1. Consider the model  yi = α + βXi +μi. Suppose that the error term has the following autoregressiveprocess.

ui = ρμi−1 + ρ2μi-2+ei  (i = 1, 2, …, n)

where |ρ1| < 1, | ρ2| < 1, ei is a white noise and cov(ei , ui-1) = cov(ei , ui-2) = 0 for all i.

(a) Suppose that ρ1 ≠ 0 andρ2 ≠ 0. What problem(s) wouldyou have if you estimate β by OLS (Ordinary Least Squares)? [5 points]

(b) How would you test H0: ρ1 =ρ2 = 0 in this model? Briefly but completely explain the testprocedure. [10 points]

(c) Ifρ1 ≠ 0 andρ2 ≠ 0, how would you estimateβ? Briefly but completely explain your estimationprocedure. [10 points]

2. Answer the following questions.

(a) Consider theregression model yi =α+βXi +γΖi+μi. Assume that all the standard assumptions i) – iv) are satisfied.Suppose you estimated a wrong model yi =α+βXi +μi. insteadof the true model. In other words, you erroneously omitted Zi. Show if your OLS estimator of is biased. [10points]

(b) Unlike in part (a), assume that the truemodel is yi =α+βXi +μi. . However, you estimated a wrong model  yi =α+β^Xi +γΖi+μi.  In other words, you erroneously included Ζi. In this case, explain ifyour OLS estimator of  β^  is biased. [10 points]