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Increasing Interdependence of Multivariate Distributions

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  • Margaret Meyer
  • Bruno Strulovici

Abstract

Orderings of interdependence among random variables are useful in many economic contexts, for example, in assessing ex post inequality under uncertainty; in comparing multidimensional inequality; in valuing portfolios of assets or insurance policies; and in assessing systemic risk. We explore five orderings of interdependence for multivariate distributions: greater weak association, the supermodular ordering, the convex-modular ordering, the dispersion ordering, and the concordance ordering. For two dimensions, all five orderings are equivalent, whereas for an arbitrary number of dimensions n > 2, the five orderings are strictly ranked. For the special case of binary random variables, we establish some equivalences among the orderings.

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Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1523.

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Date of creation: 01 Mar 2011
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Handle: RePEc:nwu:cmsems:1523

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Keywords: dependence ordering; stochastic orders; supermodularity; weak association; concordance JEL Classification Numbers: D63; D81; G11; G22;

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Cited by:
  1. 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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