Information Validates the Prior: A Theorem on Bayesian Updating and Applications
Theoretical Economics
2022-12-29 v3
Abstract
We develop a result on expected posteriors for Bayesians with heterogenous priors, dubbed information validates the prior (IVP). Under familiar ordering requirements, Anne expects a (Blackwell) more informative experiment to bring Bob's posterior mean closer to Anne's prior mean. We apply the result in two contexts of games of asymmetric information: voluntary testing or certification, and costly signaling or falsification. IVP can be used to determine how an agent's behavior responds to additional exogenous or endogenous information. We discuss economic implications.
Cite
@article{arxiv.2005.05714,
title = {Information Validates the Prior: A Theorem on Bayesian Updating and Applications},
author = {Navin Kartik and Frances Lee and Wing Suen},
journal= {arXiv preprint arXiv:2005.05714},
year = {2022}
}
Comments
Corrections of typos and other minor expositional edits. The paper is now forthcoming in American Economic Review: Insights