Robust Maximum Likelihood Updating

Abstract

There is a large body of evidence that decision makers frequently depart from Bayesian updating. This paper introduces a model, robust maximum likelihood (RML) updating, where deviations from Bayesian updating are due to multiple priors/ambiguity. Using the decision maker's prior and posteriors as the primitives of the analysis, I axiomatically characterize a representation where the decision maker's probability assessment can be described by a benchmark prior, which is interpreted as an initial best guess, and a set of plausible priors, which represents all the priors that cannot be ruled out. When new information is received, the decision maker revises her benchmark prior within the set of plausible priors via the maximum likelihood principle in a way that ensures maximally dynamically consistent behavior, and updates the new benchmark prior using Bayes' rule. I demonstrate how the set of plausible priors can be uniquely identified by comparing ex ante and ex post beliefs and show how most commonly observed updating biases can be accommodated within the model in a unified framework.