Problem Two. Consider the synthetic dataset NoncomplianceExample.xlsx. You can load this data into Stata for this problem set or work directly in Excel. We will be exploring potential outcomes and different treatment effects estimators for this problem. We are going to assume that the dataset we are looking at is the entire population. a) For each i compute the actual outcome Y; using the potential outcomes Y, Yoi and the treatment dummy Di b) Find the true, population-wide average treatment effect: E[Yi - Yoi] c) Find the average treatment effect on the treated: E[Y Yoi|D = 1] d) Classify each experimental participant into a Complier or Noncomplier (here it is a mix of always-takers and never-takers). Find the average treatment effect for compliers. e) Compute the "nave average treatment effect" where you would compare the average of those treated to those not treated, ignoring the effects of noncompliance. In other words, compute E [Y|Di = 1] E[Y|Di = 0] f) Regress Y on Dr. How does the coefficient estimate compare to what you found in part d) above? g) Let Z; be a dummy variable that records random assignment, where Z; = 1 means individual i is assigned to the treatment group and Z = 0 means i is assigned to the control group. Compute the compliance rate for people assigned to treatment, which is the fraction of individuals assigned to the treatment group who indeed get treated. How does this relate to the conditional expectation E[D;|Z = 1]? h) Compute the ITT: E[YIZ, 1]-E[YIZ = 0] i) Regress Yi on D. How does the coefficient estimate compare to what you found in part g) above? j) Now regress D on Zi. How does this regression relate to what you found in part f) above? k) Use the regression from part i) to compute the predicted values Di. I) Now regress Y on D. Look at the 95% confidence interval for this coefficient. Does this contain what you found for part d) above?