# Does GMM have any assumptions that you can't test empirically (and must instead argue qualitatively for)?

My understanding is that you can empirically test some of the main assumptions required for using a GMM estimator. Namely, I understand that you can test over-identifying restrictions with Hansen's J test and the Sargan test; and that you can test that the original error term is serially uncorrelated.

Are there other assumptions that cannot be tested empirically? If so, what are they and what intuition is required to satisfy them?