ASMF seminar – Less than expected: A simple measure of skewnessfor choice under risk

Skewness plays a key role in decision-making under risk. We propose a new and intuitive skewness measure, mass-below-the-mean (MBM) skewness, defined as the probability that an outcome falls below its expected value. MBM skewness formalizes the familiar relationship between the mean and the median in asymmetric distributions and is theoretically grounded: it is monotone with respect to van Zwet’s (1964) convex order and Oja’s (1981) generalized order. MBM skewness is also much simpler than alternative skewness measures.
We compare MBM skewness with the widely used moment-based skewness coefficient. The two measures are equivalent on binary lotteries but differ systematically on ternary lotteries, implying that analyses based on binary risks may conceal important aspects of asymmetry in payoff distributions. We then provide a choice-theoretic interpretation of MBM skewness under quantile preferences and show that it captures a form of “bad skewness” that discourages risk-taking. In a precautionary saving application, we find that binary lotteries systematically understate skewness effects and that MBM skewness detects residual effects that moment-based skewness misses. Our results suggest that broadening the measurement of skewness can yield new insights into the economics of risky choice.