Homework solution №4 Sattoriy Fayzullokh Answers 1a

3b). If E (w|z1, z2) = E (w|z2), implying that E (z’1 ν) = 0, then the estimates will be consistent.

4) Assumption 2SLS.1: For vector z, E(z'u)=0,

where z = (1, x1, …, xk, z1,…, zm).

Assumption 2SLS.2:

(a) rank E(z'z) = k+m+1; (b) rank E(z'x) = k.

(b) is the rank condition for identification that z is sufficiently linearly related to

x so that rank E(z'x) has ful column rank.

The order condition is k-1+m≥ k-1+h, where h is the number of endogenous variable.

Thus, the order condition indicates that we must have at least as many instruments as

endogenous variables.
Under homoskedasticity,

is a valid estimator of the asymptotic variance of ˆβ_2SLS .

Under heteroskedasticity, the heteroskedasticity-robust (White) standard errors is