Question

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.

Answer 1

Solving first 4 parts as per HOMEWORKLIB POLICY. Please post the rest separately. Thank you.

Ai

The given equation is

ln(earnings)=6.48-.44Female

What its saying is that the log of earnings decreases by 44% if you are a female. Or, in other words

ln(earnings+dearnings)-ln(earnings)=-.44female

where dearnings is change in earnings.

By approximation, we get

dearnings/earnings =-.44female

Meaning that being a female reduces your earnings by 44%.

Aii

SER is the standard deviation of the error term.

The error term is the variation in the data that happens because of factors other than gender. These may include job experience, education level etc. SER is the standard deviation of that error.

Aiii

As discussed in part A, this finding indeed does suggest that, assuming all other factors were held constant, female top executives earn less than male top executives.

Aiv

If all other factors are held constant (such as education level, experience etc), then there is gender discrimination. If other factors were not held constant, then nothing conclusive can be said.