2 Suppose that you estimate the following relationship using OLS: Y = Bo + BX + B Zi + ei However, the true data generating process for Y is: Y = Bo + BX + BZ + B3W + U where cov(X, u) = 0, cov(W, u) = 0 and cov(Z,u) = 0. You are told that the OLS estimator for B when estimating equation (1) is given by: B = plim () 1(Yi - Y) (Xi X) }=(Z; - Z) =1(Yk Y) (Zk Z) -1(Z Z) (x - x) m=1(Xm - X) =1(Zp - Z) (Z-1(Za Z) (Xq x)) By taking probability limits, it is trivial to show that: cov (Y, X)var (Z) - cov(Y,Z)cov (Z, X) var (X)var (Z) - (cov(X, Z)) You are not required to show the probability limit above. a) Using the probability limit specified in (3), and the true data generating process for Y (2), show that = (1) plim (B) =B + B3 (2) cov(W, X)var (Z) - cov(W, Z)cov (Z, X) var (X)var (Z) - (cov(X, Z)) (3) Note: There is no need to take plims in this question. b) Hence, under what circumstances will the OLS estimator yield consistent estimates of when estimating (1)?