Suppose the DGP is y = Xb + Zg+e (1) e~ N(0; s2In) b-OLS estimator (1) c-ols estimator in y=Xc+u (2)
(a) What is E[b]? What is E[c]?
(b) Consider the null hypothesis H0 : g= 0. Show that Cov[ b,b-c] = 0 under the null. Interpret this result.
(c) What does your result for part (b) imply about Var[ b-c] under the null?