IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this paper or follow this series

Increasing Interdependence of Multivariate Distributions

  • Margaret Meyer
  • Bruno Strulovici

Orderings of interdependence among random variables are useful in many economic contexts, for example, in assessing ex post inequality under uncertainty; in comparing multidimensional inequality; in valuing portfolios of assets or insurance policies; and in assessing systemic risk. We explore five orderings of interdependence for multivariate distributions: greater weak association, the supermodular ordering, the convex-modular ordering, the dispersion ordering, and the concordance ordering. For two dimensions, all five orderings are equivalent, whereas for an arbitrary number of dimensions n > 2, the five orderings are strictly ranked. For the special case of binary random variables, we establish some equivalences among the orderings.

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: http://www.kellogg.northwestern.edu/research/math/papers/1523.pdf
File Function: main text
Download Restriction: no

Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1523.

as
in new window

Length:
Date of creation: 01 Mar 2011
Date of revision:
Handle: RePEc:nwu:cmsems:1523
Contact details of provider: Postal:
Center for Mathematical Studies in Economics and Management Science, Northwestern University, 580 Jacobs Center, 2001 Sheridan Road, Evanston, IL 60208-2014

Phone: 847/491-3527
Fax: 847/491-2530
Web page: http://www.kellogg.northwestern.edu/research/math/
Email:


More information through EDIRC

Order Information: Email:


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. Caillaud, Bernard & Tirole, Jean, 2007. "Consensus Building: How to Persuade a Group," IDEI Working Papers 435, Institut d'Économie Industrielle (IDEI), Toulouse.
  2. Robert Shimer & Lones Smith, 2000. "Assortative Matching and Search," Econometrica, Econometric Society, vol. 68(2), pages 343-370, March.
  3. Hu, Taizhong & Xie, Chaode & Ruan, Lingyan, 2005. "Dependence structures of multivariate Bernoulli random vectors," Journal of Multivariate Analysis, Elsevier, vol. 94(1), pages 172-195, May.
  4. Marco Scarsini & A. Müller & Taizhong Hu, 2004. "Some counterexamples in positive dependence," Post-Print hal-00539628, HAL.
  5. R. Preston McAfee, 2002. "Coarse Matching," Econometrica, Econometric Society, vol. 70(5), pages 2025-2034, September.
  6. Antoni Calvó-Armengol & Matthew O. Jackson, 2003. "Networks in Labor Markets: Wage and Employment Dynamics and Inequality," Working Papers 55, Barcelona Graduate School of Economics.
  7. Bourguignon, F. & Chakravarty, S.R., 1998. "The Measurement of Multidimensional Poverty," DELTA Working Papers 98-12, DELTA (Ecole normale supérieure).
  8. Larry G. Epstein & Stephen M. Tanny, 1980. "Increasing Generalized Correlation: A Definition and Some Economic Consequences," Canadian Journal of Economics, Canadian Economics Association, vol. 13(1), pages 16-34, February.
  9. Acharya, Viral V, 2009. "A Theory of Systemic Risk and Design of Prudential Bank Regulation," CEPR Discussion Papers 7164, C.E.P.R. Discussion Papers.
  10. Dasgupta, Partha & Sen, Amartya & Starrett, David, 1973. "Notes on the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 6(2), pages 180-187, April.
  11. 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.
  12. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
  13. Thibault Gadjos & Eric Maurin, 2002. "Unequal Uncertainties and Uncertain Inequalities : An Axiomatic Approach," Working Papers 2002-32, Centre de Recherche en Economie et Statistique.
  14. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
  15. Margaret Meyer & Bruno Strulovici, 2013. "The Supermodular Stochastic Ordering," Discussion Papers 1563, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  16. Margaret A. Meyer & Dilip Mookherjee, 1987. "Incentives, Compensation, and Social Welfare," Review of Economic Studies, Oxford University Press, vol. 54(2), pages 209-226.
  17. repec:cor:louvrp:-2425 is not listed on IDEAS
  18. Antoni Calvó-Armengol & Matthew O. Jackson, 2004. "The Effects of Social Networks on Employment and Inequality," American Economic Review, American Economic Association, vol. 94(3), pages 426-454, June.
  19. 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.
  20. 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.
  21. Christofides, Tasos C. & Vaggelatou, Eutichia, 2004. "A connection between supermodular ordering and positive/negative association," Journal of Multivariate Analysis, Elsevier, vol. 88(1), pages 138-151, January.
  22. repec:oup:restud:v:77:y:2010:i:1:p:218-244 is not listed on IDEAS
  23. Levy, Haim & Paroush, Jacob, 1974. "Toward multivariate efficiency criteria," Journal of Economic Theory, Elsevier, vol. 7(2), pages 129-142, February.
  24. 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.
  25. Prat, Andrea, 2002. "Should a team be homogeneous?," European Economic Review, Elsevier, vol. 46(7), pages 1187-1207, July.
  26. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
  27. A. Atkinson, 2003. "Multidimensional Deprivation: Contrasting Social Welfare and Counting Approaches," Journal of Economic Inequality, Springer, vol. 1(1), pages 51-65, April.
  28. A. B. Atkinson & F. Bourguignon, 1982. "The Comparison of Multi-Dimensioned Distributions of Economic Status," Review of Economic Studies, Oxford University Press, vol. 49(2), pages 183-201.
  29. Ian Jewitt, 1987. "Risk Aversion and the Choice Between Risky Prospects: The Preservation of Comparative Statics Results," Review of Economic Studies, Oxford University Press, vol. 54(1), pages 73-85.
  30. Shaked, Moshe & Tong, Y. L., 1985. "Some partial orderings of exchangeable random variables by positive dependence," Journal of Multivariate Analysis, Elsevier, vol. 17(3), pages 333-349, December.
  31. Decancq, Koen, 2012. "Elementary multivariate rearrangements and stochastic dominance on a Fréchet class," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1450-1459.
  32. Joe, Harry, 1990. "Multivariate concordance," Journal of Multivariate Analysis, Elsevier, vol. 35(1), pages 12-30, October.
  33. Syngjoo Choi & Douglas Gale & Shachar Kariv, 2005. "Learning in Networks: An Experimental Study," Levine's Bibliography 122247000000000044, UCLA Department of Economics.
  34. Chew, Soo Hong & Sagi, Jacob S., 2012. "An inequality measure for stochastic allocations," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1517-1544.
  35. 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.
  36. Andrea Galeotti & Sanjeev Goyal & Matthew O. Jackson & Fernando Vega-Redondo & Leeat Yariv, 2008. "Network Games," Economics Working Papers ECO2008/07, European University Institute.
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:nwu:cmsems:1523. 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: (Fran Walker)

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.