Consider the linear model yi =xiB + ei or, in matrix notation Y= X'B + e. where X' is a vector n * 1. You estimate the model using OLS under the following assumptions (A) E (ui) = 0, (B) E (xi) = 0, i =1, ..., n, (C) E (u4) < infinity and E (xi4) < infinity, i = 1, ..., n.
Assume that E (ui * xi) = 0.3 and Var (xi) = 0.8.
A) Is the OLS estimator biased? Is it consistent? (If your answer is no, then compute the bias).
B) Assume now that E (ui2/xi) = xi2 and E (xi4) = 1.28. Derive the asymptotic distribution of B.
C) Assume now that E (xi) = 0.4. Is the OLS estimator biased? Is it consistent? ( If your answer is no, then compute the bias).
D) Propose a way to correct the bias (if present) under the assumption of point (a).