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Ranking Alternative Non-Combinable Prospects: A Stochastic Dominance Based Route to the Second Best Solution

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  • Gordon Anderson
  • Teng Wah Leo

Abstract

The problem considered here is that of dealing with the "incompleteness" property of Stochastic Dominance Orderings by quantifying the extent to which distributions differ when there is no dominant distribution at a given order. For example consider a policymaker's choice problem when facing a set of distinct, non-combinable policy options. When policies are not combinable, the classic comparative static or first best solution to the choice problem is not available. The approach proposed here is an elaboration of a technique employed in the optimal statistical testing literature. It is supposed that policies could be combined so that the ideal first best "stochastically dominant" optimal envelope policy outcome is constructed under the policymaker's given imperative. Then the second best policy whose outcome most closely approximates this ideal is selected by employing a statistic that measures proximity of alternative policies to that ideal. The statistic is shown to obey an Independence of Irrelevant Alternatives proposition. The paper concludes with 3 illustrative examples of its use.

Suggested Citation

  • Gordon Anderson & Teng Wah Leo, 2014. "Ranking Alternative Non-Combinable Prospects: A Stochastic Dominance Based Route to the Second Best Solution," Working Papers tecipa-520, University of Toronto, Department of Economics.
  • Handle: RePEc:tor:tecipa:tecipa-520
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    References listed on IDEAS

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    4. Garry F. Barrett & Stephen G. Donald, 2003. "Consistent Tests for Stochastic Dominance," Econometrica, Econometric Society, vol. 71(1), pages 71-104, January.
    5. Foster, James E. & Shorrocks, Anthony F., 1988. "Inequality and poverty orderings," European Economic Review, Elsevier, vol. 32(2-3), pages 654-661, March.
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    7. Arnaud Lefranc & Nicolas Pistolesi & Alain Trannoy, 2008. "Inequality Of Opportunities Vs. Inequality Of Outcomes: Are Western Societies All Alike?," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 54(4), pages 513-546, December.
    8. Juhl, Ted & Xiao, Zhijie, 2003. "Power Functions And Envelopes For Unit Root Tests," Econometric Theory, Cambridge University Press, vol. 19(02), pages 240-253, April.
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    11. Gordon Anderson & Oliver Linton & Teng Leo, 2012. "A polarization-cohesion perspective on cross-country convergence," Journal of Economic Growth, Springer, vol. 17(1), pages 49-69, March.
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    More about this item

    Keywords

    Policy Choice; Stochastic Dominance;

    JEL classification:

    • H0 - Public Economics - - General
    • I3 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty

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