Identification problem of the exponential tilting estimator under misspecification

This paper shows a potential pitfall of the exponential tilting (ET) estimator under misspecification. We show that the pseudo-true value of the ET estimator is not identified if the true distribution is not absolutely continuous with respect to the probability measures implied by the moment restriction model. This result implies that the ET estimator cannot be consistent for the pseudo-true value if the moment generating function of the moment function is unbounded.