You are a policy analyst in the Department of Education of a large urban school district. Your boss knows you've taken multiple regressions in graduate school and comes to you with a research report that estimates the effect of giving schools free vouchers for science related cultural institutions on test scores. Using one year of school level data researchers regressed average science test scores at the school level on a dummy variable indicating voucher receipt.

a) Write the population equation being estimated. Use TEST to denote average test scores, and VOUCHER to denote receipt of free tickets for cultural institutions.

b) Your boss really wants to know whether she should recommend this large urban school district to implement the same program, and it's your job to caution her against any possible causes of bias in the estimates such as omitted variable bias.

i) What causes omitted variable bias?

ii) Provide an example of a variable that is omitted from this model. What is the variable? What direction do you expect the coefficient on VOUCHER to be biased if you leave the variable out of the model? Please be concrete about why you think the coefficient in biased in that direction. (HINT: Think of characteristics that would make schools more likely to receive the program or not).