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

Increasing interdependence of multivariate distributions

  • Meyer, Margaret
  • Strulovici, Bruno

Orderings of interdependence are useful in many economic contexts: 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 are equivalent, whereas for three dimensions, the first four are strictly ranked and the last two are equivalent, and for four or more dimensions, all five 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.sciencedirect.com/science/article/pii/S0022053111001281
Download Restriction: Full text for ScienceDirect subscribers only

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 147 (2012)
Issue (Month): 4 ()
Pages: 1460-1489

as
in new window

Handle: RePEc:eee:jetheo:v:147:y:2012:i:4:p:1460-1489
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622869

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. 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.
  2. Chew, Soo Hong & Sagi, Jacob S., 2012. "An inequality measure for stochastic allocations," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1517-1544.
  3. Margaret Meyer & Bruno Strulovici, 2013. "The Supermodular Stochastic Ordering," Economics Series Working Papers 655, University of Oxford, Department of Economics.
  4. Shimer, R. & Smith, L., 1997. "Assortative Matching and Search," Working papers 97-2b, Massachusetts Institute of Technology (MIT), Department of Economics.
  5. Jewitt, Ian, 1987. "Risk Aversion and the Choice between Risky Prospects: The Preservation of Comparative Statics Results," Review of Economic Studies, Wiley Blackwell, vol. 54(1), pages 73-85, January.
  6. 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.
  7. François Bourguignon & Satya Chakravarty, 2003. "The Measurement of Multidimensional Poverty," Journal of Economic Inequality, Springer, vol. 1(1), pages 25-49, April.
  8. Taizhong Hu & Alfred Müller & Marco Scarsini, 2002. "Some Counterexamples in Positive Dependence," ICER Working Papers - Applied Mathematics Series 28-2003, ICER - International Centre for Economic Research, revised Jul 2003.
  9. 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.
  10. R. Preston McAfee, 2002. "Coarse Matching," Econometrica, Econometric Society, vol. 70(5), pages 2025-2034, September.
  11. 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.
  12. 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.
  13. 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.
  14. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
  15. 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.
  16. 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.
  17. Meyer, Margaret A & Mookherjee, Dilip, 1987. "Incentives, Compensation, and Social Welfare," Review of Economic Studies, Wiley Blackwell, vol. 54(2), pages 209-26, April.
  18. Levy, Haim & Paroush, Jacob, 1974. "Toward multivariate efficiency criteria," Journal of Economic Theory, Elsevier, vol. 7(2), pages 129-142, February.
  19. Decancq, Koen, 2012. "Elementary multivariate rearrangements and stochastic dominance on a Fréchet class," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1450-1459.
  20. A. Atkinson, 2003. "Multidimensional Deprivation: Contrasting Social Welfare and Counting Approaches," Journal of Economic Inequality, Springer, vol. 1(1), pages 51-65, April.
  21. Andrea Galeotti & Sanjeev Goyal & Matthew O. Jackson & Fernando Vega-Redondo & Leeat Yariv, 2010. "Network Games," Review of Economic Studies, Oxford University Press, vol. 77(1), pages 218-244.
  22. repec:cor:louvrp:-2425 is not listed on IDEAS
  23. 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.
  24. 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.
  25. Bernard Caillaud & Jean Tirole, 2006. "Consensus building: How to persuade a group," PSE Working Papers halshs-00590459, HAL.
  26. Syngjoo Choi & Douglas Gale & Shachar Kariv, 2005. "Learning in Networks: An Experimental Study," Levine's Bibliography 122247000000000044, UCLA Department of Economics.
  27. Atkinson, Anthony B & Bourguignon, Francois, 1982. "The Comparison of Multi-Dimensioned Distributions of Economic Status," Review of Economic Studies, Wiley Blackwell, vol. 49(2), pages 183-201, April.
  28. 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.
  29. 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.
  30. 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.
  31. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
  32. Joe, Harry, 1990. "Multivariate concordance," Journal of Multivariate Analysis, Elsevier, vol. 35(1), pages 12-30, October.
  33. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
  34. Prat, Andrea, 2002. "Should a team be homogeneous?," European Economic Review, Elsevier, vol. 46(7), pages 1187-1207, July.
  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.
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:eee:jetheo:v:147:y:2012:i:4:p:1460-1489. 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: (Zhang, Lei)

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.