1. (20 points) A study compares the total earnings among top executive officers across genders in the U.S. for 4670 corporations during the 1990's where each corporation reports each year the total earnings of their top 5 executive officers. Consider a population multiple linear regression model to study potential discrimination against women log earnings = Bo+By female+Bomkt_value + B3return +u (1) where dependent variable is logarithm of labor earnings, female is a binary variable that takes value one if top executive is a female, zero otherwise, mkt_value is the market value of the company (a measure of the size of the company in millions of U.S. dollars) in which the individual is a top executive and return is performance measured in percentages of the return of the stock of the company. The table below reports two regressions Dep. Vble: log earnings (1) (2) female -0.44 -0.28 (0.05) (0.04) mkt_value 0.37 (0.004) return 0.004 (0.003) Constant 6.48 3.86 (0.01) (0.03) R 0.101 0.145 R Fstat Obs. 4670 4670 Std. errors in parentheses, tat significance 15,5% Table 1 a. (2 points) Interpret the coefficient associated with female in the first column of table 1. b. (2 points)What assumption is required to interpret -0.44 in a causal way? Can there be omitted variable bias/inconsistency? Explain. c. (4 points) What signs would you expect for B, and B3 in the population model? What signs for the population correlation coefficients Corr (female, mkt_value) and Corr (female, return)? Give some eco- nomic reasons for your answers. Given these answers what is the expected bias and inconsistency of the OLS estimator by that gives rise to the estimate in column 1 of table 1. d. (4 points) Consider column 2 in table 1 and explain if what is found in that specification is consistent with the answers in part c) in terms of bias and inconsistency. e. (4 points) State the assumption of mean conditional independence for the multiple regression considered in equation (1). How does this assumption work in identifying a causal effect of discrimination? Explain using conditional expectations. 1 f. (4 points) Complete table 1 by finding , assigning asteriks to estimates that are statistically significant individually at 1% or 5% significance (use tstats for exclusion type of nulls) and determine the Fstat for joint significance of the control variables. Are the control variables in column 2 of table jointly significant at the 1%? Explain. 1. (20 points) A study compares the total earnings among top executive officers across genders in the U.S. for 4670 corporations during the 1990's where each corporation reports each year the total earnings of their top 5 executive officers. Consider a population multiple linear regression model to study potential discrimination against women log earnings = Bo+By female+Bomkt_value + B3return +u (1) where dependent variable is logarithm of labor earnings, female is a binary variable that takes value one if top executive is a female, zero otherwise, mkt_value is the market value of the company (a measure of the size of the company in millions of U.S. dollars) in which the individual is a top executive and return is performance measured in percentages of the return of the stock of the company. The table below reports two regressions Dep. Vble: log earnings (1) (2) female -0.44 -0.28 (0.05) (0.04) mkt_value 0.37 (0.004) return 0.004 (0.003) Constant 6.48 3.86 (0.01) (0.03) R 0.101 0.145 R Fstat Obs. 4670 4670 Std. errors in parentheses, tat significance 15,5% Table 1 a. (2 points) Interpret the coefficient associated with female in the first column of table 1. b. (2 points)What assumption is required to interpret -0.44 in a causal way? Can there be omitted variable bias/inconsistency? Explain. c. (4 points) What signs would you expect for B, and B3 in the population model? What signs for the population correlation coefficients Corr (female, mkt_value) and Corr (female, return)? Give some eco- nomic reasons for your answers. Given these answers what is the expected bias and inconsistency of the OLS estimator by that gives rise to the estimate in column 1 of table 1. d. (4 points) Consider column 2 in table 1 and explain if what is found in that specification is consistent with the answers in part c) in terms of bias and inconsistency. e. (4 points) State the assumption of mean conditional independence for the multiple regression considered in equation (1). How does this assumption work in identifying a causal effect of discrimination? Explain using conditional expectations. 1 f. (4 points) Complete table 1 by finding , assigning asteriks to estimates that are statistically significant individually at 1% or 5% significance (use tstats for exclusion type of nulls) and determine the Fstat for joint significance of the control variables. Are the control variables in column 2 of table jointly significant at the 1%? Explain
