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 + B female + B mkt_value + B;return + 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 4. (12 points) Consider the setup in question 1 for the definitions of the variables used there. A researcher that is interested in studying potential female labor discrimination postulates the following structural model that determines the level of education (educ) of a top executive of a corporation educ = 80 +81 female + dage +83 fincome + vi (2) where age is the age of the top executive, fincom is family husband or partner) income of the top executive, vi is the error term that represent unobservables. Suppose 81 0, 83 > 0 and 84 > 0. Moreover, logarithm of labor earnings (log earnings) for a top executive of a corporation is determined by log earnings = Yo + Veduc + y2corp_str + "zabil + u (3) where u denotes an error term, corp_str denotes the corporation structure of the company which entails the managerial efficiency and hiring practices of the corporation where top executives work and abil is innate ability of the top executive. Suppose 71 > 0,72 > 0 and 13 > 0. It is recognized that corp_str can be correlated with educ and ability and therefore the researcher proposes a proxy variable for it by assuming that it is determined in the following way corp_str = 00 + Gimtk_value + Opreturn + a3 female + 212 (4) such that 02 denotes an error term. Suppose au > 0,02 > 0 and a3 0, 83 > 0 and 84 > 0. Moreover, logarithm of labor earnings (log earnings) for a top executive of a corporation is determined by log earnings = Yo + Veduc + y2corp_str + "zabil + u (3) where u denotes an error term, corp_str denotes the corporation structure of the company which entails the managerial efficiency and hiring practices of the corporation where top executives work and abil is innate ability of the top executive. Suppose 71 > 0,72 > 0 and 13 > 0. It is recognized that corp_str can be correlated with educ and ability and therefore the researcher proposes a proxy variable for it by assuming that it is determined in the following way corp_str = 00 + Gimtk_value + Opreturn + a3 female + 212 (4) such that 02 denotes an error term. Suppose au > 0,02 > 0 and a3