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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 greater interdependence.� 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.

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Bibliographic Info

Paper provided by University of Oxford, Department of Economics in its series Economics Series Working Papers with number 655.

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Date of creation: 22 May 2013
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Handle: RePEc:oxf:wpaper:655

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Keywords: Interdependence; supermodular; correlation; copula; concordance; mixture; majorization; tournament;

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References

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Citations

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Cited by:
  1. Margaret Meyer & Bruno Strulovici, 2011. "Increasing Interdependence of Multivariate Distributions," Discussion Papers 1523, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  2. Patrick MOYES (GREThA, CNRS, UMR 5113) & Nicolas GRAVEL (Aix-Marseille University and AMSE (GREQAM)), 2011. "Ethically Robust Comparisons of Bidimensional Distributions with an Ordinal Attribute," Cahiers du GREThA 2011-36, Groupe de Recherche en Economie Théorique et Appliquée.

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