Introductory Econometrics 4th Edition by Jeffrey Wooldridge

Exercise 11

In a recent article, Evans and Schwab (1995) studied the effects of attending a Catholic high school on the probability of attending college. For concreteness, let college be a binary variable equal to unity if a student attends college, and zero otherwise. Let CathHS be a binary variable equal to one if the student attends a Catholic high school. A linear probability model is college = 0 + 1 CathHS + other factors + u, where the other factors include gender, race, family income, and parental education.
(i) Why might CathHS be correlated with u
(ii) Evans and Schwab have data on a standardized test score taken when each student was a sophomore. What can be done with this variable to improve the ceteris paribus estimate of attending a Catholic high school
(iii) Let CathRel be a binary variable equal to one if the student is Catholic. Discuss the two requirements needed for this to be a valid IV for CathHS in the preceding equation. Which of these can be tested
(iv) Not surprisingly, being Catholic has a significant effect on attending a Catholic high school. Do you think CathRel is a convincing instrument for CathHS