Introductory Econometrics 4th Edition by Jeffrey Wooldridge

تمرين 4

Consider the multiple regression model containing three independent variables, under Assumptions MLR.1 through MLR.4:
y = 0 + 1 x 1 + 2 x 2 + 3 x 3 + u.
You are interested in estimating the sum of the parameters on x1 and x2; call this 1 = 1 + 2
(i) Show that is an unbiased estimator of 1.
(ii) Find Var( ) in terms of Var( ), Var( ), and Corr( , ).