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

Exercise 2

Consider a simple model to estimate the effect of personal computer (PC) ownership on college grade point average for graduating seniors at a large public university:

GPA = ?0 + ?1PC + u,

where PC is a binary variable indicating PC ownership.

(i) Why might PC ownership be correlated with u?

(ii) Explain why PC is likely to be related to parents' annual income. Does this mean parental income is a good IV for PC? Why or why not?

(iii) Suppose that, four years ago, the university gave grants to buy computers to roughly one-half of the incoming students, and the students who received grants were randomly chosen. Carefully explain how you would use this information to construct an instrumental variable for PC.

Step 1 of 3

(i)

In the given model, ownership is correlated with because, this model suffers from omitted variable bias and that such omitted variables are correlated with ownership. One such omitted variable is family income which has an impact on the college grade point average and at the same time it has an impact on the ownership. Because the family income does not form the part of the given model, it is accounted by the error term. Given the positive correlation between the family income and ownership, there exists a correlation between ownership and