Bayesian and Classical Approaches to Structural Estimation of Risk Attitudes

Abstract

Interpersonal heterogeneity in risk attitudes is a regular feature of experimental data on decision making under risk. While there is an increasing consensus on the use of random coefficient or hierarchical models to accommodate this heterogeneity, there is a burgeoning Bayesian-classical divide concerning the choice of estimation methods. The rationale for using Bayesian methods focuses on their advantages over the traditional method of maximum likelihood which does not involve hierarchical modeling, and limited attention has been given to more recent classical methods which incorporate this feature. We provide an accessible compendium of Bayesian and classical methods to estimate hierarchical models, highlighting that despite their computational disparities, they share the fundamental concept of utilizing the population distribution of risk attitudes to identify individual-specific risk attitudes. We also introduce a classical method that applies Bayes' rule to update parameter estimates, demonstrating that the distinction between the two classes of methods is not dependent on whether the model estimation involves gradient-based maximization or Bayesian updating. Based on reanalyses of existing experimental data, we find that Bayesian and classical estimates of the same structural model mostly lead to similar conclusions about risk attitudes. Our study suggests that the main focus of the methodological discussion should be on whether the model specification incorporates the population distribution, rather than the specific estimation method used.

Keywords: risk aversion, non-expected utility, random coefficient, hierarchical Bayes, maximum simulated likelihood, expectation-maximization

JEL Classification: C81, C91, D81