Robust inference for moment condition models without rational expectations

Applied researchers using structural models under rational expectations (RE) often confront empirical evidence of misspecification. In this paper we consider a generic dynamic model that is posed as a vector of unconditional moment restrictions. We suppose that the model is globally misspecified under RE, and thus empirically flawed in a way that is not econometrically subtle. We relax the RE restriction by allowing subjective beliefs to differ from the data-generating probability (DGP) model while still maintaining that the moment conditions are satisfied under the subjective beliefs of economic agents. We use statistical measures of divergence relative to RE to bound the set of subjective probabilities. This form of misspecification alters econometric identification and inferences in a substantial way, leading us to construct robust confidence sets for various set identified functionals.