Suppose that the true data-generating process for y is given by:

y=x1β1+x2β2+ε; ε～N(0, σ2,I) the regressors are non-random, and Lim(1/NX’X)=Q=(Q11 Q12)

                                                                                                                                    (Q’12 Q22)

Finite, positive definite.

a)       If the model that we fit to the data by OLS is: Y=x1β1+u, prove that the OLSestimator of β1 is inconsisten. What is your(implicit) estimator of β2? is it consistent?

b)       Now, suppose that the model that we fit by OLS is: y= x1β1+Wδ+ν,

Where the columns of W are totally different from those of X2. Prove that the OLS estimators ofβ1 andβ2 are biased. Can you conjecture, without any proof or derivation, what other properties these estimators will have?

那个Q11,Q12哪儿是个矩阵，不知道怎么打，谢谢大家给予帮助，急用。