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Working paper 704

Gordon John Anderson and Teng Wah Leo, "Sufficient Conditions for j'th Order Stochastic Dominance for Discrete Cardinal Variables, and Their Formulae", 2021-09-01
Main Text (application/pdf) (274,797 bytes)

Abstract: In response to the increasing use of discrete cardinal data with limited numbers of outcomes, Stochastic Dominance Theory is here extended to facilitate its application. Formulae, convenient for analysis, along with necessary and sufficient conditions for different orders of dominance are derived which reveal some key facts which have eluded general attention. In this paradigm, there is a loss of degrees of freedom as the dominance order increases with a concomitant upper bound to the order of dominance that can be considered, both engendered by the restrictions on finite differences between
utility functions and the limited number of outcomes. Simple formulae for computing successive sums of cumulative distributions are found, and the relationship between lower and higher order dominance is proven in this discrete cardinal case.

Keywords: Stochastic Dominance; Discrete Variables; Cardinal Variables

JEL Classification: C14; D63; I32