Stochastic Dominance and Nonparametric Comparative Revealed Risk Aversion

Abstract

It is shown how to test revealed preference data on choices under uncertainty for consistency with first and second order stochastic dominance (FSD or SSD). The axiom derived for SSD is a necessary and sufficient condition for risk aversion. If an investor is risk averse, stochastic dominance relations can be combined with revealed preference relations to recover a larger part of an investor‘s preference. Interpersonal comparison between investors can be based on intersections of revealed preferred and worse sets. Using a variant of Yaari‘s (1969) definition of “more risk averse than”, it is shown that it is suffi cient to compare only the revealed preference relations of two investors. This makes the approach operational given a fi nite set of observations. The central rationalisability theorem provides strong support for this approach to comparative risk aversion. The entire analysis is kept completely nonparametric and can be used as an alternative or complement to parametric approaches and as a robustness check. The approach is illustrated with an application to experimental data of by Choi et al. (2007). Most subjects come close to SSD-rationality, and most subjects are comparable with each other. The distribution of risk attitudes in the population can be described by comparing subjects‘ choices with any given preference, which is also illustrated.

Keywords: Comparative risk aversion, experimental economics, induced budget experiments, interpersonal comparison, nonparametric analysis, portfolio choice, revealed preference, risk preference, stochastic dominance, uncertainty

JEL Classification: C14, C91, D11, D12, D81, G11