Consider the causal effect of a policy Di ∈ {0, 1} on an outcome of interest Yi . For each unit i in the population, the potential outcomes are given by Yi(0) and Yi(1). Let ∆ be the difference in expected observed outcomes between treated and untreated units, ∆ = E[Yi |Di = 1]−E[Yi |Di = 0], and define the average treatment effect on the untreated, AT U, as AT U = E[Yi(1) − Yi(0)|Di = 0]. (a) (8 points) Show that the difference in means ∆ can be written as ∆ = AT U + B, where B is 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