A Simple Approach for Measuring Higher-Order Arrow-Pratt Coefficients of Risk Aversion

Although the importance of the second-order Arrow-Pratt coefficients of risk aversion is well established, the importance of higher-order risk attitudes has only recently begun to be recognized. In this paper, we introduce a nonparametric approach to directly measure higher-order Arrow-Pratt coefficients of risk aversion in an expected utility framework using choices between compound lotteries and show how it can be easily implemented in behavioral studies. Specifically, we provide a theoretical basis for using risk apportionment to reveal the intensity of higher-order risk attitudes, and then draw upon our theoretical results to develop a simple, systematic, and generalizable procedure for eliciting higher-order Arrow-Pratt coefficients. We demonstrate our approach in a laboratory experiment and find that the modal second-order, third-order, and fourth-order Arrow-Pratt coefficients are positive and small. Further, we find that degrees of risk aversion are positively correlated across orders. Additionally, we discuss alternative implementations of our procedure. This paper was accepted by Peng Sun, behavioral economics and decision analysis. Funding: R. J. Huang acknowledges financial support from the National Science and Technology Council of Taiwan [Grants MOST 110-2410-H-008 -017 -MY3]. R. J. Huang and L. Y. Tzeng gratefully acknowledge financial support from E.SUN Bank. L. Zhao acknowledges financial support from the National Natural Science Foundation of China [Grants 72125003 and 72131003]. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2023.02300 .