1. Christopher Dougherty EC220 - Introduction to econometrics (chapter 5) Slideshow: exercise 5.5 Original citation: Dougherty, C. (2012) EC220 - Introduction to econometrics (chapter 5). [Teaching Resource] © 2012 The Author This version available at: http://learningresources.lse.ac.uk/131/http://learningresources.lse.ac.uk/131/ Available in LSE Learning Resources Online: May 2012 This work is licensed under a Creative Commons Attribution-ShareAlike 3.0 License. This license allows the user to remix, tweak, and build upon the work even for commercial purposes, as long as the user credits the author and licenses their new creations under the identical terms. http://creativecommons.org/licenses/by-sa/3.0/ http://creativecommons.org/licenses/by-sa/3.0/ http://learningresources.lse.ac.uk/

2. `1 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. EXERCISE 5.5

3. 2. 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. EXERCISE 5.5

4. 3. 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(e 1.592 – 1), the coefficient being significant at the 0.1 percent level. EXERCISE 5.5

5. 4. 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 table gives the corresponding figures for all the educational qualifications. EXERCISE 5.5 Professional159.2391.30.1% PhD30.936.2not sig. Master’s62.887.40.1% Bachelor’s50.565.70.1% Associate’s17.118.65% Drop-out–25.3–22.41%

6. 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. EXERCISE 5.5

7. 6. 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 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. EXERCISE 5.5 Professionaln = 6Associate’sn = 48 PhDn = 3High school diploman = 297 Master’sn = 31High school drop-outn = 46 Bachelor’sn = 98

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