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Sufficient conditions for jth order stochastic dominance for discrete cardinal variables, and their formulae

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  • Anderson, Gordon
  • Leo, Teng Wah

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. Framed in terms of Successive Sums of Cumulative Distribution Functions and Lower Partial Moments, convenient formulae, along with necessary and sufficient conditions for different orders of dominance are derived, which reveal some key facts that have eluded general attention. Engendered by restrictions on the finite differences between utility functions and the limited number of outcomes, degrees of freedom are lost as the dominance order increases, imposing an upper bound on the order that can be considered. Simple formulae for computing successive sums of cumulative distributions are developed, and the relationship between lower and higher order dominance is proven in this discrete cardinal case.

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  • Anderson, Gordon & Leo, Teng Wah, 2021. "Sufficient conditions for jth order stochastic dominance for discrete cardinal variables, and their formulae," Economics Letters, Elsevier, vol. 209(C).
    • Handle: RePEc:eee:ecolet:v:209:y:2021:i:c:s0165176521004213
    DOI: 10.1016/j.econlet.2021.110144
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    References listed on IDEAS

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    Cited by:

    1. Gordon John Anderson & Teng Wah Leo, 2021. "On Extending Stochastic Dominance Comparisons to Ordinal Variables and Generalising Hammond Dominance," Working Papers tecipa-705, University of Toronto, Department of Economics.
    2. Anderson, Gordon & Fu, Rui & Leo, Teng Wah, 2022. "Health, loneliness and the ageing process in the absence of cardinal measure: Rendering intangibles tangible," The Journal of the Economics of Ageing, Elsevier, vol. 22(C).

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    More about this item

    Keywords

    Stochastic dominance; Discrete variables; Cardinal variables; Lower Partial Moments;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • I32 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - Measurement and Analysis of Poverty

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