Conditional Moment Models under Weak Identification

We consider models defined by a set of conditional moment restrictions where weak identification may arise. Weak identification is directly defined through the conditional moments that are allowed to flatten as the sample size increases. We propose a minimum distance estimator of the structural parameters that is robust to potential weak identification and that uses neither instrumental variables nor smoothing. Hence, its properties only depend upon identification weakness, and not on the interplay between some tuning parameter, as the growth rate of the number of instruments, and the unknown degree of weakness. Our estimator is consistent and asymptotically normal, and its rate of convergence is the same as competing estimators based on many weak instruments. Heteroskedasticity-robust inference is possible through Wald testing without prior knowledge of the identification pattern. In simulations, we find that our estimator is competitive with estimators based on many instruments.