Introductory Econometrics 4th Edition by Jeffrey Wooldridge

Exercise 10

Suppose that you wish to estimate the effect of class attendance on student performance, as in Example 6.3. A basic model is
stndfnl = 0 + 1 atndrte + 2 priGPA + 3 ACT + u,
where the variables are defined as in Chapter 6.
(i) Let dist be the distance from the students' living quarters to the lecture hall. Do you think dist is uncorrelated with u
(ii) Assuming that dist and u are uncorrelated, what other assumption must dist satisfy to be a valid IV for atndrte
(iii) Suppose, as in equation (6.18), we add the interaction term priGPA-atndrte:
stndfnl = 0 + 1 atn.drte + 2 priGPA + 3 ACT + 4 priGPA-atndrte + u.
If atndrte is correlated with u, then, in general, so is priGPA-atndrte. What might be a good IV for priGPA-atndrte [Hint: If E(upriGPA, ACT, dist) = 0, as happens when priGPA, ACT, and dist are all exogenous, then any function of priGPA and dist is uncor-related with u.]