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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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Bibliographic Info

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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Web page: http://www.kellogg.northwestern.edu/research/math/
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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. 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).
  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. Gollier, Christian, 2014. "Gamma discounters are short-termist," TSE Working Papers 14-499, Toulouse School of Economics (TSE).
  4. 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).
  5. Gajdos, Thibault & Weymark, John A., 2012. "Introduction to inequality and risk," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1313-1330.
  6. Gollier, Christian, 2014. "Gamma discounters are short-termist," IDEI Working Papers 828, Institut d'Économie Industrielle (IDEI), Toulouse.

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