Rational Expectations in Empirical Bayes

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.