Problem 1 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 a dummy variable that is equal to 1 for females and 0 for males. A regression on the logarithm of earnings onto Female yields In (Earnings) =6.48 - 0.44 Female, (0.01) (0.05) i The estimated coefficient on Female is equal to -0.44. Explain what this value means. ii Does this regression suggest that female executives earn less than male executives ? Ex- plain . iii 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 returns (a measure of firm performance , in percentage points ), are added to the regression . In(Earnings) =3.86 - 0.28Female + 0.37 In(MarketValue) + 0.004 Return, (0.03) (0.04) i The coefficient on In( MarketValue) is equal to 0.37. Explain what this value means. ii The coefficient on Female is now -0.28. Explain why it has changed compared to the regression in a). c) Are large firms more likely to have female top executives than small firms? Explain. Problem 2 Suppose that a researcher collects data on houses that have sold in a particular neighborhood over the past year and obtains the regression results in table 1 below. The dependent variable is In(Price), the log of the price of the house; size is the total size of the lot (in square feet ); Bedrooms gives the number of bedrooms in the house; Recreation indicated whether the house has a recreational room; Garage is an indicator for garage; Prefer is a dummy equal to 1 if the house is located in a preferred neighborhood , and 0 otherwise . a) Using the results in column (1), what is the expected change in price of building a 500-square- foot addition to a house? Construct a 95% confidence interval for the percentage change in price