Extreme Points and First-Order Stochastic Dominance: Theory and Applications

Abstract

We characterize the extreme points of first-order stochastic dominance (FOSD) intervals and show how these intervals are at the heart of many topics in economics. An FOSD interval is a set of distributions that dominate a distribution and are simultaneously dominated by another distribution, in the sense of FOSD. The convexity of FOSD intervals means that their extreme points are fundamental to understanding their properties. We show that a distribution is an extreme point of an FOSD interval if and only if the distribution either coincides with one of the FOSD bounds or is flat. Wherever the distribution is flat, at least one end of the flat portion must be attached to one of the FOSD bounds.