Tests of Bayesian Rationality
What are the testable implications of the Bayesian rationality hypothesis? This paper argues that the absolute continuity of posteriors with respect to priors constitutes the entirety of the empirical content of this hypothesis. I consider a decision-maker who chooses a sequence of actions and an econometrician who observes the decision- maker’s actions, but not her signals. The econometrician is interested in testing the hypothesis that the decision-maker follows Bayes’ rule to update her belief. I show that without a priori knowledge of the set of models considered by the decision-maker, there are almost no observations that would lead the econometrician to conclude that the decision-maker is not Bayesian. The absolute continuity of posteriors with respect to priors remains the only implication of Bayesian rationality, even if the set of actions is sufficiently rich that the decision-maker’s actions fully reveal her beliefs, and even if the econometrician observes a large number of ex ante identical agents who observe i.i.d. signals and face the same sequence of decision problems.
Molavi, Pooya. 2021. Tests of Bayesian Rationality.LINK