Take a regression model with i.i.d. observations (Yi ,Xi ) with X 2 R Y Xe E[e j X] 0 E

Take a regression model with i.i.d. observations (Yi ,Xi ) with X 2 R Y Æ X¯Åe E[e j X] Æ 0

­Æ E

£

X2e2¤

.

Let b¯ be the OLS estimator of ¯ with residuals bei Æ Yi ¡Xi b¯. Consider the estimators of ­

e­

Æ

1 n

Xn iÆ1 X2 i e2 i

b­

Æ

1 n

Xn iÆ1 X2 i be2 i .

(a) Find the asymptotic distribution of p

n

¡

e­

¡­

¢

as n!1.

(b) Find the asymptotic distribution of p

n

¡

b­

¡­

¢

as n!1.

(c) How do you use the regression assumption E[ei j Xi ] Æ 0 in your answer to (b)?