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 that is equal to 1 for females and 0 for males. A regression of the logarithm of earnings on Female yields: ln(Earnings) = 6.48 - 0.44 Female, SER = 2.65 (0.01) (0.05) The estimated coefficient on Female is -0.44 and the SER is 265. Explain what these values mean. Does this regression suggest that female top executives earn less than top male executives and 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 million of dollars) and stock return (a measure of firm performance, in percentage points), are added to the regression: ln(Earnings) = 3.86 - 0.28 Female + 0.37ln(MarketValue) + 0.004 Return, (0.03) (0.04) (0.004) (0.003) n = 46,670, R2 hat = 0.345. The coefficient on ln(MarketValue) is 0.37. Explain what this value means. 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.
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 that is equal to 1 for females and 0 for males. A regression of the logarithm of earnings on Female yields:
ln(Earnings) = 6.48 - 0.44 Female, SER = 2.65
(0.01) (0.05)
The estimated coefficient on Female is -0.44 and the SER is 265. Explain what these values mean. Does this regression suggest that female top executives earn less than top male executives and 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 million of dollars) and stock return (a measure of firm performance, in percentage points), are added to the regression:
ln(Earnings) = 3.86 - 0.28 Female + 0.37ln(MarketValue) + 0.004 Return,
(0.03) (0.04) (0.004) (0.003)
n = 46,670, R2 hat = 0.345.
The coefficient on ln(MarketValue) is 0.37. Explain what this value means. 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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