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. Despite a growing consensus on the use of the random coefficient or hierarchical model to accommodate this heterogeneity, there is a burgeoning Bayesian-classical divide concerning the choice of estimation methods. The rationale for the use of Bayesian methods focuses on their advantages over the traditional method of maximum likelihood that does not address hierarchical modeling, and limited attention has been paid to more comparable classical methods. We provide an accessible overview of the Bayesian and classical methods to estimate the hierarchical model, 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 recursive estimator of classical origin, demonstrating that the distinction between the two classes of methods is not dependent on whether parameter estimation entails recursive updating or gradient-based maximization. Using existing experimental data, we find that the Bayesian and classical estimates of the same structural model lead to broadly 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