# Detecting heterogeneous risk attitudes with mixed gambles

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## Abstract

We propose a task for eliciting attitudes toward risk that is close to real-world risky decisions which typically involve gains and losses. The task consists of accepting or rejecting gambles that provide a gain with probability \(p\) and a loss with probability \(1-p\). We employ finite mixture models to uncover heterogeneity in risk preferences and find that (i) behavior is heterogeneous, with one half of the subjects behaving as expected utility maximizers, (ii) for the others, reference-dependent models perform better than those where subjects derive utility from final outcomes, (iii) models with sign-dependent decision weights perform better than those without, and (iv) there is no evidence for loss aversion. The procedure is sufficiently simple so that it can be easily used in field or lab experiments where risk elicitation is not the main experiment.

## Keywords

Individual risk-taking behavior Latent heterogeneity Finite mixture models Reference-dependence Loss aversion## JEL Classification

C91 D81## Notes

### Acknowledgments

We thank James Cox, Erik Eyster, Glenn Harrison, Botond Koszegi, and Peter Wakker for various comments and suggestions. We also thank seminar and conference participants at HEC Paris, University of Lausanne, University Jaume I Castellon, Economic Science Association World Meeting in Copenhagen, International Meeting on Behavioral and Experimental Economics in Barcelona, D-TEA Workshop in Paris, and the 68th European Meetings of the Econometric Society in Toulouse. Support from HEC Paris Foundation, Swiss National Science Foundation grant 135602, NOVA FORUM, and Fundação para a Ciência e Tecnologia is gratefully acknowledged.

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