IDEAS home Printed from
MyIDEAS: Login to save this paper or follow this series

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.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL:
Download Restriction: no

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

in new window

Date of creation: 22 May 2013
Date of revision:
Handle: RePEc:oxf:wpaper:655
Contact details of provider: Postal: Manor Rd. Building, Oxford, OX1 3UQ
Web page:

More information through EDIRC

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. 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.
  2. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
  3. Caillaud, Bernard & Tirole, Jean, 2007. "Consensus Building: How to Persuade a Group," IDEI Working Papers 435, Institut d'Économie Industrielle (IDEI), Toulouse.
  4. Allen, Franklin & Babus, Ana & Carletti, Elena, 2012. "Asset commonality, debt maturity and systemic risk," Journal of Financial Economics, Elsevier, vol. 104(3), pages 519-534.
  5. Fernandez, Raquel & Gali, Jordi, 1997. "To Each According to ...?: Markets, Tournaments, and The Matching Problem with Borrowing Constraints," Working Papers 97-11, C.V. Starr Center for Applied Economics, New York University.
  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. Alkire, Sabina & Foster, James, 2011. "Counting and multidimensional poverty measurement," Journal of Public Economics, Elsevier, vol. 95(7), pages 476-487.
  8. 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.
  9. Jonathan Levin & Susan Athey, 2001. "The Value of Information in Monotone Decision Problems," Working Papers 01003, Stanford University, Department of Economics.
  10. Paul Embrechts, 2009. "Copulas: A Personal View," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(3), pages 639-650.
  11. Acharya, Viral V & Pedersen, Lasse H & Philippon, Thomas & Richardson, Matthew P, 2012. "Measuring Systemic Risk," CEPR Discussion Papers 8824, C.E.P.R. Discussion Papers.
  12. Andrew T. Foerster & Pierre-Daniel G. Sarte & Mark W. Watson, 2008. "Sectoral vs. aggregate shocks : a structural factor analysis of industrial production," Working Paper 08-07, Federal Reserve Bank of Richmond.
  13. A. Atkinson, 2003. "Multidimensional Deprivation: Contrasting Social Welfare and Counting Approaches," Journal of Economic Inequality, Springer, vol. 1(1), pages 51-65, April.
  14. 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.
  15. 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.
  16. 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.
  17. Massimo Marinacci & Luigi Montrucchio, 2003. "Ultramodular functions," ICER Working Papers - Applied Mathematics Series 13-2003, ICER - International Centre for Economic Research.
  18. 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.
  19. 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.
  20. Joe, Harry, 1990. "Multivariate concordance," Journal of Multivariate Analysis, Elsevier, vol. 35(1), pages 12-30, October.
  21. Brendan K. Beare, 2010. "Copulas and Temporal Dependence," Econometrica, Econometric Society, vol. 78(1), pages 395-410, 01.
  22. 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.
  23. Müller, Alfred & Scarsini, Marco, 2000. "Some Remarks on the Supermodular Order," Journal of Multivariate Analysis, Elsevier, vol. 73(1), pages 107-119, April.
  24. repec:fip:fedhpr:y:2010:i:may:p:65-71 is not listed on IDEAS
  25. Arlotto, Alessandro & Scarsini, Marco, 2009. "Hessian orders and multinormal distributions," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2324-2330, November.
  26. Chew, Soo Hong & Sagi, Jacob S., 2012. "An inequality measure for stochastic allocations," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1517-1544.
  27. 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.
  28. 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.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:oxf:wpaper:655. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Monica Birds)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.