Necessity of doing "Flasification Test" to prove validity of instruments after using GMM: xtabond2 or xtdpdgmm

[lakhi narayan]

Hi! I have seen in some papers that, after doing IV regression or 2SLS estimation, many times authors do falsification test to prove the validity of instruments. For example, in a model where y is the dependent variable, x1, x2 are independent variables and x3 is endogeneous variable, for which instrument z has been used. Then in the falsification test y=x1+x2+x3+z is estimated and if z becomes insiginificant, then this falsification test proves that z is a valid instrument and it does not have any significant direct impact on dependent variable, it affects the outcome variable (y) only via the endogeneous variable.
So I just to know do we need to do such tests after doing GMM (either by using xtabond2 or xtdpdsys). If it is not necessary then how can we prove that he instruments dont have any diect effect on the outcome variable or dependent variable, it affects the outcome variable only via the endogeneous variables?

[Sebastian Kripfganz]

The falsification test you are describing is generally flawed. In the regression of y on x1 x2 x3 z, you cannot get consistent estimates of the direct effect of z if x3 is an endogenous regressor. You would still need an instrument for x3, but you cannot at the same time use z as an instrument for x3 and as a regressor itself. This only works if you have another instrument, say z2, but then it remains an untestable assumption that z2 has no direct effect.

After GMM estimation, if the model is overidentified (i.e., you have more instruments than regressors), the usual approach would be to conduct tests for the validity of the overidentifying restrictions (Hansen test). Say, you instruments z1 and z2 for regressor x3, then you have 1 overidentifying restriction (i.e., 1 more instrument than you need) and you can test whether this one additional instrument is valid, assuming (!) that the other instrument is valid. If the test rejects, there is evidence that one of the two instruments is valid. Unless you have strong prior beliefs that either z1 or z2 must be valid, the test however does not tell you which of the two would be invalid.

In summary, there is no free lunch. There will always be some assumption that cannot be verified with statistical tests.

[lakhi narayan]

Thank you so much Prof. Kripfganz for your reply.