Question

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 for graduating seniors at a large public university
Why might PC ownership be correlated with u?
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?
Suppose that, four years ago, the university gave grants to buy computers to roughly one-half of the incoming students, and the students that received grants were randomly chosen. Carefully explain how you would use this information to construct an IV for PC.
Using the IV you describe in (c), state the two equations/models you would use in a 2 staged least squares estimation:

Answer 1

Suppose the unobservable factors influencing the GPA is student's skills. These skills cannot be numerically administered and hence sit in u. Now, personal computer may be related to skills in the way that good skills in turn would mean better usage of PC, which in turn would mean better GPA, with the relative advantage of both PC and u.

PC is likely to be related to parent's annual income because the price of PC is high enough to be affordable by only certain annual income families. Now, the student with the parents in that bracket annual income, who can afford the PC can also be considered to have acquired the skills over time from the parents and other opportunities, but the parent's income cannot directly affect the GPA. Thus, the parents income can not be considered as a good IV.

Now, if the university grant comes into picture, we can define a new IV as the access to PC, instead of PC ownership. Accessibility would bring every student on the same platform, and the correlation with the u would reduce.

For 2 staged least squares estimation,

PC* = b0+b1accessibility to PC + e

GPA= β0+ β1PC*+u