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The Supermodular Stochastic Ordering

  • Margaret Meyer
  • Bruno Strulovici

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.

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Paper provided by University of Oxford, Department of Economics in its series Economics Series Working Papers with number 655.

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Date of creation: 22 May 2013
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Handle: RePEc:oxf:wpaper:655
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