Long Question [50 points] There has been much debate about the intergenerational mobility in the US. You decide to study the question by running a regression of incomei=0+1incomeparenti+i where incomeparent is the average income of the parents of an individual i in real terms (i.e., adjusted for inflation) when the individual was young (before 20 years old), and income in i in the income of the individual. a. [10 points] How would you test that the hypothesis that there is intergenerational mobility? Write the test formally. b. [10 points] Your first regression results in the following output (you standardized all the coefficients): incomeiR2=(0.56)2+(0.23)0.6incomeparenti=0.6 Sketch the regression line and add a 45 line starting from the origin point to the graph. Interpret the regression results in line of the mobility debate. What would the interpretation be if the fitted line coincided with the 45 line? c. [10 points] Test the hypothesis defined in 1 (no mobility hypothesis) at 5% and 1%. [Write the test formally, the test statistics, define the rule, and conclude.] d. [10 points] Suppose you believe mobility will be different for men and women in the sample and run a multivariate regression model: incomei=(0.62)2.3+(0.45)0.8incomeparenti+(0.11)0.2incomeparentiFemalei+ R2=0.68 where Female is a dummy equal to one if the individual is a woman. Write down the hypothesis that the effect for women is different that men. Sketch the two regression lines together with the 45 line and interpret the results again. e. [10 points] What else do you think might be missing? Explain your answer. Long Question [50 points] There has been much debate about the intergenerational mobility in the US. You decide to study the question by running a regression of incomei=0+1incomeparenti+i where incomeparent is the average income of the parents of an individual i in real terms (i.e., adjusted for inflation) when the individual was young (before 20 years old), and income in i in the income of the individual. a. [10 points] How would you test that the hypothesis that there is intergenerational mobility? Write the test formally. b. [10 points] Your first regression results in the following output (you standardized all the coefficients): incomeiR2=(0.56)2+(0.23)0.6incomeparenti=0.6 Sketch the regression line and add a 45 line starting from the origin point to the graph. Interpret the regression results in line of the mobility debate. What would the interpretation be if the fitted line coincided with the 45 line? c. [10 points] Test the hypothesis defined in 1 (no mobility hypothesis) at 5% and 1%. [Write the test formally, the test statistics, define the rule, and conclude.] d. [10 points] Suppose you believe mobility will be different for men and women in the sample and run a multivariate regression model: incomei=(0.62)2.3+(0.45)0.8incomeparenti+(0.11)0.2incomeparentiFemalei+ R2=0.68 where Female is a dummy equal to one if the individual is a woman. Write down the hypothesis that the effect for women is different that men. Sketch the two regression lines together with the 45 line and interpret the results again. e. [10 points] What else do you think might be missing? Explain your