Introduction to Econometrics 3rd Edition by James Stock, Mark Watson

تمرين 9

The discussion following Equation (8.28) interprets the coefficient on interacted binary variables using the conditional mean zero assumption. This exercise shows that interpretation also applies under conditional mean independence. Consider the hypothetical experiment in Exercise 7.11.
a. Suppose that you estimate the regression using only the data on returning students. Show that 1 is the class size effect for returning students, that is, that

. Explain why is an unbiased estimator of 1.
b. Suppose that you estimate the regression using only the data on new students. Show that tq is the class size effect for new students, that is, that Explain why is an unbiased estimator of

c. Consider the regression for both returning and new students, Use the conditional mean independence assumption to show that (the difference in the class size effects).
d. Suppose that you estimate the interaction regression in (c) using the combined data and that Show that and are unbiased but that is in general biased.