overall | 4.625563 .2538233 3.736352 5.399758 | N = 1380 between | .225498 4.057739 5.19628 | n = 46 within | .1254968 4.110718 5.070093 | T = 30 | | logp overall | 3.648067 .3364439 2.579455 4.588055 | N = 1380 between | .1927783 3.22723 4.021831 | n = 46 within | .2798008 2.780289 4.372397 | T = 30 | | logy overall | 1.615786 .248717 .8676362 2.253795 | N = 1380 between | .1363281 1.294913 2.063736 | n = 46 within | .2098697 1.035539 2.106283 | T = 30 . . *--------------------------------------------------- . * Section 4: Non-spatial panel models . *--------------------------------------------------- . * 4.1 Pooled OLS . reg logc logp logy Source | SS df MS Number of obs = 1,380 -------------+---------------------------------- F(2, 1377) = 199.28 Model | 21.564818 2 10.7824090 Prob > F = 0.0000 Residual | 74.518523 1,377 .054116576 R-squared = 0.2244 -------------+---------------------------------- Adj R-squared = 0.2233 Total | 96.083341 1,379 .069676098 Root MSE = .23284 ------------------------------------------------------------------------------ logc | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- logp | -.3857227 .0309752 -12.45 0.000 -.4464987 -.3249467 logy | .3724439 .0264568 14.08 0.000 .3205328 .4243551 _cons | 4.396312 .0531992 82.64 0.000 4.291951 4.500674 ------------------------------------------------------------------------------ . estimates store pool . . * 4.2 Region fixed effects . xtreg logc logp logy, fe Fixed-effects (within) regression Number of obs = 1,380 Group variable: state Number of groups = 46 R-squared: Obs per group: Within = 0.4059 min = 30 Between = 0.0681 avg = 30.0 Overall = 0.1050 max = 30 F(2,1332) = 455.52 corr(u_i, Xb) = -0.8072 Prob > F = 0.0000 ------------------------------------------------------------------------------ logc | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- logp | -.2307217 .0276419 -8.35 0.000 -.2849426 -.1765008 logy | -.0145419 .0389849 -0.37 0.709 -.0910300 .0619462 _cons | 4.619736 .0542965 85.09 0.000 4.513180 4.726293 ------------------------------------------------------------------------------ sigma_u | .21834832 sigma_e | .09498463 rho | .84090063 (fraction of variance due to u_i) ------------------------------------------------------------------------------ F test that all u_i=0: F(45, 1332) = 85.78 Prob > F = 0.0000 . estimates store rfe . . * 4.3 Time fixed effects . reg logc logp logy i.year Source | SS df MS Number of obs = 1,380 -------------+---------------------------------- F(31, 1348) = 41.04 Model | 48.7107267 31 1.57131054 Prob > F = 0.0000 Residual | 47.3726143 1,348 .03514290 R-squared = 0.5070 -------------+---------------------------------- Adj R-squared = 0.4957 Total | 96.083341 1,379 .069676098 Root MSE = .18747 ------------------------------------------------------------------------------ logc | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- logp | -.8612867 .0389729 -22.10 0.000 -.9377676 -.7848058 logy | .8045032 .0466019 17.26 0.000 .7130647 .8959417 _cons | 3.958816 .0638297 62.02 0.000 3.833551 4.084081 ------------------------------------------------------------------------------ . estimates store tfe . . * 4.4 Two-way fixed effects . xtreg logc logp logy i.year, fe Fixed-effects (within) regression Number of obs = 1,380 Group variable: state Number of groups = 46 R-squared: Obs per group: Within = 0.7891 min = 30 Between = 0.0121 avg = 30.0 Overall = 0.0456 max = 30 F(31,1303) = 157.60 corr(u_i, Xb) = -0.5688 Prob > F = 0.0000 ------------------------------------------------------------------------------ logc | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- logp | -.4020279 .0272553 -14.75 0.000 -.4555018 -.3485541 logy | .1193476 .0478095 2.50 0.013 .0255202 .2131749 _cons | 4.515994 .0533810 84.59 0.000 4.411254 4.620733 ------------------------------------------------------------------------------ sigma_u | .21428785 sigma_e | .05601281 rho | .93607854 (fraction of variance due to u_i) ------------------------------------------------------------------------------ . estimates store rtfe . . * 4.5 Comparison table . estimates table pool rfe tfe rtfe, b(%7.2f) star(0.1 0.05 0.01) stf(%9.0f) ------------------------------------------------------ Variable | pool rfe tfe rtfe -------------+---------------------------------------- logp | -0.39*** -0.23*** -0.86*** -0.40*** logy | 0.37*** -0.01 0.80*** 0.12** _cons | 4.40*** 4.62*** 3.96*** 4.52*** ------------------------------------------------------ Legend: * p<.1; ** p<.05; *** p<.01 . . *--------------------------------------------------- . * Section 6: Spatial Durbin Model (SDM) . *--------------------------------------------------- . * 6.1 SDM with two-way fixed effects . xsmle logc logp logy, fe type(both) wmat(Wst) mod(sdm) effects nsim(999) nolog Spatial Durbin model with fixed-effects Number of obs = 1,380 Group variable: state Number of groups = 46 Time variable: year Obs per group: min = 30 avg = 30.0 max = 30 Wald chi2(4) = 379.19 Log-likelihood = 1971.5204 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ logc | Coefficient Std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- Main | logp | -.3068973 .0282114 -10.88 0.000 -.3621907 -.2516039 logy | .0781427 .0481269 1.62 0.104 -.0161843 .1724697 -------------+---------------------------------------------------------------- Wx | logp | -.2060671 .0649703 -3.17 0.002 -.3334065 -.0787277 logy | .1803542 .0885162 2.04 0.042 .0068656 .3538428 -------------+---------------------------------------------------------------- Spatial | rho | .2649571 .0327948 8.08 0.000 .2006804 .3292339 -------------+---------------------------------------------------------------- sigma2_e| .0027866 ------------------------------------------------------------------------------ Direct | -.3131508 .0285649 -10.96 0.000 -.3691370 -.2571645 Indirect | -.3138174 .0812337 -3.86 0.000 -.4730325 -.1546023 Total | -.6269682 .0866710 -7.23 0.000 -.7968403 -.4570961 | Direct | .0941302 .0488720 1.93 0.054 -.0016572 .1899176 Indirect | .2683417 .1099814 2.44 0.015 .0527821 .4839013 Total | .3624719 .1216523 2.98 0.003 .1240378 .6009060 . estimates store sdm1 . . * 6.2 SDM with Lee-Yu bias correction . xsmle logc logp logy, fe type(both) leeyu wmat(Wst) mod(sdm) effects nsim(999) nolog Spatial Durbin model with fixed-effects (Lee-Yu) Number of obs = 1,334 Group variable: state Number of groups = 46 Time variable: year Obs per group: min = 29 avg = 29.0 max = 29 Wald chi2(4) = 392.50 Log-likelihood = 1932.4681 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ logc | Coefficient Std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- Main | logp | -.3044782 .0283901 -10.72 0.000 -.3601218 -.2488346 logy | .0770150 .0486311 1.58 0.113 -.0183001 .1723301 -------------+---------------------------------------------------------------- Wx | logp | -.2083124 .0654876 -3.18 0.001 -.3366657 -.0799591 logy | .1869831 .0894718 2.09 0.037 .0116216 .3623446 -------------+---------------------------------------------------------------- Spatial | rho | .2596348 .0332441 7.81 0.000 .1944776 .3247920 -------------+---------------------------------------------------------------- sigma2_e| .0027512 ------------------------------------------------------------------------------ Direct | -.3104271 .0287814 -10.79 0.000 -.3668377 -.2540166 Indirect | -.3122946 .0825781 -3.78 0.000 -.4741447 -.1504446 Total | -.6227218 .0878439 -7.09 0.000 -.7948927 -.4505509 | Direct | .0935487 .0494610 1.89 0.059 -.0033931 .1904905 Indirect | .2739264 .1115282 2.46 0.014 .0553351 .4925177 Total | .3674751 .1235608 2.97 0.003 .1253004 .6096498 . estimates store sdm2 . . * 6.3 Comparison . estimates table sdm1 sdm2, b(%7.3f) star(0.1 0.05 0.01) stf(%9.0f) ---------------------------------------------- Variable | sdm1 sdm2 -------------+-------------------------------- Main | logp | -0.307*** -0.304*** logy | 0.078 0.077 Wx | logp | -0.206*** -0.208*** logy | 0.180** 0.187** Spatial | rho | 0.265*** 0.260*** ---------------------------------------------- Legend: * p<.1; ** p<.05; *** p<.01 . . *--------------------------------------------------- . * Section 7: Wald specification tests . *--------------------------------------------------- . quietly xsmle logc logp logy, fe type(both) leeyu wmat(Wst) mod(sdm) effects nsim(999) nolog . . * Wald test: Reduce to SAR? (NO if p < 0.05) . test ([Wx]logp = 0) ([Wx]logy = 0) ( 1) [Wx]logp = 0 ( 2) [Wx]logy = 0 chi2( 2) = 12.87 Prob > chi2 = 0.0016 . . * Wald test: Reduce to SLX? (NO if p < 0.05) . test ([Spatial]rho = 0) ( 1) [Spatial]rho = 0 chi2( 1) = 61.04 Prob > chi2 = 0.0000 . . * Wald test: Reduce to SEM? (NO if p < 0.05) . testnl ([Wx]logp = -[Spatial]rho*[Main]logp) ([Wx]logy = -[Spatial]rho*[Main]logy) (1) [Wx]logp = -[Spatial]rho*[Main]logp (2) [Wx]logy = -[Spatial]rho*[Main]logy chi2( 2) = 8.49 Prob > chi2 = 0.0143 . . *--------------------------------------------------- . * Section 8: Dynamic spatial panel models . *--------------------------------------------------- . * 8.1 Non-dynamic SDM (baseline) . xsmle logc logp logy, fe type(both) wmat(Wst) mod(sdm) effects nsim(999) nolog Spatial Durbin model with fixed-effects Number of obs = 1,380 ------------------------------------------------------------------------------ logc | Coefficient Std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- Main | logp | -.3068973 .0282114 -10.88 0.000 -.3621907 -.2516039 logy | .0781427 .0481269 1.62 0.104 -.0161843 .1724697 Wx | logp | -.2060671 .0649703 -3.17 0.002 -.3334065 -.0787277 logy | .1803542 .0885162 2.04 0.042 .0068656 .3538428 Spatial | rho | .2649571 .0327948 8.08 0.000 .2006804 .3292339 ------------------------------------------------------------------------------ . eststo SDM0 . . * 8.2 Dynamic: tau * y_it-1 . xsmle logc logp logy, dlag(1) fe type(both) wmat(Wst) mod(sdm) effects nsim(999) nolog Dynamic Spatial Durbin model with fixed-effects Number of obs = 1,334 ------------------------------------------------------------------------------ logc | Coefficient Std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- Main | logp | -.1516305 .0226714 -6.69 0.000 -.1960657 -.1071954 logy | .0285493 .0376124 0.76 0.448 -.0451697 .1022683 Wx | logp | -.0714289 .0521683 -1.37 0.171 -.1736769 .0308190 logy | .0592735 .0706984 0.84 0.402 -.0792929 .1978399 Spatial | rho | .1021753 .0307624 3.32 0.001 .0418821 .1624685 Temporal | tau | .6543218 .0196285 33.33 0.000 .6158507 .6927928 ------------------------------------------------------------------------------ . eststo dySDM1 . . * 8.3 Dynamic: psi * W * y_it-1 . xsmle logc logp logy, dlag(2) fe type(both) wmat(Wst) mod(sdm) effects nsim(999) nolog Dynamic Spatial Durbin model with fixed-effects Number of obs = 1,334 ------------------------------------------------------------------------------ logc | Coefficient Std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- Main | logp | -.2981475 .0280193 -10.64 0.000 -.3530643 -.2432307 logy | .0637218 .0478561 1.33 0.183 -.0300745 .1575181 Wx | logp | -.1425379 .0647518 -2.20 0.028 -.2694490 -.0156268 logy | .1320869 .0888243 1.49 0.137 -.0420055 .3061793 Spatial | rho | .1523264 .0369871 4.12 0.000 .0798330 .2248199 Temporal | psi | .2712508 .0339714 7.98 0.000 .2046680 .3378335 ------------------------------------------------------------------------------ . eststo dySDM2 . . * 8.4 Dynamic: tau * y_it-1 + psi * W * y_it-1 . xsmle logc logp logy, dlag(3) fe type(both) wmat(Wst) mod(sdm) effects nsim(999) nolog Dynamic Spatial Durbin model with fixed-effects Number of obs = 1,334 ------------------------------------------------------------------------------ logc | Coefficient Std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- Main | logp | -.1498627 .0226523 -6.62 0.000 -.1942603 -.1054651 logy | .0271398 .0376004 0.72 0.470 -.0465556 .1008351 Wx | logp | -.0636842 .0524156 -1.21 0.224 -.1664169 .0390485 logy | .0471982 .0712803 0.66 0.508 -.0925087 .1869052 Spatial | rho | .0803516 .0322458 2.49 0.013 .0171509 .1435524 Temporal | tau | .6389621 .0208541 30.64 0.000 .5980889 .6798353 psi | .0494172 .0325896 1.52 0.130 -.0144571 .1132915 ------------------------------------------------------------------------------ . eststo dySDM3 . . * 8.5 Comparison table . esttab SDM0 dySDM1 dySDM2 dySDM3, mtitle("SDM" "dySDM1" "dySDM2" "dySDM3") -------------------------------------------------------------------- (1) (2) (3) (4) SDM dySDM1 dySDM2 dySDM3 -------------------------------------------------------------------- Main logp -0.307*** -0.152*** -0.298*** -0.150*** (-10.88) (-6.69) (-10.64) (-6.62) logy 0.078 0.029 0.064 0.027 (1.62) (0.76) (1.33) (0.72) Wx logp -0.206*** -0.071 -0.143** -0.064 (-3.17) (-1.37) (-2.20) (-1.21) logy 0.180** 0.059 0.132 0.047 (2.04) (0.84) (1.49) (0.66) Spatial rho 0.265*** 0.102*** 0.152*** 0.080** (8.08) (3.32) (4.12) (2.49) Temporal tau 0.654*** 0.639*** (33.33) (30.64) psi 0.271*** 0.049 (7.98) (1.52) -------------------------------------------------------------------- N 1380 1334 1334 1334 -------------------------------------------------------------------- t statistics in parentheses * p<0.1, ** p<0.05, *** p<0.01 . . log close name: log: analysis.log log type: text closed on: 01 Dec 2023, 10:15:00 ----------------------------------------------------------------------