Question: 2. (15 points) Consider the wage equation wage = Bo + Bieduc + u, u = educ . e (2) where e is a random

2. (15 points) Consider the wage equation wage = Bo + Bieduc + u, u = educ . e (2) where e is a random variable with E(e) = 0 and Var(e) = o. Assume that e is independent of educa Denote the OLS estimator of B1 to be B1. (a) Discuss whether the zero conditional mean assumption (Assumption SLR.4) is satisfied, and whether B1 is unbiased. (b) Discuss whether the homoskedasticity assumption (Assumption SLR.5) is satisfied.(c) Now, we transform model so that the regression error displays homoskedasticity: wa e 1 u 9 = 60 + a + educ educ educ (3) 1 = 60 + ,61 + 6. educ Denote the corresponding OLS estimator of l to be 51. Show that 51 is an unbiased estimator for l. Given a random sample, will the estimate [3'1 have the same value as the estimate 31

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