Question

1.You are interested in estimating the effects of owning a tablet (such as an iPad) on the grades of high school students (the idea is that owning a tablet might help students take notes and study more effectively). You have data on tablet ownership and GPA for a sample of 1000 students. You wish to estimate this model:

GPA=B0+B₁tablet+u

where GPA is the student's grade point average measured on a scale of 0-4, and tablet is a dummy variable that equals one if a student owns a tablet and zero otherwise.

a. What does u represent in this model? Give an example of a variable that might be contained in u. If tablet is correlated with u, what does this mean for a linear regression (OLS) estimate of B₁?

b. You discover that another school district decided to buy tablets for its high school students. However, the district did not have enough money to buy a tablet for every student, so they randomly chose some students to receive a tablet (while others did not get one). How could you use this information to construct an instrumental variable (IV) to estimate the effect of tablet usage on GPA? What two conditions does your instrumental variable have to satisfy in order to generate consistent estimates? Which one of these can you test? How would you do this?

c. Do you think the instrumental variable you described above in part b) satisfies the two key conditions of a good instrumental variable?