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.