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The Supermodular Stochastic Ordering

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  • Margaret Meyer
  • Bruno Strulovici

Abstract

In many economic applications involving comparisons of multivariate distributions, supermodularity of an objective function is a natural property for capturing a preference for greaterinterdependence. One multivariate distribution dominates another according to the supermodular stochastic ordering if it yields a higher expectation than the other for all supermodular objective functions. We prove that this ordering is equivalent to one distribution being derivable from another by a sequence of elementary, bivariate, interdependence-increasing transformations, and develop methods for determining whether such a sequence exists. For random vectors resulting from common and idiosyncratic shocks, we provide non-parametric sufficient conditions for supermodular dominance. Moreover, we characterize the orderings corresponding to supermodular objective functions that are also increasing or symmetric. We use the symmetric supermodular ordering to compare distributions generated by heterogeneous lotteries. Applications to welfare economics, committee decision-making, insurance, finance, and parameter estimation are discussed. JEL Classification Numbers: D63, D81, G11, G22

Suggested Citation

  • Margaret Meyer & Bruno Strulovici, 2013. "The Supermodular Stochastic Ordering," Discussion Papers 1563, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  • Handle: RePEc:nwu:cmsems:1563
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    Cited by:

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    2. Gravel, Nicolas & Moyes, Patrick, 2012. "Ethically robust comparisons of bidimensional distributions with an ordinal attribute," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1384-1426.
    3. Pawel Dziewulski & John Quah, 2014. "Testing for production with complementarities," Economics Series Working Papers 722, University of Oxford, Department of Economics.
    4. Meyer, Margaret & Strulovici, Bruno, 2012. "Increasing interdependence of multivariate distributions," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1460-1489.
    5. Kızıldemir, Bünyamin & Privault, Nicolas, 2015. "Supermodular ordering of Poisson arrays," Statistics & Probability Letters, Elsevier, vol. 98(C), pages 136-143.
    6. Gollier, Christian, 2021. "A general theory of risk apportionment," Journal of Economic Theory, Elsevier, vol. 192(C).
    7. Ian M. Schmutte & Nathan Yoder, 2022. "Information Design for Differential Privacy," Papers 2202.05452, arXiv.org, revised Nov 2022.
    8. Marling, Tina Gottschalk & Range, Troels Martin & Sudhölter, Peter & Østerdal, Lars Peter, 2018. "Decomposing bivariate dominance for social welfare comparisons," Mathematical Social Sciences, Elsevier, vol. 95(C), pages 1-8.
    9. Veli Safak, 2020. "Matching Multidimensional Types: Theory and Application," Papers 2006.14243, arXiv.org.

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    More about this item

    Keywords

    Interdependence; Supermodular; Correlation; Copula; Concordance; Mixture; Majorization; Tournament;
    All these keywords.

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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