The Empirical Content of Bayesianism

TL;DR

This paper investigates when observed beliefs of agents align with Bayesian updating, establishing a key condition involving the distribution of posteriors and discussing limitations of previous empirical tests.

Contribution

It provides a precise characterization of Bayesian consistency in observed beliefs and clarifies the assumptions underlying empirical tests of Bayesianism.

Findings

Beliefs are Bayesian if the mean of the posterior distribution is absolutely continuous with respect to the prior.

Existing empirical results depend on additional assumptions like correct beliefs about signal distributions.

The main condition is both necessary and sufficient for Bayesian consistency in observed beliefs.

Abstract

This paper characterizes the conditions under which the observed beliefs of a group of agents are consistent with Bayesian updating. Beliefs are consistent with Bayesianism if they arise from the application of Bayes' rule given some subjective distribution for the state and the signals agents observe between periods. The paper's main finding is that beliefs are consistent with Bayesianism if and only if the mean of the distribution of posteriors is uniformly absolutely continuous with respect to the prior. Furthermore, the paper shows that the existing results on the empirical content of Bayesianism rely on additional restrictions on permissible subjective distributions, such as the requirement that agents have correct beliefs about the distribution of signals.