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# This problem is inspired by a study of the gender gap in earnings in top corporate...

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This problem is inspired by a study of the gender gap in earnings in top corporate jobs. The study compares total compensation among top executives in a large set of U.S. public corporations in the 1990s. (Each year these publicly traded corporations must report total compensation levels for their top five executives.) a. Let Female be an indicator variable that is equal to 1 for females and 0 for males. A regression of the logarithm of earnings on Female yields In(Earnings) = 6.48 -0.44Female; SER = 2.65 (0.01) (0.05) i The estimated coefficient on Femaleis -0.44-0.44. Explain what this value means. ii. The SER is 2.65. Explain what this value means. iii. Does this regression suggest that female top executives earn less than top male executives? Explain. iv. Does this regression suggest that there is sex discrimination? Explain. b. Two new variables, the market value of the firm (a measure of firm size, in millions of dollars) and stock return (a measure of firm performance, in percentage points), are added to the regression: In(Earnings) = 3.86 -0.28 Female + 0.37 ln(Market Value) + 0.0004 Return; (0.03) (0.04) (0.004) (0.003) R2 = 0.345, n = 46,670 i. The coefficient on In(Market Value) is 0.37. Explain what this value means. ii. The coefficient on Female is now -0.28. Explain why it has changed from the regression in (a). C. Are large firms more likely than small firms to have female top executives? Explain.

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