Optimal Decision Rules for Weak GMM

Abstract

This paper derives the limit experiment for nonlinear GMM models with weak and partial identification. We propose a theoretically-motivated class of default priors on a nonparametric nuisance parameter. These priors imply computationally tractable Bayes decision rules in the limit problem, while leaving the prior on the structural parameter free to be selected by the researcher. We further obtain quasi-Bayes decision rules as the limit of sequences in this class, and derive weighted average power-optimal identification-robust frequentist tests. Finally, we prove a Bernstein-von Mises-type result for the quasi-Bayes posterior under weak and partial identification.

Culling the herd of moments with penalized empirical likelihood

“…In empirical macroeconomics identification failure and moment misspecification are common issues (Mavroeidis 2005). Under the GMM framework, inference under weak moments (Andrews and Mikusheva 2020, Kleibergen 2005, Stock and Wright 2000, estimation under many weak moments (Han and Phillips 2006), and robust procedures for invalid moments , DiTraglia 2016) have been developed. EL's attractive theoretical properties are studied extensively (Kitamura 2001, Matsushita and Otsu 2013, Otsu 2010.…”