Rational Expectations in Empirical Bayes

TL;DR

This paper introduces a new framework for nonparametric empirical Bayes estimation that emphasizes prior-posterior consistency and stability, enhancing interpretability in Bayesian models.

Contribution

It characterizes empirical Bayes estimators as fixed points of a belief operator, proving their uniqueness and improving transparency in EB applications.

Findings

Fixed points of the belief operator are unique.

The approach enhances interpretability of EB estimators.

Application to discrimination models demonstrates practical benefits.

Abstract

We propose a principled framework for nonparametric empirical Bayes (EB) estimation, based on the idea that the prior should be consistent with the observed posterior and that Bayesian updating should be stable. Focusing on discretized priors, we characterize EB estimators as fixed points of a posterior belief operator. We establish the uniqueness of such fixed points and illustrate how the approach improves transparency and interpretability in standard EB settings, including a recent model of discrimination.