  This paper studies optimal decision rules, including estimators and tests,
for weakly identified GMM models. We derive the limit experiment for weakly
identified GMM, and propose a theoretically-motivated class of priors which
give rise to quasi-Bayes decision rules as a limiting case. Together with
results in the previous literature, this establishes desirable properties for
the quasi-Bayes approach regardless of model identification status, and we
recommend quasi-Bayes for settings where identification is a concern. We
further propose weighted average power-optimal identification-robust
frequentist tests and confidence sets, and prove a Bernstein-von Mises-type
result for the quasi-Bayes posterior under weak identification.
