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 (1) log earnings Bo +3 female + 3mkt_value + Bareturn + u 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) female I-0.44 (0.05) mkt_value return Constant R R Fstat Obs. (2) -0.28 (0.04) 0.37 (0.004) 0.004 (0.003) 3.86 6.48 (0.01) (0.03) 0.101 0.145 4670 4670 Std errors in parentheses, stat significance 1%, N 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 32 and 3, 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 time he that is rise to the actimate in column Loft 1