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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
Handle: RePEc:oxf:wpaper:655
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  1. Marco Scarsini & Alfred Muller, 2000. "Some remarks on the supermodular order," Post-Print hal-00540239, HAL.
  2. A. Atkinson, 2003. "Multidimensional Deprivation: Contrasting Social Welfare and Counting Approaches," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 1(1), pages 51-65, April.
  3. Thibault Gadjos & Eric Maurin, 2002. "Unequal Uncertainties and Uncertain Inequalities : An Axiomatic Approach," Working Papers 2002-32, Centre de Recherche en Economie et Statistique.
  4. Joe, Harry, 1990. "Multivariate concordance," Journal of Multivariate Analysis, Elsevier, vol. 35(1), pages 12-30, October.
  5. Alkire, Sabina & Foster, James, 2011. "Counting and multidimensional poverty measurement," Journal of Public Economics, Elsevier, vol. 95(7), pages 476-487.
  6. Caillaud, Bernard & Tirole, Jean, 2007. "Consensus Building: How to Persuade a Group," IDEI Working Papers 435, Institut d'Économie Industrielle (IDEI), Toulouse.
  7. 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.
  8. Itzhak Gilboa & Elchanan Ben-Porath & David Schmeidler, 1997. "On the Measurement of Inequality under Uncertainty," Post-Print hal-00481334, HAL.
  9. 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.
  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. 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.
  12. 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.
  13. 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.
  14. David P. Myatt & Chris Wallace, 2012. "Endogenous Information Acquisition in Coordination Games," Review of Economic Studies, Oxford University Press, vol. 79(1), pages 340-374.
  15. Jonathan Levin & Susan Athey, 2001. "The Value of Information in Monotone Decision Problems," Working Papers 01003, Stanford University, Department of Economics.
  16. 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.
  17. Viral V. Acharya & Lasse H. Pedersen & Thomas Philippon & Matthew Richardson, 2010. "Measuring systemic risk," Working Paper 1002, Federal Reserve Bank of Cleveland.
  18. David A. Hennessy & Harvey E. Lapan, 2003. "A Definition of 'More Systematic Risk' with Some Welfare Implications," Economica, London School of Economics and Political Science, vol. 70(279), pages 493-507, 08.
  19. Allen, Franklin & Babus, Ana & Carletti, Elena, 2013. "Asset Commonality, Debt Maturity and Systemic Risk," Working Papers 10-30, University of Pennsylvania, Wharton School, Weiss Center.
  20. Raquel Fernández & Jordi Gali, 1999. "To Each According to …? Markets, Tournaments, and the Matching Problem with Borrowing Constraints," Review of Economic Studies, Oxford University Press, vol. 66(4), pages 799-824.
  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. Arlotto, Alessandro & Scarsini, Marco, 2009. "Hessian orders and multinormal distributions," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2324-2330, November.
  23. Chew, Soo Hong & Sagi, Jacob S., 2012. "An inequality measure for stochastic allocations," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1517-1544.
  24. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
  25. Massimo Marinacci & Luigi Montrucchio, 2003. "Ultramodular functions," ICER Working Papers - Applied Mathematics Series 13-2003, ICER - International Centre for Economic Research.
  26. 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.
  27. Brendan K. Beare, 2010. "Copulas and Temporal Dependence," Econometrica, Econometric Society, vol. 78(1), pages 395-410, 01.
  28. repec:fip:fedhpr:y:2010:i:may:p:65-71 is not listed on IDEAS
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