Take the linear equation Y X0e and consider the following estimators of . 1. b : 2SLS using the instruments Z1. 2. e :

Take the linear equation Y Æ X0¯Åe and consider the following estimators of ¯.

1. b¯ : 2SLS using the instruments Z1.

2. e¯ : 2SLS using the instruments Z2.

3. ¯ : GMMusing the instruments Z Æ (Z1,Z2) and the weight matrix W Æ

à ¡

Z0 1Z1

¢¡1

¸ 0 0

¡

Z0 2Z2

¢¡1 (1¡¸)

!

for ¸ 2 (0, 1).

Find an expression for ¯ which shows that it is a specific weighted average of b¯ and e¯.