The Supermodular Stochastic Ordering

56 Pages Posted: 30 May 2013

See all articles by Margaret A. Meyer

Margaret A. Meyer

University of Oxford - Nuffield Department of Medicine

Bruno H. Strulovici

Northwestern University

Date Written: May 2013

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.

Keywords: Concordance, Copula, Correlation, Interdependence, Majorization, Mixture, Supermodular, Tournament

JEL Classification: D63, D81, G11, G22

Suggested Citation

Meyer, Margaret A. and Strulovici, Bruno H., The Supermodular Stochastic Ordering (May 2013). CEPR Discussion Paper No. DP9486, Available at SSRN: https://ssrn.com/abstract=2271937

Margaret A. Meyer (Contact Author)

University of Oxford - Nuffield Department of Medicine ( email )

New Road
Oxford, OX1 1NF
United Kingdom

Bruno H. Strulovici

Northwestern University ( email )

2001 Sheridan Road
Evanston, IL 60208
United States

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