Consider the following Impossible Data Set. lnthis data set= the population is divided into 4 subgroups. All agents inside each subgroup are identical. The goal ofeach agent is to maximize their lifetime income by choosing whether to get a degree ornot The cost ofthe degree is $500,000. Proportion ofie Population Lifetime Income without a Degree Lifetime Income with a Degree 0.4 $1 00,000 .00 $ | 30000000 0.3 5] 00,000 .00 $1,600,000.00 0.2 51.400.000.00 $1,800,000.00 0.] 51.500.000.00 $2.500,000.00 Constnict the RealWorld Data Set (1:, Construct the data set that shows the lifetime income of each agent ifthe}.r were allowed to self-select). Calculate the ATE in each data set and explain Why their values are different; Calculate the size ofthe selection bias Whenthe agents can self-select into taking a degIee or not. mg: ATE = ETT + Selection Bias). What is the objective of Random Treatment Assignment