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...

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
    "ln (Earnings)" = 6.48 - 0.44
Female, SER
= 2.65.
                     (0.01) (0.05)
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:
''ln(Earnings)" = 3.86 - 0.28 Female + 0.37ln(MarketValue) + 0.004
Return,
                 (0.03)    (0.04)                (0.004)                   (0.003)

                      n
= 46,670, (adjusted) R²= 0.345.
i. The coefficient on ln(MarketValue) 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.