Risk Aversion Reversals

Standard stochastic choice models used to estimate risk aversion can lead to risk-aversion reversals, where a more risk-averse individual chooses a riskier lottery more frequently than a less risk-averse individual. We study when reversals are implied by the preference specification rather than the noise specification. We say that two utilities imply reversals in a given noise framework if reversals arise for every specification of noise for each individual. For weak utility, a flexible class that includes logit and probit and allows for menu-dependent noise, two utilities imply reversals if and only if their curvature ratio is unbounded. This condition holds for CARA, CRRA, and their generalizations, for which reversals arise for empirically relevant coefficients and lotteries, raising concerns about resulting estimates and out-of-sample predictions. Finally, we show that equicautious HARA, sum-ex, and sum-power utilities do not imply reversals and that, moreover, these families remain well-behaved for multinomial choice.