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The Supermodular Stochastic Ordering

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  • Margaret Meyer
  • Bruno Strulovici

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

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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 1563.

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Date of creation: 06 May 2013
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Handle: RePEc:nwu:cmsems:1563

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

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  1. Alkire, Sabina & Foster, James, 2011. "Counting and multidimensional poverty measurement," Journal of Public Economics, Elsevier, vol. 95(7-8), pages 476-487, August.
  2. Thibault Gajdos & Eric Maurin, 2004. "Unequal Uncertainties and Uncertain Inequalities: An Axiomatic Approach," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00085940, HAL.
  3. Caillaud, Bernard & Tirole, Jean, 2007. "Consensus Building: How to Persuade a Group," IDEI Working Papers 435, Institut d'Économie Industrielle (IDEI), Toulouse.
  4. Arlotto, Alessandro & Scarsini, Marco, 2009. "Hessian orders and multinormal distributions," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2324-2330, November.
  5. Shaked, Moshe & Shanthikumar, J. George, 1997. "Supermodular Stochastic Orders and Positive Dependence of Random Vectors," Journal of Multivariate Analysis, Elsevier, vol. 61(1), pages 86-101, April.
  6. Francis X. Diebold & Kamil Yilmaz, 2011. "On the Network Topology of Variance Decompositions: Measuring the Connectedness of Financial Firms," Koç University-TUSIAD Economic Research Forum Working Papers 1124, Koc University-TUSIAD Economic Research Forum.
  7. Joe, Harry, 1990. "Multivariate concordance," Journal of Multivariate Analysis, Elsevier, vol. 35(1), pages 12-30, October.
  8. repec:fip:fedhpr:y:2010:i:may:p:65-71 is not listed on IDEAS
  9. Müller, Alfred & Scarsini, Marco, 2000. "Some Remarks on the Supermodular Order," Journal of Multivariate Analysis, Elsevier, vol. 73(1), pages 107-119, April.
  10. Yoram Kroll & Liema Davidovitz, 2003. "Inequality Aversion versus Risk Aversion," Economica, London School of Economics and Political Science, vol. 70(277), pages 19-29, February.
  11. Viral V. Acharya & Lasse H. Pedersen & Thomas Philippon & Matthew Richardson, 2010. "Measuring systemic risk," Working Paper 1002, Federal Reserve Bank of Cleveland.
  12. Allen, Franklin & Babus, Ana & Carletti, Elena, 2011. "Asset Commonality, Debt Maturity and Systemic Risk," CEPR Discussion Papers 8476, C.E.P.R. Discussion Papers.
  13. Susan Athey & Jonathan Levin, 1998. "The Value of Information In Monotone Decision Problems," Working papers 98-24, Massachusetts Institute of Technology (MIT), Department of Economics.
  14. Andrew T. Foerster & Pierre-Daniel G. Sarte & Mark W. Watson, 2008. "Sectoral vs. Aggregate Shocks: A Structural Factor Analysis of Industrial Production," NBER Working Papers 14389, National Bureau of Economic Research, Inc.
  15. Brendan K. Beare, 2010. "Copulas and Temporal Dependence," Econometrica, Econometric Society, vol. 78(1), pages 395-410, 01.
  16. David P. Myatt & Chris Wallace, 2009. "Endogenous Information Acquisition in Coordination Games," Economics Series Working Papers 445, University of Oxford, Department of Economics.
  17. Ben-Porath, Elchanan & Gilboa, Itzhak & Schmeidler, David, 1997. "On the Measurement of Inequality under Uncertainty," Journal of Economic Theory, Elsevier, vol. 75(1), pages 194-204, July.
  18. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
  19. Rustam Ibragimov, 2005. "Copula-Based Dependence Characterizations and Modeling for Time Series," Harvard Institute of Economic Research Working Papers 2094, Harvard - Institute of Economic Research.
  20. Chew, Soo Hong & Sagi, Jacob S., 2012. "An inequality measure for stochastic allocations," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1517-1544.
  21. Paul Embrechts, 2009. "Copulas: A Personal View," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(3), pages 639-650.
  22. Raquel Fernandez & Jordi Gali, 1997. "To Each According To...? Markets, Tournaments, and the Matching Problem with Borrowing Constraints," NBER Working Papers 5930, National Bureau of Economic Research, Inc.
  23. Beare, Brendan K., 2010. "Archimedean Copulas and Temporal Dependence," University of California at San Diego, Economics Working Paper Series qt0xh8q1g3, Department of Economics, UC San Diego.
  24. Massimo Marinacci & Luigi Montrucchio, 2003. "Ultramodular functions," ICER Working Papers - Applied Mathematics Series 13-2003, ICER - International Centre for Economic Research.
  25. A. Atkinson, 2003. "Multidimensional Deprivation: Contrasting Social Welfare and Counting Approaches," Journal of Economic Inequality, Springer, vol. 1(1), pages 51-65, April.
  26. Boland, Philip J. & Proschan, Frank, 1988. "Multivariate arrangement increasing functions with applications in probability and statistics," Journal of Multivariate Analysis, Elsevier, vol. 25(2), pages 286-298, May.
  27. Cousin, Areski & Laurent, Jean-Paul, 2008. "Comparison results for exchangeable credit risk portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1118-1127, June.
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Cited by:
  1. Margaret Meyer & Bruno Strulovici, 2011. "Increasing Interdependence of Multivariate Distributions," Discussion Papers 1523, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  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.

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