Consider the model y = X???? + u, where y isT × 1, ???? is a k × 1 vector of parameters, andX (T × k) is a stochasticmatrix having full column rank with probability 1; E(u|X) = ???? w.p. 1 and E(uu′|X) = ????2IT w.p. 1; and plim 1T X′X = Q (k × k) is a finite positive definite matrix. Let ????̂ be the OLS estimator and û = y − X????̂ the vector of residuals from the above regression.

(a) Show that ????̂ is a consistent estimator for ????.

(b) Obtain the limiting distribution of

√

T(????̂ − ????), stating clearly any additional assumptions or standard results you employ.

(c) Let s2 = ̂u′ ̂u T − k be the estimated disturbance variance. Show that s2 is a consistent estimator of ????2.