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 ˆβ2SLS .
Under heteroskedasticity, the heteroskedasticity-robust (White) standard errors is
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