Introductory Econometrics: A Modern Approach 6th Edition by Jeffrey M Wooldridge

Exercise 20

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 + ?1CathHS + 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?

Step 1 of 4

Given model is:

The other factors include gender, race, family income and parental education

(i)

The variable may be correlated with the error term of the modelbecause there are omitted factors from this given model which are accounted in the error term which is correlated with as the result, the error term may exhibit certain degree of correlation with . Such omitted factors in the model could be ability of the students, distance of the college from home, courses offered for study in the college and the religion to which the student belong to..

Moreover, students may self-select the college they want to attend.