Applied researchers using structural models of economic dynamics under ratio-nal expectations (RE) often confront empirical evidence of misspeciﬁcation. In this paper we consider a generic dynamic model that is posed as a vector unconditional moment restrictions. We suppose that the model is globally misspeciﬁed, and thus empirically ﬂawed in a way that is not econometrically subtle. In RE models the expectations used in deﬁning the moment conditions are both consistent with the beliefs of the economic agents within the model and population limit of the empirical distribution. We relax this assumption by allowing subjective beliefs to diﬀer from rational expectations while still maintaining that the moment conditions are satisﬁed under the subjective beliefs of economic agents whose behavior is captured by the dynamic economic model. This form of misspeciﬁcation alters econometric identiﬁ-cation and inferences in a substantial way. The underlying parameter vector ceases to be identiﬁed and the subjective beliefs may unduly weak. Therefore, we explore the consequences of restricting the statistical divergence between subjective belief distortions and their RE counterparts. In so doing, we are lead to address some new econometric challenges.