Question 1 Consider the following Impossible Data Set. In this data set, the population is divided into 4 subgroups. All agents inside each subgroup are identical. The goal of each agent is to maximize their lifetime income by choosing whether to get a degree or not. The cost of the degree is $500,000. Proportion of the Population 0.4 0.3 0.2 0.1 Lifetime Income without a Degree Lifetime Income with a Degree $1,200,000.00 $1,600,000.00 $1,800,000.00 $2,500,000.00 $1,000,000.00 $1,000,000.00 $1,400,000.00 $1,500,000.00 a) Construct the Real-World Data Set (ie, Construct the data set that shows the lifetime income of each agent if they were allowed to self-select). 10 points. b) Calculate the ATE in each data set and explain why their values are different. 5 points. c) Calculate the size of the selection bias when the agents can self-select into taking a degree or not. (hint: ATE = ETT + Selection Bias). 5 points. d) What is the objective of Random Treatment Assignment? 5 points.