--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- name: log: /Users/kaew/Documents/EE325/2024/STATA sessions/STATA session 3_logfile.log log type: text opened on: 23 Oct 2024, 08:32:17 . do "/Users/kaew/Documents/EE325/2024/STATA sessions/STATA _session3.do" . . clear . //Example 1 . use "/Users/kaew/Documents/EE325/DATA_STATA/Table11.1.dta" . bro . . // BPG-test or LM test(manual) . reg y x Source | SS df MS Number of obs = 9 -------------+---------------------------------- F(1, 7) = 106.46 Model | 1327891.27 1 1327891.27 Prob > F = 0.0000 Residual | 87312.7333 7 12473.2476 R-squared = 0.9383 -------------+---------------------------------- Adj R-squared = 0.9295 Total | 1415204 8 176900.5 Root MSE = 111.68 ------------------------------------------------------------------------------ y | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- x | 148.7667 14.4183 10.32 0.000 114.6728 182.8605 _cons | 3417.833 81.13632 42.12 0.000 3225.976 3609.69 ------------------------------------------------------------------------------ . predict u_hat, residual . generate u_hat_sq = u_hat^2 . regress u_hat_sq x Source | SS df MS Number of obs = 9 -------------+---------------------------------- F(1, 7) = 3.97 Model | 259304539 1 259304539 Prob > F = 0.0865 Residual | 456854875 7 65264982.2 R-squared = 0.3621 -------------+---------------------------------- Adj R-squared = 0.2709 Total | 716159414 8 89519926.8 Root MSE = 8078.7 ------------------------------------------------------------------------------ u_hat_sq | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- x | -2078.88 1042.952 -1.99 0.086 -4545.071 387.3105 _cons | 20095.82 5869.021 3.42 0.011 6217.786 33973.84 ------------------------------------------------------------------------------ . . // r-squared = 0.3621 => LM-statistic =n*r-squared = 9*0.3621 = 3.2589 . // chi-square(d.f. = 1) 5% significant level = .... . // LM-statistic > Chi-square. So, we cannot reject Ho . // of heteroskedasticity. . . // BPGtest or LM test (STATA command) . reg y x Source | SS df MS Number of obs = 9 -------------+---------------------------------- F(1, 7) = 106.46 Model | 1327891.27 1 1327891.27 Prob > F = 0.0000 Residual | 87312.7333 7 12473.2476 R-squared = 0.9383 -------------+---------------------------------- Adj R-squared = 0.9295 Total | 1415204 8 176900.5 Root MSE = 111.68 ------------------------------------------------------------------------------ y | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- x | 148.7667 14.4183 10.32 0.000 114.6728 182.8605 _cons | 3417.833 81.13632 42.12 0.000 3225.976 3609.69 ------------------------------------------------------------------------------ . estat hettest Breusch–Pagan/Cook–Weisberg test for heteroskedasticity Assumption: Normal error terms Variable: Fitted values of y H0: Constant variance chi2(1) = 1.38 Prob > chi2 = 0.2405 . ** Since p-value (prob>chi2) is more than 0.05, we cannot reject Ho at 5% . ** significant level. We can conclude that we do not have heteroskedasticity. . . . // White-test (STATA command) . . reg y x Source | SS df MS Number of obs = 9 -------------+---------------------------------- F(1, 7) = 106.46 Model | 1327891.27 1 1327891.27 Prob > F = 0.0000 Residual | 87312.7333 7 12473.2476 R-squared = 0.9383 -------------+---------------------------------- Adj R-squared = 0.9295 Total | 1415204 8 176900.5 Root MSE = 111.68 ------------------------------------------------------------------------------ y | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- x | 148.7667 14.4183 10.32 0.000 114.6728 182.8605 _cons | 3417.833 81.13632 42.12 0.000 3225.976 3609.69 ------------------------------------------------------------------------------ . whitetst White's general test statistic : 5.153769 Chi-sq( 2) P-value = .076 . ** Since p-value (prob>chi2) is more than 0.05, we cannot reject Ho at 5% . ** significant level. We can conclude that we do not have heteroskedasticity. . . reg y x, robust Linear regression Number of obs = 9 F(1, 7) = 77.69 Prob > F = 0.0000 R-squared = 0.9383 Root MSE = 111.68 ------------------------------------------------------------------------------ | Robust y | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- x | 148.7667 16.87768 8.81 0.000 108.8573 188.676 _cons | 3417.833 107.1315 31.90 0.000 3164.508 3671.159 ------------------------------------------------------------------------------ . . . clear . . //Example 2 . //BPG test manual or LM test (Manual) . use "/Users/kaew/Documents/EE325/DATA_STATA/Table 11.5.dta" . reg rd sales Source | SS df MS Number of obs = 14 -------------+---------------------------------- F(1, 12) = 2.48 Model | 208733442 1 208733442 Prob > F = 0.1410 Residual | 1.0083e+09 12 84021567.1 R-squared = 0.1715 -------------+---------------------------------- Adj R-squared = 0.1025 Total | 1.2170e+09 13 93614788.2 Root MSE = 9166.3 ------------------------------------------------------------------------------ rd | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- sales | .0437234 .0277404 1.58 0.141 -.0167178 .1041646 _cons | 1337.874 5015.141 0.27 0.794 -9589.18 12264.93 ------------------------------------------------------------------------------ . predict u_hat, residual . generate u_hat_sq = u_hat^2 . regress u_hat_sq sales Source | SS df MS Number of obs = 14 -------------+---------------------------------- F(1, 12) = 9.09 Model | 9.1628e+16 1 9.1628e+16 Prob > F = 0.0108 Residual | 1.2100e+17 12 1.0083e+16 R-squared = 0.4309 -------------+---------------------------------- Adj R-squared = 0.3835 Total | 2.1263e+17 13 1.6356e+16 Root MSE = 1.0e+08 ------------------------------------------------------------------------------ u_hat_sq | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- sales | 916.0775 303.8929 3.01 0.011 253.9517 1578.203 _cons | -7.25e+07 5.49e+07 -1.32 0.212 -1.92e+08 4.72e+07 ------------------------------------------------------------------------------ . . // r-squared = 0.4309 => LM-statistic =n*r-squared = 14*0.4309 = 6.0326 . // chi-square(d.f. = 1) 5% significant level = ...... . // LM-statistic > Chi-square. So, we reject Ho in favor . // of heteroskedasticity. . . ** Since we have heteroskedascity, we need to use the ,robust option. . reg rd sales, robust Linear regression Number of obs = 14 F(1, 12) = 1.13 Prob > F = 0.3083 R-squared = 0.1715 Root MSE = 9166.3 ------------------------------------------------------------------------------ | Robust rd | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- sales | .0437234 .0410918 1.06 0.308 -.0458079 .1332547 _cons | 1337.874 4892.447 0.27 0.789 -9321.852 11997.6 ------------------------------------------------------------------------------ . . // BPGtest or LM test (STATA command) . regress rd sales Source | SS df MS Number of obs = 14 -------------+---------------------------------- F(1, 12) = 2.48 Model | 208733442 1 208733442 Prob > F = 0.1410 Residual | 1.0083e+09 12 84021567.1 R-squared = 0.1715 -------------+---------------------------------- Adj R-squared = 0.1025 Total | 1.2170e+09 13 93614788.2 Root MSE = 9166.3 ------------------------------------------------------------------------------ rd | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- sales | .0437234 .0277404 1.58 0.141 -.0167178 .1041646 _cons | 1337.874 5015.141 0.27 0.794 -9589.18 12264.93 ------------------------------------------------------------------------------ . estat hettest Breusch–Pagan/Cook–Weisberg test for heteroskedasticity Assumption: Normal error terms Variable: Fitted values of rd H0: Constant variance chi2(1) = 8.83 Prob > chi2 = 0.0030 . ** Since p-value (prob>chi2) is less than 0.05, we reject Ho at 5% . ** significant level. We can conclude that we have heteroskedasticity. . ** Since we have heteroskedascity, we need to use the ,robust option. . reg rd sales, robust Linear regression Number of obs = 14 F(1, 12) = 1.13 Prob > F = 0.3083 R-squared = 0.1715 Root MSE = 9166.3 ------------------------------------------------------------------------------ | Robust rd | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- sales | .0437234 .0410918 1.06 0.308 -.0458079 .1332547 _cons | 1337.874 4892.447 0.27 0.789 -9321.852 11997.6 ------------------------------------------------------------------------------ . . . clear . . //Example 2 . //BPG test manual or LM test (Manual) . use "/Users/kaew/Documents/EE325/DATA_STATA/Table 11.5.dta" . . //White-test (Manual) . reg rd sales Source | SS df MS Number of obs = 14 -------------+---------------------------------- F(1, 12) = 2.48 Model | 208733442 1 208733442 Prob > F = 0.1410 Residual | 1.0083e+09 12 84021567.1 R-squared = 0.1715 -------------+---------------------------------- Adj R-squared = 0.1025 Total | 1.2170e+09 13 93614788.2 Root MSE = 9166.3 ------------------------------------------------------------------------------ rd | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- sales | .0437234 .0277404 1.58 0.141 -.0167178 .1041646 _cons | 1337.874 5015.141 0.27 0.794 -9589.18 12264.93 ------------------------------------------------------------------------------ . predict u_hat, residual . generate u_hat_sq = u_hat^2 . gen salessq=sales^2 . regress u_hat_sq sales salessq Source | SS df MS Number of obs = 14 -------------+---------------------------------- F(2, 11) = 4.23 Model | 9.2405e+16 2 4.6203e+16 Prob > F = 0.0435 Residual | 1.2022e+17 11 1.0929e+16 R-squared = 0.4346 -------------+---------------------------------- Adj R-squared = 0.3318 Total | 2.1263e+17 13 1.6356e+16 Root MSE = 1.0e+08 ------------------------------------------------------------------------------ u_hat_sq | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- sales | 577.6563 1307.934 0.44 0.667 -2301.087 3456.4 salessq | .0008456 .0031711 0.27 0.795 -.006134 .0078253 _cons | -4.67e+07 1.12e+08 -0.42 0.685 -2.94e+08 2.00e+08 ------------------------------------------------------------------------------ . // r-squared = 0.4346 => LM-statistic =n*r-squared = 14*0.4309 = 6.090 . // chi-square(d.f. = 1) 5% significant level = ...... . // LM-statistic > Chi-square. So, we reject Ho in favor . // of heteroskedasticity. . . . // White-test (STATA command) . reg rd sales Source | SS df MS Number of obs = 14 -------------+---------------------------------- F(1, 12) = 2.48 Model | 208733442 1 208733442 Prob > F = 0.1410 Residual | 1.0083e+09 12 84021567.1 R-squared = 0.1715 -------------+---------------------------------- Adj R-squared = 0.1025 Total | 1.2170e+09 13 93614788.2 Root MSE = 9166.3 ------------------------------------------------------------------------------ rd | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- sales | .0437234 .0277404 1.58 0.141 -.0167178 .1041646 _cons | 1337.874 5015.141 0.27 0.794 -9589.18 12264.93 ------------------------------------------------------------------------------ . whitetst White's general test statistic : 6.084199 Chi-sq( 2) P-value = .0477 . ** Since p-value (prob>chi2) is more than 0.05, we cannot reject Ho at 5% . ** significant level. We can conclude that we do not have heteroskedasticity. . . reg rd sales, robust Linear regression Number of obs = 14 F(1, 12) = 1.13 Prob > F = 0.3083 R-squared = 0.1715 Root MSE = 9166.3 ------------------------------------------------------------------------------ | Robust rd | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- sales | .0437234 .0410918 1.06 0.308 -.0458079 .1332547 _cons | 1337.874 4892.447 0.27 0.789 -9321.852 11997.6 ------------------------------------------------------------------------------ . . . clear . use "/Users/kaew/Documents/EE325/DATA_STATA/Table 10.7.dta" . gen lnc=log(c) . gen lnincome=log(yd) . gen lnw =log(w) . reg lnc lnincome lnw i Source | SS df MS Number of obs = 54 -------------+---------------------------------- F(3, 50) = 37832.66 Model | 16.1637474 3 5.3879158 Prob > F = 0.0000 Residual | .007120721 50 .000142414 R-squared = 0.9996 -------------+---------------------------------- Adj R-squared = 0.9995 Total | 16.1708681 53 .305110719 Root MSE = .01193 ------------------------------------------------------------------------------ lnc | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- lnincome | .8048728 .0174978 46.00 0.000 .7697273 .8400182 lnw | .2012702 .0175926 11.44 0.000 .1659345 .236606 i | -.0026891 .0007619 -3.53 0.001 -.0042194 -.0011587 _cons | -.467712 .042778 -10.93 0.000 -.5536342 -.3817899 ------------------------------------------------------------------------------ . . tsset year Time variable: year, 1947 to 2000 Delta: 1 unit . estat dwatson Durbin–Watson d-statistic( 4, 54) = 1.289232 . . newey lnc lnincome lnw i, lag(3) Regression with Newey–West standard errors Number of obs = 54 Maximum lag = 3 F( 3, 50) = 22341.20 Prob > F = 0.0000 ------------------------------------------------------------------------------ | Newey–West lnc | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- lnincome | .8048728 .0171172 47.02 0.000 .7704919 .8392536 lnw | .2012702 .0154469 13.03 0.000 .1702441 .2322963 i | -.0026891 .0008798 -3.06 0.004 -.0044563 -.0009219 _cons | -.467712 .0439367 -10.65 0.000 -.5559616 -.3794625 ------------------------------------------------------------------------------ . . reg lnc lnincome lnw i, robust Linear regression Number of obs = 54 F(3, 50) = 27845.23 Prob > F = 0.0000 R-squared = 0.9996 Root MSE = .01193 ------------------------------------------------------------------------------ | Robust lnc | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- lnincome | .8048728 .0175834 45.77 0.000 .7695554 .8401901 lnw | .2012702 .017408 11.56 0.000 .1663052 .2362352 i | -.0026891 .0008601 -3.13 0.003 -.0044167 -.0009614 _cons | -.467712 .0476482 -9.82 0.000 -.5634163 -.3720078 ------------------------------------------------------------------------------ . end of do-file . log close name: log: /Users/kaew/Documents/EE325/2024/STATA sessions/STATA session 3_logfile.log log type: text closed on: 23 Oct 2024, 08:32:33 ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------