Question: Consider the model, defined by the following assumptions: A1 (Linearity): Y = X+U, A2 (Exogeneity): E(U|X) = 0 or A2* E(UX) = 0 and

Consider the model, defined by the following assumptions: A1 (Linearity): Y = X+U, A2 (Exogeneity): E(U|X) = 0 or A2* E(UX) = 0 and E(U) = 0, for i = A3 (Homoskedasticity): Var(U|X) = 0 In, A4 (No Multicollinearity): rank (X) = k, where X is an n k matrix A5: U|X 2 N(0,0 In). a) [4 points] Derive the least square estimator of B, i.e., BOLS. b) [4 points] Show that OLS estimator is unbiased. = 1, ..., n, c) [4 points] Propose an unbiased estimator of . Show that under usual assumptions (A1) (A4), this proposed estimator is unbiased. - d) [3 points] Describe the distribution of U'U/0.

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