Exaggerated Likelihoods

Abstract

We present a portable model of distorted learning which embodies Tversky and Kahneman’s (1971) “belief in the law of small numbers.” When adjusting beliefs in response to new information the decision maker overweights the sample, updating as if the sample size were inflated. The degree of distortion is embodied in a single parameter specific to the agent and not to the particular stochastic setting. We show that the beliefs of such an agent preserve many dynamic properties of fully rational Bayesian beliefs. Though exaggerated likelihood delivers similar predictions to diagnostic expectations in a static setting, the models imply dramatically different belief dynamics. We present examples of distorted Kalman filtering in a Gaussian environment as well as a non-linear setting with stochastic volatility.