EXERCISE 5.5 The Stata output shows the result of a semilogarithmic regression of earnings on highest educational qualification obtained, work experience,

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EXERCISE 5.5 The Stata output shows the result of a semilogarithmic regression of earnings on highest educational qualification obtained, work experience, and the sex of the respondent, the educational qualifications being a professional degree, a PhD, a Master’s degree, a Bachelor’s degree, an Associate of Arts degree, and no qualification (high school drop-out). The high school diploma was the reference category. Provide an interpretation of the coefficients and perform t tests. `1

EXERCISE 5.5 . reg LGEARN EDUCPROF EDUCMAST EDUCPHD EDUCBA EDUCAA EDUCDO EXP MALE Source | SS df MS Number of obs = 540 -------------+------------------------------ F( 8, 531) = 29.64 Model | 57.6389757 8 7.20487196 Prob > F = 0.0000 Residual | 129.068668 531 .243067171 R-squared = 0.3087 -------------+------------------------------ Adj R-squared = 0.2983 Total | 186.707643 539 .34639637 Root MSE = .49302 ------------------------------------------------------------------------------ LGEARN | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- EDUCPROF | 1.59193 .2498069 6.37 0.000 1.101199 2.082661 EDUCPHD | .3089521 .4943698 0.62 0.532 -.6622084 1.280113 EDUCMAST | .6280672 .0993222 6.32 0.000 .4329546 .8231798 EDUCBA | .5053643 .0561215 9.00 0.000 .3951168 .6156118 EDUCAA | .170838 .0765684 2.23 0.026 .0204238 .3212522 EDUCDO | -.2527803 .08179 -3.09 0.002 -.413452 -.0921085 EXP | .0230536 .0050845 4.53 0.000 .0130654 .0330419 MALE | .2755451 .0437642 6.30 0.000 .189573 .3615173 _cons | 2.125885 .0915997 23.21 0.000 1.945943 2.305828 The answer is given on the next slide. Remember that the dependent variable is the (natural) logarithm of hourly earnings. 2

EXERCISE 5.5 . reg LGEARN EDUCPROF EDUCMAST EDUCPHD EDUCBA EDUCAA EDUCDO EXP MALE Source | SS df MS Number of obs = 540 -------------+------------------------------ F( 8, 531) = 29.64 Model | 57.6389757 8 7.20487196 Prob > F = 0.0000 Residual | 129.068668 531 .243067171 R-squared = 0.3087 -------------+------------------------------ Adj R-squared = 0.2983 Total | 186.707643 539 .34639637 Root MSE = .49302 ------------------------------------------------------------------------------ LGEARN | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- EDUCPROF | 1.59193 .2498069 6.37 0.000 1.101199 2.082661 EDUCPHD | .3089521 .4943698 0.62 0.532 -.6622084 1.280113 EDUCMAST | .6280672 .0993222 6.32 0.000 .4329546 .8231798 EDUCBA | .5053643 .0561215 9.00 0.000 .3951168 .6156118 EDUCAA | .170838 .0765684 2.23 0.026 .0204238 .3212522 EDUCDO | -.2527803 .08179 -3.09 0.002 -.413452 -.0921085 EXP | .0230536 .0050845 4.53 0.000 .0130654 .0330419 MALE | .2755451 .0437642 6.30 0.000 .189573 .3615173 _cons | 2.125885 .0915997 23.21 0.000 1.945943 2.305828 The regression results indicate that those with professional degrees earn 159 percent more than high school graduates, or 391 percent more if calculated as 100(e1.592 – 1), the coefficient being significant at the 0.1 percent level. 3

EXERCISE 5.5 Professional 159.2 391.3 0.1% PhD 30.9 36.2 not sig. . reg LGEARN EDUCPROF EDUCMAST EDUCPHD EDUCBA EDUCAA EDUCDO EXP MALE Source | SS df MS Number of obs = 540 -------------+------------------------------ F( 8, 531) = 29.64 Model | 57.6389757 8 7.20487196 Prob > F = 0.0000 Residual | 129.068668 531 .243067171 R-squared = 0.3087 -------------+------------------------------ Adj R-squared = 0.2983 Total | 186.707643 539 .34639637 Root MSE = .49302 ------------------------------------------------------------------------------ LGEARN | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- EDUCPROF | 1.59193 .2498069 6.37 0.000 1.101199 2.082661 EDUCPHD | .3089521 .4943698 0.62 0.532 -.6622084 1.280113 EDUCMAST | .6280672 .0993222 6.32 0.000 .4329546 .8231798 EDUCBA | .5053643 .0561215 9.00 0.000 .3951168 .6156118 EDUCAA | .170838 .0765684 2.23 0.026 .0204238 .3212522 EDUCDO | -.2527803 .08179 -3.09 0.002 -.413452 -.0921085 EXP | .0230536 .0050845 4.53 0.000 .0130654 .0330419 MALE | .2755451 .0437642 6.30 0.000 .189573 .3615173 _cons | 2.125885 .0915997 23.21 0.000 1.945943 2.305828 Professional 159.2 391.3 0.1% PhD 30.9 36.2 not sig. Master’s 62.8 87.4 0.1% Bachelor’s 50.5 65.7 0.1% Associate’s 17.1 18.6 5% Drop-out –25.3 –22.4 1% The table gives the corresponding figures for all the educational qualifications. 4

EXERCISE 5.5 . reg LGEARN EDUCPROF EDUCMAST EDUCPHD EDUCBA EDUCAA EDUCDO EXP MALE Source | SS df MS Number of obs = 540 -------------+------------------------------ F( 8, 531) = 29.64 Model | 57.6389757 8 7.20487196 Prob > F = 0.0000 Residual | 129.068668 531 .243067171 R-squared = 0.3087 -------------+------------------------------ Adj R-squared = 0.2983 Total | 186.707643 539 .34639637 Root MSE = .49302 ------------------------------------------------------------------------------ LGEARN | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- EDUCPROF | 1.59193 .2498069 6.37 0.000 1.101199 2.082661 EDUCPHD | .3089521 .4943698 0.62 0.532 -.6622084 1.280113 EDUCMAST | .6280672 .0993222 6.32 0.000 .4329546 .8231798 EDUCBA | .5053643 .0561215 9.00 0.000 .3951168 .6156118 EDUCAA | .170838 .0765684 2.23 0.026 .0204238 .3212522 EDUCDO | -.2527803 .08179 -3.09 0.002 -.413452 -.0921085 EXP | .0230536 .0050845 4.53 0.000 .0130654 .0330419 MALE | .2755451 .0437642 6.30 0.000 .189573 .3615173 _cons | 2.125885 .0915997 23.21 0.000 1.945943 2.305828 Males earn 27.6 percent (31.8 percent) more than females, and every year of work experience increases earnings by 2.3 percent. 5

Professional n = 6 Associate’s n = 48 EXERCISE 5.5 . reg LGEARN EDUCPROF EDUCMAST EDUCPHD EDUCBA EDUCAA EDUCDO EXP MALE Source | SS df MS Number of obs = 540 -------------+------------------------------ F( 8, 531) = 29.64 Model | 57.6389757 8 7.20487196 Prob > F = 0.0000 Residual | 129.068668 531 .243067171 R-squared = 0.3087 -------------+------------------------------ Adj R-squared = 0.2983 Total | 186.707643 539 .34639637 Root MSE = .49302 ------------------------------------------------------------------------------ LGEARN | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- EDUCPROF | 1.59193 .2498069 6.37 0.000 1.101199 2.082661 EDUCPHD | .3089521 .4943698 0.62 0.532 -.6622084 1.280113 EDUCMAST | .6280672 .0993222 6.32 0.000 .4329546 .8231798 EDUCBA | .5053643 .0561215 9.00 0.000 .3951168 .6156118 EDUCAA | .170838 .0765684 2.23 0.026 .0204238 .3212522 EDUCDO | -.2527803 .08179 -3.09 0.002 -.413452 -.0921085 EXP | .0230536 .0050845 4.53 0.000 .0130654 .0330419 MALE | .2755451 .0437642 6.30 0.000 .189573 .3615173 _cons | 2.125885 .0915997 23.21 0.000 1.945943 2.305828 Professional n = 6 Associate’s n = 48 PhD n = 3 High school diploma n = 297 Master’s n = 31 High school drop-out n = 46 Bachelor’s n = 98 The coefficients of those with professional degrees and PhDs should be treated cautiously since there were only six individuals in the former category and three in the latter. For the other categories the numbers of observations were: masters 31; bachelor’s 98; associate’s 48; high school diploma (or GED) 297; and drop-out 46. 6

Copyright Christopher Dougherty 2000–2007 Copyright Christopher Dougherty 2000–2007. This slideshow may be freely copied for personal use. 16.11.07