Consider the model Y X0e with E[Ze] 0 and R0 0 (13.31) with Y 2 R, X 2 Rk , Z 2

Consider the model Y Æ X0¯Åe with E[Ze] Æ 0 and R0¯ Æ 0 (13.31)

with Y 2 R, X 2 Rk , Z 2 R`, ` È k. The matrix R is k £ q with 1 · q Ç k. You have a random sample

(Yi ,Xi ,Zi : i Æ 1, ...,n).

For simplicity, assume the efficient weight matrixW Æ

¡

E

£

Z Z0e2¤¢¡1 is known.

(a) Write out the GMMestimator b¯ ignoring constraint (13.31).

(b) Write out the GMMestimator e¯ adding the constraint (13.31).

(c) Find the asymptotic distribution of p

n

¡ e¯¡¯

¢

as n!1under Assumption (13.31).