Conditional moment models under semi-strong identification

We consider conditional moment models under semi-strong identification. Identification strength is directly defined through the conditional moments that flatten as the sample size increases. Our new minimum distance estimator is consistent, asymptotically normal, robust to semi-strong identification, and does not rely on the choice of a user-chosen parameter, such as the number of instruments or some smoothing parameter. Heteroskedasticity-robust inference is possible through Wald testing without prior knowledge of the identification pattern. Simulations show that our estimator is competitive with alternative estimators based on many instruments, being well-centered with better coverage rates for confidence intervals.