Consider the following Impossible Data Set. Assume that the cost of the degree is $900,000, the objective of people is to maximize their lifetime income, and the population size is large.

e. Compute the sampling distribution of the estimator for ATE when agents can self-select into taking a degree. f. Compute the sampling distribution of the estimator for ETT when degrees are randomly assigned. g. Construct a linear model that characterizes the relationship between having a degree and lifetime income when degrees are randomly assigned (i.e., calibrate the parameters in the model y=0 +1x+ such that it accounts for the averages in the Impossible Data Set, where the exogenous variable is having a degree and the endogenous variable is lifetime income). h. Construct a linear model that characterizes the relationship between having a degree and lifetime income when agents can self-select into taking a degree.

% of Population 10 30 Lifetime Income w/Degree $3,500,000 $4,000,000 $4,500,000 $5,000,000 $5,500,000 Lifetime Income w/o Degree $3,100,000 $3,200,000 $3,300,000 $3,400,000 $3,500,000 20 15 25