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Homework 3: Answer Key Econometrics: ECO 721 Fall 2009 1 . The baseline regression: . use cps_subset.dta, clear . gen lnwage = ln(wage) . gen age2 = age*age . gen immXadvdgree = immigrant*advdgree . . *** baseline and unrestricted regression *** . regress lnwage female black hispanic immigrant age age2 advdgree /// > immXadvdgree Source | SS df MS Number of obs = 16652 -------------+------------------------------ F( 8, 16643) = 581.86 Model | 1048.27821 8 131.034776 Prob > F = 0.0000 Residual | 3748.02959 16643 .225201562 R-squared = 0.2186 -------------+------------------------------ Adj R-squared = 0.2182 Total | 4796.3078 16651 .288049234 Root MSE = .47455 ------------------------------------------------------------------------------ lnwage | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- female | -.2155466 .0073986 -29.13 0.000 -.2300487 -.2010444 black | -.1542623 .0111612 -13.82 0.000 -.1761394 -.1323851 hispanic | -.2430557 .0157904 -15.39 0.000 -.2740065 -.2121049 immigrant | -.095411 .0134239 -7.11 0.000 -.1217232 -.0690988 age | .0632326 .0023583 26.81 0.000 .0586102 .0678551 age2 | -.0006733 .000029 -23.25 0.000 -.0007301 -.0006166 advdgree | .4415743 .0131133 33.67 0.000 .4158709 .4672777 immXadvdgree | .0851195 .0352153 2.42 0.016 .0160938 .1541452 _cons | 1.433662 .0461975 31.03 0.000 1.34311 1.524214 ------------------------------------------------------------------------------ a . Test the hypothesis that 1 = & 0 : 2 . What do you conclude? t = & 0 : 216 + 0 : 2 0 : 007 = 2 : 28 Reject the null. b . Interpret the e/ect of female on wages. All else equal, women earn 21% less than men 1

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c. Interpret the e/ect of immigrant status on wages. Immigrants without advanced degrees earn 9.5% less than men, all else equal. But immi- grants with advanced degrees earn only 1% less than similar non-immigrants. d . Interpret the e/ect of age on wages. Age has a quadratic e/ect on wages with an inverted-U shape. Wages are maximized when a person is 47 years old. e. How would you test the hypothesis that black and hispanic have equal e/ects on wages . Write the restricted regression, the test statistic along with numerator and denominator degrees of freedom. . gen blplushis = black + hispanic . regress lnwage female blplushis immigrant age age2 advdgree /// > immXadvdgree Source | SS df MS Number of obs = 16652 -------------+------------------------------ F( 7, 16644) = 660.74 Model | 1042.99842 7 148.999775 Prob > F = 0.0000 Residual | 3753.30938 16644 .22550525 R-squared = 0.2175 -------------+------------------------------ Adj R-squared = 0.2171 Total | 4796.3078 16651 .288049234 Root MSE = .47487 ------------------------------------------------------------------------------ lnwage | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- female | -.2134442 .0073909 -28.88 0.000 -.2279311 -.1989573 blplushis | -.182188 .009562 -19.05 0.000
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