Consider the causal effect of a policy Di E {0,1} on an outcome of interest Y. For each unit i in the population, the potential outcomes are given by Y;(0) and Yi(1). Let A be the difference in expected observed outcomes between treated and untreated units, A=E[Y\D; = 1] - E[Y|D; = 0], and define the average treatment effect on the untreated, ATU, as ATU = E[Y(1) Y7(0)|D; = 0). = ATU + B, where B is a (a) (8 points) Show that the difference in means A can be written as A selection bias term that you need to find. Show your steps. (b) (3 points) Suppose you have a random sample from the population for which you observe Yi and Di. Are you able to estimate the selection bias B that you found in (a) based on this sample? If your answer is yes, propose an estimator for B. If your answer is no, explain why. Consider the causal effect of a policy Di E {0,1} on an outcome of interest Y. For each unit i in the population, the potential outcomes are given by Y;(0) and Yi(1). Let A be the difference in expected observed outcomes between treated and untreated units, A=E[Y\D; = 1] - E[Y|D; = 0], and define the average treatment effect on the untreated, ATU, as ATU = E[Y(1) Y7(0)|D; = 0). = ATU + B, where B is a (a) (8 points) Show that the difference in means A can be written as A selection bias term that you need to find. Show your steps. (b) (3 points) Suppose you have a random sample from the population for which you observe Yi and Di. Are you able to estimate the selection bias B that you found in (a) based on this sample? If your answer is yes, propose an estimator for B. If your answer is no, explain why