The model is Y X0e with E[e j X] 0. An econometrician is worried about the impact of some unusually large values of

The model is Y Æ X0¯Åe with E[e j X] Æ 0. An econometrician is worried about the impact of some unusually large values of the regressors. The model is thus estimated on the subsample for which jXi j · c for some fixed

c. Let e¯ denote the OLS estimator on this subsample. It equals e¯ Æ

Ã

Xn iÆ1 Xi X0 i

1{jXi j · c}

!¡1 Ã

Xn iÆ1 XiYi1{jXi j · c}

!

.

(a) Show that e¯ ¡!

p

¯.

(b) Find the asymptotic distribution of p

n

¡ e¯¡¯

¢

.