Research Publication

January 2021 | Preliminary Paper

New Preliminary Paper: “Robust Estimation and Inference when Beliefs are Subjective”

Xiahong Chen and Peter G. Hansen

Abstract

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.