** * Chapter 15 *Chapter 15 - Instrumental Variables Estimation and Two Stage Least Squares *Example 15.1: Estimating the Return to Education for Married Women use http://fmwww.bc.edu/ec-p/data/wooldridge/mroz . reg lwage educ Source | SS df MS Number of obs = 428 -------------+------------------------------ F( 1, 426) = 56.93 Model | 26.3264237 1 26.3264237 Prob > F = 0.0000 Residual | 197.001028 426 .462443727 R-squared = 0.1179 -------------+------------------------------ Adj R-squared = 0.1158 Total | 223.327451 427 .523015108 Root MSE = .68003 ------------------------------------------------------------------------------ lwage | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- educ | .1086487 .0143998 7.55 0.000 .0803451 .1369523 _cons | -.1851969 .1852259 -1.00 0.318 -.5492674 .1788735 ------------------------------------------------------------------------------ . ivreg lwage (educ = fatheduc ), first First-stage regressions ----------------------- Source | SS df MS Number of obs = 428 -------------+------------------------------ F( 1, 426) = 88.84 Model | 384.841983 1 384.841983 Prob > F = 0.0000 Residual | 1845.35428 426 4.33181756 R-squared = 0.1726 -------------+------------------------------ Adj R-squared = 0.1706 Total | 2230.19626 427 5.22294206 Root MSE = 2.0813 ------------------------------------------------------------------------------ educ | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- fatheduc | .2694416 .0285863 9.43 0.000 .2132538 .3256295 _cons | 10.23705 .2759363 37.10 0.000 9.694685 10.77942 ------------------------------------------------------------------------------ Instrumental variables (2SLS) regression Source | SS df MS Number of obs = 428 -------------+------------------------------ F( 1, 426) = 2.84 Model | 20.8673618 1 20.8673618 Prob > F = 0.0929 Residual | 202.460089 426 .475258426 R-squared = 0.0934 -------------+------------------------------ Adj R-squared = 0.0913 Total | 223.327451 427 .523015108 Root MSE = .68939 ------------------------------------------------------------------------------ lwage | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- educ | .0591735 .0351418 1.68 0.093 -.0098994 .1282463 _cons | .4411035 .4461018 0.99 0.323 -.4357311 1.317938 ------------------------------------------------------------------------------ Instrumented: educ Instruments: fatheduc ------------------------------------------------------------------------------ ________________________________________ Example 15.2: Estimating the Return to Education for Men use http://fmwww.bc.edu/ec-p/data/wooldridge/wage2 . ivreg lwage (educ = sibs ), first First-stage regressions ----------------------- Source | SS df MS Number of obs = 935 -------------+------------------------------ F( 1, 933) = 56.67 Model | 258.055048 1 258.055048 Prob > F = 0.0000 Residual | 4248.7642 933 4.55387374 R-squared = 0.0573 -------------+------------------------------ Adj R-squared = 0.0562 Total | 4506.81925 934 4.82528828 Root MSE = 2.134 ------------------------------------------------------------------------------ educ | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- sibs | -.2279164 .0302768 -7.53 0.000 -.287335 -.1684979 _cons | 14.13879 .1131382 124.97 0.000 13.91676 14.36083 ------------------------------------------------------------------------------ Instrumental variables (2SLS) regression Source | SS df MS Number of obs = 935 -------------+------------------------------ F( 1, 933) = 21.59 Model | -1.5197389 1 -1.5197389 Prob > F = 0.0000 Residual | 167.176033 933 .179181172 R-squared = . -------------+------------------------------ Adj R-squared = . Total | 165.656294 934 .177362199 Root MSE = .4233 ------------------------------------------------------------------------------ lwage | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- educ | .1224327 .0263506 4.65 0.000 .0707194 .1741459 _cons | 5.130026 .3551712 14.44 0.000 4.432999 5.827053 ------------------------------------------------------------------------------ Instrumented: educ Instruments: sibs ------------------------------------------------------------------------------ . reg lwage educ Source | SS df MS Number of obs = 935 -------------+------------------------------ F( 1, 933) = 100.70 Model | 16.1377074 1 16.1377074 Prob > F = 0.0000 Residual | 149.518587 933 .16025572 R-squared = 0.0974 -------------+------------------------------ Adj R-squared = 0.0964 Total | 165.656294 934 .177362199 Root MSE = .40032 ------------------------------------------------------------------------------ lwage | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- educ | .0598392 .0059631 10.03 0.000 .0481366 .0715418 _cons | 5.973062 .0813737 73.40 0.000 5.813366 6.132759 ------------------------------------------------------------------------------ ________________________________________ Example 15.3: Estimating the Effect of Smoking on Birth Weight use http://fmwww.bc.edu/ec-p/data/wooldridge/bwght . ivreg lbwght (packs = cigprice ), first First-stage regressions ----------------------- Source | SS df MS Number of obs = 1388 -------------+------------------------------ F( 1, 1386) = 0.13 Model | .011648626 1 .011648626 Prob > F = 0.7179 Residual | 123.684481 1386 .089238442 R-squared = 0.0001 -------------+------------------------------ Adj R-squared = -0.0006 Total | 123.696129 1387 .089182501 Root MSE = .29873 ------------------------------------------------------------------------------ packs | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- cigprice | .0002829 .000783 0.36 0.718 -.0012531 .0018188 _cons | .0674257 .1025384 0.66 0.511 -.1337215 .2685728 ------------------------------------------------------------------------------ Instrumental variables (2SLS) regression Source | SS df MS Number of obs = 1388 -------------+------------------------------ F( 1, 1386) = 0.12 Model | -1171.28083 1 -1171.28083 Prob > F = 0.7312 Residual | 1221.70115 1386 .881458263 R-squared = . -------------+------------------------------ Adj R-squared = . Total | 50.4203246 1387 .036352073 Root MSE = .93886 ------------------------------------------------------------------------------ lbwght | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- packs | 2.988674 8.698884 0.34 0.731 -14.07573 20.05307 _cons | 4.448137 .9081547 4.90 0.000 2.66663 6.229643 ------------------------------------------------------------------------------ Instrumented: packs Instruments: cigprice ------------------------------------------------------------------------------ ________________________________________ Example 15.4: Using College Proximity as an IV for Education use http://fmwww.bc.edu/ec-p/data/wooldridge/card ivreg lwage (educ = nearc4 ) exper expersq black smsa south, first First-stage regressions ----------------------- Source | SS df MS Number of obs = 3010 -------------+------------------------------ F( 6, 3003) = 451.87 Model | 10230.4843 6 1705.08072 Prob > F = 0.0000 Residual | 11331.5958 3003 3.77342516 R-squared = 0.4745 -------------+------------------------------ Adj R-squared = 0.4734 Total | 21562.0801 3009 7.16586243 Root MSE = 1.9425 ------------------------------------------------------------------------------ educ | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- exper | -.4100081 .0336939 -12.17 0.000 -.4760735 -.3439427 expersq | .0007323 .0016499 0.44 0.657 -.0025029 .0039674 black | -1.006138 .0896454 -11.22 0.000 -1.181911 -.8303656 smsa | .4038769 .0848872 4.76 0.000 .2374339 .5703199 south | -.291464 .0792247 -3.68 0.000 -.4468042 -.1361238 nearc4 | .3373208 .0825004 4.09 0.000 .1755577 .4990839 _cons | 16.65917 .1763889 94.45 0.000 16.31332 17.00503 ------------------------------------------------------------------------------ Instrumental variables (2SLS) regression Source | SS df MS Number of obs = 3010 -------------+------------------------------ F( 6, 3003) = 120.83 Model | 133.463217 6 22.2438695 Prob > F = 0.0000 Residual | 459.178394 3003 .152906558 R-squared = 0.2252 -------------+------------------------------ Adj R-squared = 0.2237 Total | 592.641611 3009 .196956335 Root MSE = .39103 ------------------------------------------------------------------------------ lwage | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- educ | .1322888 .0492332 2.69 0.007 .0357545 .228823 exper | .107498 .0213006 5.05 0.000 .0657327 .1492632 expersq | -.0022841 .0003341 -6.84 0.000 -.0029392 -.0016289 black | -.130802 .0528723 -2.47 0.013 -.2344716 -.0271324 smsa | .1313237 .0301298 4.36 0.000 .0722465 .1904009 south | -.1049005 .0230731 -4.55 0.000 -.1501412 -.0596599 _cons | 3.752783 .8293408 4.53 0.000 2.126649 5.378916 ------------------------------------------------------------------------------ Instrumented: educ Instruments: exper expersq black smsa south nearc4 ------------------------------------------------------------------------------ reg lwage educ exper expersq black smsa south Source | SS df MS Number of obs = 3010 -------------+------------------------------ F( 6, 3003) = 204.93 Model | 172.165615 6 28.6942691 Prob > F = 0.0000 Residual | 420.475997 3003 .140018647 R-squared = 0.2905 -------------+------------------------------ Adj R-squared = 0.2891 Total | 592.641611 3009 .196956335 Root MSE = .37419 ------------------------------------------------------------------------------ lwage | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- educ | .074009 .0035054 21.11 0.000 .0671357 .0808823 exper | .0835958 .0066478 12.57 0.000 .0705612 .0966305 expersq | -.0022409 .0003178 -7.05 0.000 -.0028641 -.0016177 black | -.1896316 .0176266 -10.76 0.000 -.2241929 -.1550702 smsa | .161423 .0155733 10.37 0.000 .1308876 .1919583 south | -.1248615 .0151182 -8.26 0.000 -.1545046 -.0952184 _cons | 4.733664 .0676026 70.02 0.000 4.601112 4.866217 ------------------------------------------------------------------------------ ________________________________________ Example 15.5: Return to Education for Working Women use http://fmwww.bc.edu/ec-p/data/wooldridge/mroz . ivreg lwage (educ = motheduc fatheduc) exper expersq, first First-stage regressions ----------------------- Source | SS df MS Number of obs = 428 -------------+------------------------------ F( 4, 423) = 28.36 Model | 471.620998 4 117.90525 Prob > F = 0.0000 Residual | 1758.57526 423 4.15738833 R-squared = 0.2115 -------------+------------------------------ Adj R-squared = 0.2040 Total | 2230.19626 427 5.22294206 Root MSE = 2.039 ------------------------------------------------------------------------------ educ | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- exper | .0452254 .0402507 1.12 0.262 -.0338909 .1243417 expersq | -.0010091 .0012033 -0.84 0.402 -.0033744 .0013562 motheduc | .157597 .0358941 4.39 0.000 .087044 .2281501 fatheduc | .1895484 .0337565 5.62 0.000 .1231971 .2558997 _cons | 9.10264 .4265614 21.34 0.000 8.264196 9.941084 ------------------------------------------------------------------------------ Instrumental variables (2SLS) regression Source | SS df MS Number of obs = 428 -------------+------------------------------ F( 3, 424) = 8.14 Model | 30.3074295 3 10.1024765 Prob > F = 0.0000 Residual | 193.020022 424 .4552359 R-squared = 0.1357 -------------+------------------------------ Adj R-squared = 0.1296 Total | 223.327451 427 .523015108 Root MSE = .67471 ------------------------------------------------------------------------------ lwage | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- educ | .0613966 .0314367 1.95 0.051 -.0003945 .1231878 exper | .0441704 .0134325 3.29 0.001 .0177679 .0705729 expersq | -.000899 .0004017 -2.24 0.026 -.0016885 -.0001094 _cons | .0481003 .4003281 0.12 0.904 -.7387745 .8349751 ------------------------------------------------------------------------------ Instrumented: educ Instruments: exper expersq motheduc fatheduc ------------------------------------------------------------------------------ * test the relevance of the instruments . reg educ exper expersq motheduc fatheduc if wage!=. Source | SS df MS Number of obs = 428 -------------+------------------------------ F( 4, 423) = 28.36 Model | 471.620998 4 117.90525 Prob > F = 0.0000 Residual | 1758.57526 423 4.15738833 R-squared = 0.2115 -------------+------------------------------ Adj R-squared = 0.2040 Total | 2230.19626 427 5.22294206 Root MSE = 2.039 ------------------------------------------------------------------------------ educ | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- exper | .0452254 .0402507 1.12 0.262 -.0338909 .1243417 expersq | -.0010091 .0012033 -0.84 0.402 -.0033744 .0013562 motheduc | .157597 .0358941 4.39 0.000 .087044 .2281501 fatheduc | .1895484 .0337565 5.62 0.000 .1231971 .2558997 _cons | 9.10264 .4265614 21.34 0.000 8.264196 9.941084 ------------------------------------------------------------------------------ . test motheduc fatheduc ( 1) motheduc = 0 ( 2) fatheduc = 0 F( 2, 423) = 55.40 Prob > F = 0.0000 ________________________________________ Example 15.7: Return to Education for Working Women use http://fmwww.bc.edu/ec-p/data/wooldridge/mroz reg educ exper expersq motheduc fatheduc if lwage<. Source | SS df MS Number of obs = 428 -------------+------------------------------ F( 4, 423) = 28.36 Model | 471.620998 4 117.90525 Prob > F = 0.0000 Residual | 1758.57526 423 4.15738833 R-squared = 0.2115 -------------+------------------------------ Adj R-squared = 0.2040 Total | 2230.19626 427 5.22294206 Root MSE = 2.039 ------------------------------------------------------------------------------ educ | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- exper | .0452254 .0402507 1.12 0.262 -.0338909 .1243417 expersq | -.0010091 .0012033 -0.84 0.402 -.0033744 .0013562 motheduc | .157597 .0358941 4.39 0.000 .087044 .2281501 fatheduc | .1895484 .0337565 5.62 0.000 .1231971 .2558997 _cons | 9.10264 .4265614 21.34 0.000 8.264196 9.941084 ------------------------------------------------------------------------------ predict double uhat1, res reg lwage educ exper expersq uhat1 Source | SS df MS Number of obs = 428 -------------+------------------------------ F( 4, 423) = 20.50 Model | 36.2573159 4 9.06432898 Prob > F = 0.0000 Residual | 187.070135 423 .442246183 R-squared = 0.1624 -------------+------------------------------ Adj R-squared = 0.1544 Total | 223.327451 427 .523015108 Root MSE = .66502 ------------------------------------------------------------------------------ lwage | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- educ | .0613966 .0309849 1.98 0.048 .000493 .1223003 exper | .0441704 .0132394 3.34 0.001 .0181471 .0701937 expersq | -.000899 .0003959 -2.27 0.024 -.0016772 -.0001208 uhat1 | .0581666 .0348073 1.67 0.095 -.0102501 .1265834 _cons | .0481003 .3945753 0.12 0.903 -.7274721 .8236727 ------------------------------------------------------------------------------ reg lwage educ exper expersq Source | SS df MS Number of obs = 428 -------------+------------------------------ F( 3, 424) = 26.29 Model | 35.0223023 3 11.6741008 Prob > F = 0.0000 Residual | 188.305149 424 .444115917 R-squared = 0.1568 -------------+------------------------------ Adj R-squared = 0.1509 Total | 223.327451 427 .523015108 Root MSE = .66642 ------------------------------------------------------------------------------ lwage | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- educ | .1074896 .0141465 7.60 0.000 .0796837 .1352956 exper | .0415665 .0131752 3.15 0.002 .0156697 .0674633 expersq | -.0008112 .0003932 -2.06 0.040 -.0015841 -.0000382 _cons | -.5220407 .1986321 -2.63 0.009 -.9124668 -.1316145 ------------------------------------------------------------------------------ ivreg lwage (educ = motheduc fatheduc) exper expersq Instrumental variables (2SLS) regression Source | SS df MS Number of obs = 428 -------------+------------------------------ F( 3, 424) = 8.14 Model | 30.3074295 3 10.1024765 Prob > F = 0.0000 Residual | 193.020022 424 .4552359 R-squared = 0.1357 -------------+------------------------------ Adj R-squared = 0.1296 Total | 223.327451 427 .523015108 Root MSE = .67471 ------------------------------------------------------------------------------ lwage | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- educ | .0613966 .0314367 1.95 0.051 -.0003945 .1231878 exper | .0441704 .0134325 3.29 0.001 .0177679 .0705729 expersq | -.000899 .0004017 -2.24 0.026 -.0016885 -.0001094 _cons | .0481003 .4003281 0.12 0.904 -.7387744 .834975 ------------------------------------------------------------------------------ Instrumented: educ Instruments: exper expersq motheduc fatheduc ------------------------------------------------------------------------------ ________________________________________ Example 15.8: Return to Education for Working Women use http://fmwww.bc.edu/ec-p/data/wooldridge/mroz . ivreg lwage (educ = motheduc fatheduc) exper expersq Instrumental variables (2SLS) regression Source | SS df MS Number of obs = 428 -------------+------------------------------ F( 3, 424) = 8.14 Model | 30.3074295 3 10.1024765 Prob > F = 0.0000 Residual | 193.020022 424 .4552359 R-squared = 0.1357 -------------+------------------------------ Adj R-squared = 0.1296 Total | 223.327451 427 .523015108 Root MSE = .67471 ------------------------------------------------------------------------------ lwage | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- educ | .0613966 .0314367 1.95 0.051 -.0003945 .1231878 exper | .0441704 .0134325 3.29 0.001 .0177679 .0705729 expersq | -.000899 .0004017 -2.24 0.026 -.0016885 -.0001094 _cons | .0481003 .4003281 0.12 0.904 -.7387744 .834975 ------------------------------------------------------------------------------ Instrumented: educ Instruments: exper expersq motheduc fatheduc ------------------------------------------------------------------------------ ssc install overid, replace overid Test of overidentifying restrictions: .378071 Chi-sq( 1) P-value = .5386 . ivreg lwage (educ = motheduc fatheduc huseduc) exper expersq Instrumental variables (2SLS) regression Source | SS df MS Number of obs = 428 -------------+------------------------------ F( 3, 424) = 11.52 Model | 33.3927427 3 11.1309142 Prob > F = 0.0000 Residual | 189.934709 424 .447959218 R-squared = 0.1495 -------------+------------------------------ Adj R-squared = 0.1435 Total | 223.327451 427 .523015108 Root MSE = .6693 ------------------------------------------------------------------------------ lwage | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- educ | .0803918 .021774 3.69 0.000 .0375934 .1231901 exper | .0430973 .0132649 3.25 0.001 .0170242 .0691704 expersq | -.0008628 .0003962 -2.18 0.030 -.0016415 -.0000841 _cons | -.1868574 .2853959 -0.65 0.513 -.7478243 .3741096 ------------------------------------------------------------------------------ Instrumented: educ Instruments: exper expersq motheduc fatheduc huseduc ------------------------------------------------------------------------------ overid Test of overidentifying restrictions: 1.115043 Chi-sq( 2) P-value = .5726 ________________________________________ Example 15.9: Return of Education to Fertility * applying 2SLS to pooled cross sections use http://fmwww.bc.edu/ec-p/data/wooldridge/fertil1 ivreg kids (educ = meduc feduc) age agesq black east northcen west farm othrural town smcity y74 y76 y78 y80 y82 y84 Instrumental variables (2SLS) regression Source | SS df MS Number of obs = 1129 -------------+------------------------------ F( 17, 1111) = 7.72 Model | 395.36632 17 23.2568424 Prob > F = 0.0000 Residual | 2690.14298 1111 2.42137082 R-squared = 0.1281 -------------+------------------------------ Adj R-squared = 0.1148 Total | 3085.5093 1128 2.73538059 Root MSE = 1.5561 ------------------------------------------------------------------------------ kids | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- educ | -.1527395 .0392232 -3.89 0.000 -.2296993 -.0757796 age | .5235536 .1390348 3.77 0.000 .2507532 .796354 agesq | -.005716 .0015705 -3.64 0.000 -.0087976 -.0026345 black | 1.072952 .1737155 6.18 0.000 .732105 1.4138 east | .2285554 .1338537 1.71 0.088 -.0340792 .49119 northcen | .3744188 .122061 3.07 0.002 .1349228 .6139148 west | .2076398 .1676568 1.24 0.216 -.1213199 .5365995 farm | -.0770015 .1513718 -0.51 0.611 -.3740083 .2200052 othrural | -.1952451 .181551 -1.08 0.282 -.5514666 .1609764 town | .08181 .1246821 0.66 0.512 -.162829 .3264489 smcity | .2124996 .160425 1.32 0.186 -.1022706 .5272698 y74 | .2721292 .172944 1.57 0.116 -.0672045 .6114629 y76 | -.0945483 .1792324 -0.53 0.598 -.4462205 .2571239 y78 | -.0572543 .1825536 -0.31 0.754 -.415443 .3009343 y80 | -.053248 .1847175 -0.29 0.773 -.4156825 .3091865 y82 | -.4962149 .1765888 -2.81 0.005 -.8427 -.1497298 y84 | -.5213604 .1779205 -2.93 0.003 -.8704586 -.1722623 _cons | -7.241244 3.136642 -2.31 0.021 -13.39565 -1.086834 ------------------------------------------------------------------------------ Instrumented: educ Instruments: age agesq black east northcen west farm othrural town smcity y74 y76 y78 y80 y82 y84 meduc feduc ------------------------------------------------------------------------------ reg kids educ age agesq black east northcen west farm othrural town smcity y74 y76 y78 y80 y82 y84 Source | SS df MS Number of obs = 1129 -------------+------------------------------ F( 17, 1111) = 9.72 Model | 399.610888 17 23.5065228 Prob > F = 0.0000 Residual | 2685.89841 1111 2.41755033 R-squared = 0.1295 -------------+------------------------------ Adj R-squared = 0.1162 Total | 3085.5093 1128 2.73538059 Root MSE = 1.5548 ------------------------------------------------------------------------------ kids | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- educ | -.1284268 .0183486 -7.00 0.000 -.1644286 -.092425 age | .5321346 .1383863 3.85 0.000 .2606065 .8036626 agesq | -.005804 .0015643 -3.71 0.000 -.0088733 -.0027347 black | 1.075658 .1735356 6.20 0.000 .7351631 1.416152 east | .217324 .1327878 1.64 0.102 -.0432192 .4778672 northcen | .363114 .1208969 3.00 0.003 .125902 .6003261 west | .1976032 .1669134 1.18 0.237 -.1298978 .5251041 farm | -.0525575 .14719 -0.36 0.721 -.3413592 .2362443 othrural | -.1628537 .175442 -0.93 0.353 -.5070887 .1813814 town | .0843532 .124531 0.68 0.498 -.1599893 .3286957 smcity | .2118791 .160296 1.32 0.187 -.1026379 .5263961 y74 | .2681825 .172716 1.55 0.121 -.0707039 .6070689 y76 | -.0973795 .1790456 -0.54 0.587 -.448685 .2539261 y78 | -.0686665 .1816837 -0.38 0.706 -.4251483 .2878154 y80 | -.0713053 .1827707 -0.39 0.697 -.42992 .2873093 y82 | -.5224842 .1724361 -3.03 0.003 -.8608214 -.184147 y84 | -.5451661 .1745162 -3.12 0.002 -.8875846 -.2027477 _cons | -7.742457 3.051767 -2.54 0.011 -13.73033 -1.754579 ------------------------------------------------------------------------------ reg educ meduc feduc age agesq black east northcen west farm othrural town smcity y74 y76 y78 y80 y82 y84 Source | SS df MS Number of obs = 1129 -------------+------------------------------ F( 18, 1110) = 24.82 Model | 2256.26171 18 125.347873 Prob > F = 0.0000 Residual | 5606.85432 1110 5.05122011 R-squared = 0.2869 -------------+------------------------------ Adj R-squared = 0.2754 Total | 7863.11603 1128 6.97084755 Root MSE = 2.2475 ------------------------------------------------------------------------------ educ | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- meduc | .1723015 .0221964 7.76 0.000 .1287499 .2158531 feduc | .2074188 .0254604 8.15 0.000 .1574629 .2573747 age | -.2243687 .2000013 -1.12 0.262 -.616792 .1680546 agesq | .0025664 .0022605 1.14 0.256 -.001869 .0070018 black | .3667819 .2522869 1.45 0.146 -.1282311 .861795 east | .2488042 .1920135 1.30 0.195 -.1279462 .6255546 northcen | .0913945 .1757744 0.52 0.603 -.2534931 .4362821 west | .1010676 .2422408 0.42 0.677 -.3742339 .5763691 farm | -.3792615 .2143864 -1.77 0.077 -.7999099 .0413869 othrural | -.560814 .2551196 -2.20 0.028 -1.061385 -.060243 town | .0616337 .1807832 0.34 0.733 -.2930816 .416349 smcity | .0806634 .2317387 0.35 0.728 -.3740319 .5353587 y74 | .0060993 .249827 0.02 0.981 -.4840872 .4962858 y76 | .1239104 .2587922 0.48 0.632 -.3838667 .6316874 y78 | .2077861 .2627738 0.79 0.429 -.3078033 .7233755 y80 | .3828911 .2642433 1.45 0.148 -.1355816 .9013638 y82 | .5820401 .2492372 2.34 0.020 .0930108 1.071069 y84 | .4250429 .2529006 1.68 0.093 -.0711741 .92126 _cons | 13.63334 4.396773 3.10 0.002 5.006421 22.26027 ------------------------------------------------------------------------------ predict v, res reg kids educ age agesq black east northcen west farm othrural town smcity y74 y76 y78 y80 y82 y84 v Source | SS df MS Number of obs = 1129 -------------+------------------------------ F( 18, 1110) = 9.21 Model | 400.802376 18 22.2667987 Prob > F = 0.0000 Residual | 2684.70692 1110 2.41865489 R-squared = 0.1299 -------------+------------------------------ Adj R-squared = 0.1158 Total | 3085.5093 1128 2.73538059 Root MSE = 1.5552 ------------------------------------------------------------------------------ kids | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- educ | -.1527395 .0392012 -3.90 0.000 -.2296562 -.0758227 age | .5235536 .1389568 3.77 0.000 .250906 .7962012 agesq | -.005716 .0015697 -3.64 0.000 -.0087959 -.0026362 black | 1.072952 .173618 6.18 0.000 .7322958 1.413609 east | .2285554 .1337787 1.71 0.088 -.0339321 .491043 northcen | .3744188 .1219925 3.07 0.002 .1350569 .6137807 west | .2076398 .1675628 1.24 0.216 -.1211357 .5364153 farm | -.0770015 .1512869 -0.51 0.611 -.373842 .2198389 othrural | -.1952451 .1814491 -1.08 0.282 -.5512671 .1607769 town | .08181 .1246122 0.66 0.512 -.162692 .3263119 smcity | .2124996 .160335 1.33 0.185 -.1020943 .5270935 y74 | .2721292 .172847 1.57 0.116 -.0670144 .6112729 y76 | -.0945483 .1791319 -0.53 0.598 -.4460236 .2569269 y78 | -.0572543 .1824512 -0.31 0.754 -.4152424 .3007337 y80 | -.053248 .1846139 -0.29 0.773 -.4154795 .3089836 y82 | -.4962149 .1764897 -2.81 0.005 -.842506 -.1499238 y84 | -.5213604 .1778207 -2.93 0.003 -.8702631 -.1724578 v | .0311374 .0443634 0.70 0.483 -.0559081 .1181829 _cons | -7.241244 3.134883 -2.31 0.021 -13.39221 -1.09028 ------------------------------------------------------------------------------ ________________________________________ Example 15.10: Job Training and Worker Productivity * applying 2SLS to panel data use http://fmwww.bc.edu/ec-p/data/wooldridge/jtrain tsset fcode year sort fcode year drop if year==1989 . ivreg D.lscrap (D.hrsemp = D.grant) Instrumental variables (2SLS) regression Source | SS df MS Number of obs = 45 -------------+------------------------------ F( 1, 43) = 3.20 Model | .274952567 1 .274952567 Prob > F = 0.0808 Residual | 17.0148863 43 .39569503 R-squared = 0.0159 -------------+------------------------------ Adj R-squared = -0.0070 Total | 17.2898389 44 .392950883 Root MSE = .62904 ------------------------------------------------------------------------------ D.lscrap | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- hrsemp | D1 | -.0141532 .0079147 -1.79 0.081 -.0301148 .0018084 _cons | -.0326684 .1269512 -0.26 0.798 -.2886898 .223353 ------------------------------------------------------------------------------ Instrumented: D.hrsemp Instruments: D.grant ------------------------------------------------------------------------------ . reg D.lscrap D.hrsemp Source | SS df MS Number of obs = 45 -------------+------------------------------ F( 1, 43) = 2.84 Model | 1.07071319 1 1.07071319 Prob > F = 0.0993 Residual | 16.2191257 43 .377188969 R-squared = 0.0619 -------------+------------------------------ Adj R-squared = 0.0401 Total | 17.2898389 44 .392950883 Root MSE = .61416 ------------------------------------------------------------------------------ D.lscrap | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- hrsemp | D1 | -.0076007 .0045112 -1.68 0.099 -.0166984 .0014971 _cons | -.1035161 .103736 -1.00 0.324 -.3127197 .1056875 ------------------------------------------------------------------------------