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 = β0 + β1PC + 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.