Bayesian interpretation of Generalized empirical likelihood by maximum entropy

TL;DR

This paper introduces a Bayesian approach to parametric estimation in moment condition models, extending the maximum entropy method and demonstrating its robustness and interpretability as a generalized empirical likelihood.

Contribution

It extends the MEM procedure to parametric moment conditions and shows that many GEL estimators can be viewed as maximum entropy solutions, broadening application scope.

Findings

GEL estimators can be interpreted as maximum entropy solutions.

The Bayesian approach is robust to approximate moment conditions.

The method extends the applicability of GEL and GMM techniques.

Abstract

We study a parametric estimation problem related to moment condition models. As an alternative to the generalized empirical likelihood (GEL) and the generalized method of moments (GMM), a Bayesian approach to the problem can be adopted, extending the MEM procedure to parametric moment conditions. We show in particular that a large number of GEL estimators can be interpreted as a maximum entropy solution. Moreover, we provide a more general field of applications by proving the method to be robust to approximate moment conditions.