The observed data is {Yi ,Xi ,Zi } 2 RRk R`, k 1 and ` k 1, i 1, ...,n. The

The observed data is {Yi ,Xi ,Zi } 2 R£Rk £R`, k È 1 and ` È k È 1, i Æ 1, ...,n. The model is Y Æ X0¯Åe with E[Ze] Æ 0.

(a) Given a weightmatrixW È 0 write down the GMMestimator b¯ for ¯.

(b) Suppose the model is misspecified. Specifically, assume that for some ± 6Æ 0, e Æ ±n¡1/2 Åu (13.32)

E[u j Z] Æ 0 with ¹Z Æ E[Z] 6Æ 0. Show that (13.32) implies that E[Ze] 6Æ 0.

(c) Express p

n

¡ b¯¡¯

¢

as a function ofW, n, ±, and the variables (Xi , Zi , ui ).

(d) Find the asymptotic distribution of p

n

¡ b¯¡¯

¢

under Assumption (13.32).