When Should Demographics Enter the Prior? Conditional Exchangeability in Bayesian Estimation of Risk Preferences

Abstract

Hierarchical Bayesian models for the estimation of individual risk preferences typically assume that subjects are unconditionally exchangeable: prior to seeing any data, every subject is treated as a draw from a common population distribution. We examine the consequences of relaxing that assumption to one of conditional exchangeability, where the hyper-parameters of the population distribution are allowed to depend on observable covariates. Using simulated data, where the true parameters are known, we compare the recovery properties of unconditionally and conditionally exchangeable specifications across both Expected Utility and Rank-Dependent Utility models. A parsimonious conditionally exchangeable specification recovers individual risk preferences well when the data-generating process actually contains demographic structure, and imposes only a modest penalty when it does not, but overly rich covariate specifications can substantially erode the borrowing-of-strength that makes hierarchical models attractive in the first place. The trade-off is sharp, but navigable, and is of direct relevance to applied work that uses estimated risk preferences as inputs to normative welfare analysis or as controls for other inferences.