Price Probabilities: A Class of Bayesian and Non-Bayesian Prediction Rules

Abstract

In this paper, I use the standard machinery of dynamic general equilibrium models to generate a rich class of probabilities and discuss their properties. This class includes probabilities consistent with Bayes' rule and known non-Bayesian rules. If the prior support is correctly specified, I prove that all members of this class perform as well as Bayes' rule in terms of likelihood. If the prior support is misspecified, I demonstrate how rules that underreact to new information can significantly outperform Bayes'. Because underreaction is never worse and sometimes better than Bayesian predictions, my result challenges the prevailing opinion that Bayes' rule is the only rational way to learn.

Keywords: Non-Bayesian Learning, Prediction Market, Market Selection

JEL Classification: C53, D81, D83