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

2. (15 points) Consider the wage equation wage = Bo + Bieduc + u, u = educ. e where e is a random variable with E(e) Denote the OLS estimator of B to be 3. = 0 and Var(e) = o. Assume that e is independent of educ. (a) Discuss whether the zero conditional mean assumption (Assumption SLR.4) is satisfied, and whether 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: wage educ = 1 1 educ 1 educ + B + (2) U educ + B +e. (3) Denote the corresponding OLS estimator of to be 3. Show that B is an unbiased estimator for . Given a random sample, will the estimate have the same value as the estimate B?

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