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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 compensat 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 the executives.) 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 In(Earnings) = 6 42 -0 45Female, SER=2 87 (0.01) (0.05)

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 compensat 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 the executives.) 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 In(Earnings) = 6 42 -0 45Female, SER=2 87 (0.01) (0.05)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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.) 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 In(Earnings) = 6.42 -0 45Female, SER=2.87 (0 01) (0.05) Calculate the average hourly earnings for top male and female executives. The hourly earnings for top male executives is $ per hour. (Round your response to two decimal places.) The hourly earnings for top female executives is $per hour. (Round your response to two decimal places) What is the estimated average difference between earnings of top male executives and top female executives? The estimated average difference between earnings of top male executives and top female executives is $ per hour. (Round your response to two decimal places.) What is the estimator of the standard deviation of the regression error? The estimator of the standard deviation of the regression error is (Round your response to two decimal places) Calculate the t-statistic for Female The t-statistic for Female is (Round your response to two decimal places.) Looking at the t-statistic, does this regression suggest that female top executives earn less than top male executives? O A. No. O B. Yes. Does this imply that there is gender discrimination? O A. No. O B. Yes. 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 - 0.28Female +0.37In(MarketValue) + 0.004Return, (0.03) (0.04) (0.004) (0.003)
Transcribed Image Text: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.) 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 In(Earnings) = 6.42 -0 45Female, SER=2.87 (0 01) (0.05) Calculate the average hourly earnings for top male and female executives. The hourly earnings for top male executives is $ per hour. (Round your response to two decimal places.) The hourly earnings for top female executives is $per hour. (Round your response to two decimal places) What is the estimated average difference between earnings of top male executives and top female executives? The estimated average difference between earnings of top male executives and top female executives is $ per hour. (Round your response to two decimal places.) What is the estimator of the standard deviation of the regression error? The estimator of the standard deviation of the regression error is (Round your response to two decimal places) Calculate the t-statistic for Female The t-statistic for Female is (Round your response to two decimal places.) Looking at the t-statistic, does this regression suggest that female top executives earn less than top male executives? O A. No. O B. Yes. Does this imply that there is gender discrimination? O A. No. O B. Yes. 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 - 0.28Female +0.37In(MarketValue) + 0.004Return, (0.03) (0.04) (0.004) (0.003)
Does this imply that there is gender discrimination? O A. No. O B. Yes. 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 - 0.28Female +0.37In(MarketValue) +0.004Return, (0.003) (0.03) (0.04) (0.004) he n= 46,670, R = 0.345 If MarketValue increases by 3.68%, what is the increase in earnings? ot If MarketValue increases by 3.68%, earnings increase by (Round your response to two decimal places.) The coefficient on Female is now - 0.28. Why has it changed from the first regression? O A. The first regression suffered from omitted variable bias. O B. Female is correlated with the two new included variables OC. MarketValue is important for explaining In(Eamings). O D. All of the above. Assume that the coefficient estimated in the second regression is correct. Forget about the effect of the Return variable, whose effect seems small and statistically insignificant. Calculate the correlation between Female and In(MarketValue) using the omitted variable bias equation. 47 ot Let X = Female, u = MarketValue, and = 0.46. The correlation between Female and In(MarketValue), pxu, is (Round your response to three decimal places.) Are large firms more likely to have female top executives than small firms? O A. There is no relationship between the genders, O B. No O C. Yes
Transcribed Image Text:Does this imply that there is gender discrimination? O A. No. O B. Yes. 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 - 0.28Female +0.37In(MarketValue) +0.004Return, (0.003) (0.03) (0.04) (0.004) he n= 46,670, R = 0.345 If MarketValue increases by 3.68%, what is the increase in earnings? ot If MarketValue increases by 3.68%, earnings increase by (Round your response to two decimal places.) The coefficient on Female is now - 0.28. Why has it changed from the first regression? O A. The first regression suffered from omitted variable bias. O B. Female is correlated with the two new included variables OC. MarketValue is important for explaining In(Eamings). O D. All of the above. Assume that the coefficient estimated in the second regression is correct. Forget about the effect of the Return variable, whose effect seems small and statistically insignificant. Calculate the correlation between Female and In(MarketValue) using the omitted variable bias equation. 47 ot Let X = Female, u = MarketValue, and = 0.46. The correlation between Female and In(MarketValue), pxu, is (Round your response to three decimal places.) Are large firms more likely to have female top executives than small firms? O A. There is no relationship between the genders, O B. No O C. Yes
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