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

Question:

This problem is inspired by a study of the "gender gap" in earnings in top corporate jobs [Bertrand and Hallock (2001)]. 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 onto Female yields

i. The estimated coefficient on Female is -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 gender 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:

This problem is inspired by a study of the

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 to have female top executives than small firms? Explain.