Question: Take the model Y X0e with E[e j Z] 0. Let bgmm be the GMM estimator using the weight matrixWn Z0Z

Take the model Y Æ X0¯Åe with E[e j Z] Æ 0. Let b¯gmm be the GMM estimator using the weight matrixWn Æ

¡

Z0Z

¢¡1 . Under the assumption E

£

e2 j Z

¤

Æ ¾2 show that p

n

¡ b¯¡¯

¢

¡!

d N

³

0,¾2 ¡

Q0M¡1Q

¢¡1

´

where Q Æ E

£

Z X0¤

and M Æ E

£

Z Z0¤

.

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