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Sufficient Conditions for j'th Order Stochastic Dominance for Discrete Cardinal Variables, and Their Formulae

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  • Gordon John Anderson
  • Teng Wah Leo

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.

Suggested Citation

  • Gordon John Anderson & Teng Wah Leo, 2021. "Sufficient Conditions for j'th Order Stochastic Dominance for Discrete Cardinal Variables, and Their Formulae," Working Papers tecipa-704, University of Toronto, Department of Economics.
    • Handle: RePEc:tor:tecipa:tecipa-704
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    References listed on IDEAS

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    1. Whitmore, G A, 1970. "Third-Degree Stochastic Dominance," American Economic Review, American Economic Association, vol. 60(3), pages 457-459, June.
    2. Bawa, Vijay S, et al, 1985. "On Determination of Stochastic Dominance Optimal Sets," Journal of Finance, American Finance Association, vol. 40(2), pages 417-431, June.
    3. James P. Quirk & Rubin Saposnik, 1962. "Admissibility and Measurable Utility Functions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 29(2), pages 140-146.
    4. Ekern, Steinar, 1980. "Increasing Nth degree risk," Economics Letters, Elsevier, vol. 6(4), pages 329-333.
    5. Nicolas Gravel & Brice Magdalou & Patrick Moyes, 2021. "Ranking distributions of an ordinal variable," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(1), pages 33-80, February.
    6. Hadar, Josef & Russell, William R, 1969. "Rules for Ordering Uncertain Prospects," American Economic Review, American Economic Association, vol. 59(1), pages 25-34, March.
    7. Russell Davidson & Jean-Yves Duclos, 2000. "Statistical Inference for Stochastic Dominance and for the Measurement of Poverty and Inequality," Econometrica, Econometric Society, vol. 68(6), pages 1435-1464, November.
    8. Bawa, Vijay S., 1975. "Optimal rules for ordering uncertain prospects," Journal of Financial Economics, Elsevier, vol. 2(1), pages 95-121, March.
    9. Fang, Yi & Post, Thierry, 2017. "Higher-degree stochastic dominance optimality and efficiency," European Journal of Operational Research, Elsevier, vol. 261(3), pages 984-993.
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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;
    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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