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What is the meaning of the instrument Exogeneity?
Wooldridge now writes: “instrument exogeneity means that z should have no partial effect on y (after x and ommited variables have been controlled for), and z should be uncorrelated with the omitted variables.”
Can instrument Exogeneity be tested?
Exogeneity requires that Cov(Z,U)=0. This cannot be tested. To see why suppose that Z is in fact an endogenous instrument, i.e. that Suppose that Z is in fact an invalid instrument, i.e. that Cov(Z,U)≠0.
How to test the exogeneity of an instrument?
The exogeneity of the instrument criterion refers to bullet point 3 above, and an over-identified model is required to test this criterion. The remaining 2 criteria, however, can easily be tested. Remember that cov(z, x) ≠ 0 means z cannot be directly related to y, except through x.
What’s the difference between Wald and endogeneity tests?
Then the exogeneity test is a Wald test that δ 2 = 0 (ie jointly testing that all coefficients in the vector δ 2 are 0). Rejecting the test means that X 2 is not exogenous. Hausman’s test for endogeneity: This test is very similar to the above Wald test, and should be quite similar (I think exactly the same) under homoscedasticity.
When does an instrument have to be endogenous?
Endogeneity is what happens when one or more of your right-hand-side variables is correlated with u, so for your instrument to be endogenous, it would have to be correlated with u and not y. The exogeneity of the instrument criterion refers to bullet point 3 above, and an over-identified model is required to test this criterion.
What’s the difference between Hansen’s J and Sargan’s test?
Approach: If we assume homoskedasticity, the Sargan’s test is a special case of Hansen’s J test. We first run TSLS with all instruments, and get the residuals, and then regress these on the instruments. The sample size times R 2 of this regression is approximately χ 2 with number of excess instruments as degrees of freedom.