Reporting probabilistic expectations with dynamic uncertainty about possible distributions

Abstract

We study how experimental subjects report subjective probability distributions in the presence of ambiguity characterized by uncertainty over a fixed set of possible probability distributions generating future outcomes. Subjects observe draws from the true but unknown probability distribution generating outcomes at the beginning of each period of the experiment and state at selected periods a) the likelihoods that each probability distribution in the set is the true distribution, and b) the likelihoods of future outcomes. We estimate heterogeneity of rules used to update uncertainty about the true distribution and rules used to report distributions of future outcomes. We find that approximately 65% of subjects report distributions by properly weighing the possible distributions using their expressed uncertainty over them, while 22% of subjects report distributions close to the distribution they perceive as most likely. We find significant heterogeneity in how subjects update their expressed uncertainty. On average, subjects tend to overweigh the importance of their prior uncertainty relative to new information, leading to ambiguity that is substantially more persistent than would be predicted using Bayes’ rule. Counterfactual simulations suggest that this persistence will likely hold in settings not covered by our experiment.