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Increasing interdependence of multivariate distributions

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  • Meyer, Margaret
  • Strulovici, Bruno

Abstract

Orderings of interdependence are useful in many economic contexts: 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 are equivalent, whereas for three dimensions, the first four are strictly ranked and the last two are equivalent, and for four or more dimensions, all five are strictly ranked. For the special case of binary random variables, we establish some equivalences among the orderings.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 147 (2012)
Issue (Month): 4 ()
Pages: 1460-1489

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Handle: RePEc:eee:jetheo:v:147:y:2012:i:4:p:1460-1489

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Web page: http://www.elsevier.com/locate/inca/622869

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Keywords: Dependence ordering; Stochastic orders; Supermodularity; Weak association; Concordance;

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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.
  2. DECANCQ, Koen, . "Elementary multivariate rearrangements and stochastic dominance on a Fréchet class," CORE Discussion Papers RP -2425, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Gollier, Christian, 2014. "Gamma discounters are short-termist," TSE Working Papers 14-499, Toulouse School of Economics (TSE).
  4. Gajdos, Thibault & Weymark, John A., 2012. "Introduction to inequality and risk," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1313-1330.
  5. Gollier, Christian, 2014. "Gamma discounters are short-termist," IDEI Working Papers 828, Institut d'Économie Industrielle (IDEI), Toulouse.
  6. Sonne-Schmidt, Christoffer & Tarp, Finn & Osterdal, Lars Peter, 2013. "Ordinal multidimensional inequality," Working Paper Series UNU-WIDER Research Paper , World Institute for Development Economic Research (UNU-WIDER).

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