The Supermodular Stochastic Ordering

Margaret Meyer and Bruno Strulovici

Discussion Papers from Northwestern University, Center for Mathematical Studies in Economics and Management Science

Abstract: In many economic applications involving comparisons of multivariate distributions, supermodularity of an objective function is a natural property for capturing a preference for greaterinterdependence. 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. JEL Classification Numbers: D63, D81, G11, G22

Keywords: Interdependence; Supermodular; Correlation; Copula; Concordance; Mixture; Majorization; Tournament (search for similar items in EconPapers)
Date: 2013-05-06
New Economics Papers: this item is included in nep-mic
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Working Paper: The Supermodular Stochastic Ordering (2013)
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