F 1 515 152590 Model 69768312 1 69768312 Prob F 00000 Residual 235471791 515

# F 1 515 152590 model 69768312 1 69768312 prob f 00000

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F( 1, 515) = 1525.90 Model | 6976.8312 1 6976.8312 Prob > F = 0.0000 Residual | 2354.71791 515 4.57226779 R-squared = 0.7477 -------------+------------------------------ Adj R-squared = 0.7472 Total | 9331.54911 516 18.0843975 Root MSE = 2.1383 ------------------------------------------------------------------------------ wage | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- educ | 1.356374 .0347229 39.06 0.000 1.288158 1.42459 _cons | -1.036165 .52312 -1.98 0.048 -2.063876 -.008453 ------------------------------------------------------------------------------ One more option, which is less powerful, but yet very popular, is to simply run separate regressions for each sex. This yields the same lines as shown in the original graph, but cannot test for statistically significant differences by sex. And the Regression for Just Males 23 . regress wage educ if female==0; Source | SS df MS Number of obs = 483 -------------+------------------------------ F( 1, 481) = 1092.28 Model | 4587.09535 1 4587.09535 Prob > F = 0.0000 Residual | 2019.99161 481 4.19956676 R-squared = 0.6943 -------------+------------------------------ Adj R-squared = 0.6936 Total | 6607.08696 482 13.7076493 Root MSE = 2.0493 ------------------------------------------------------------------------------ wage | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- educ | 1.173098 .035495 33.05 0.000 1.103354 1.242843 _cons | 3.477994 .5284448 6.58 0.000 2.439648 4.516339 ------------------------------------------------------------------------------ “The log-on degree” The Economist , March 14, 2015 “A new report from PayScale, a research firm, calculates the returns to a college degree. Its authors compare the career earnings of graduates with the present-day cost of a degree at their alma maters, net of financial aid. College is usually worth it, but not always, it transpires. And what you study matters far more than where you study it.” (p. 30) “Engineers and computer scientists do best, earning an impressive 20-year annualised return of 12% on their college fees (the S&P 500 yielded just 7.8%). Engineering graduates from run-of-the-mill colleges do only slightly worse than those from highly selective ones.” (p. 30) 24
ECO220Y1Y, Lecture 22, Page 9 of 9 25 Model: 𝑅 ൌ 𝛽 ൅ 𝛽 𝑈 ൅ 𝛽 𝐴 ൅ 𝛽 𝐴 ∗ 𝑈 ൅ 𝜀 𝐸 : dummy = 1 if in engineering/cs/math program 𝐴 : dummy = 1 if in arts/humanities program 𝑅 : 20-year average annual return on degree (%) 𝑈 : university admission rate 2012-13 (%) Model: 𝑅 ൌ 𝛽 ൅ 𝛽 𝑈 ൅ 𝛽 𝐴 ൅ 𝛽 𝐴 ∗ 𝑈 ൅ 𝜀 26 slope = 𝛽 Engineering/ computer science/math Arts/ humanities slope = ሺ𝛽 ൅ 𝛽 𝐸 : dummy = 1 if in engineering/cs/math program 𝐴 : dummy = 1 if in arts/humanities program 𝛽 𝛽 ൅ 𝛽 𝛽 𝛽 measures the difference in the intercepts 𝛽 measures the difference in the slopes 50 𝑅 𝑈 0 100 0 20 െ15 Article cont’d… “Business and economics degrees also pay well, delivering a solid 8.7% average return. Courses in the arts or the humanities offer vast spiritual rewards, of course, but less impressive material ones. Some yield negative returns. An arts degree from the Maryland Institute College of Art had a hefty 20-year net negative return of \$92,000, for example.” (p. 30) Let 𝑅 be the 20-year average annual return on a degree (%) and 𝑈 the university admission rate, 2012-2013 (%), 𝐸 an indictor for Engineering/computer science/maths, and 𝐴 an indicator for Arts/humanities. Which model specification fits with the figure? Cool interactive chart: 27

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