The reference interval in higher-order stochastic dominance

TL;DR

This paper investigates how the choice of reference interval affects higher-order stochastic dominance relations, revealing that the impact varies with the dominance order and the moments considered, which complicates economic applications.

Contribution

It provides new theoretical insights into the dependence of stochastic dominance relations on reference intervals and dominance order, clarifying when the reference interval matters or not.

Findings

Dominance relations strengthen as the reference interval shrinks for orders above three.

For mean-preserving dominance, the reference interval is irrelevant under certain moment conditions.

Higher-order stochastic dominance introduces complexities in economic modeling.

Abstract

Given two random variables taking values in a bounded interval, we study whether one dominates the other in higher-order stochastic dominance depends on the reference interval in the model setting. We obtain two results. First, the stochastic dominance relations get strictly stronger when the reference interval shrinks if and only if the order of stochastic dominance is larger than three. Second, for mean-preserving stochastic dominance relations, the reference interval is irrelevant if and only if the difference between the degree of the stochastic dominance and the number of moments is no larger than three. These results highlight complications arising from using higher-order stochastic dominance in economic applications.