1. Suppose that the population model determining y is given by: y = 0 + 1x1 + 2x2 + u, and it satisfies the Least-Squares assumptions plus homoskedasticity.

(a) Write down the first order conditions to obtain the OLS estimators of the model. You do not need to solve through it.

(b) Suppose you would like to use the linear regression model to analyze the effects of private tutoring expenditure. In particular, we want to estimate T estScorei = 0 + 1P reivousT estScorei + 2T utoringExpi + ui , where T estScorei is the sum of test scores of two different subjects (English and mathematics) of student i, P reivousT estScorei is the test score for the two subjects last year, and T utoringExpi is monthly tutoring expenditure for student i. One of your friends told you that P arentsEducationi , the combined number of years of your parents education, could be an important variable that is omitted from your specification. He pointed out that this omission can cause bias in your estimates. Judge your friend's claim. If he is not right, why? If he is right, what would be the sign of the bias?