[go: up one dir, main page]
More Web Proxy on the site http://driver.im/
IDEAS home Printed from https://ideas.repec.org/a/eee/jetheo/v147y2012i4p1460-1489.html
   My bibliography  Save this article

Increasing interdependence of multivariate distributions

Author

Listed:
  • Meyer, Margaret
  • Strulovici, Bruno
Abstract
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.

Suggested Citation

  • Meyer, Margaret & Strulovici, Bruno, 2012. "Increasing interdependence of multivariate distributions," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1460-1489.
    • Handle: RePEc:eee:jetheo:v:147:y:2012:i:4:p:1460-1489
    DOI: 10.1016/j.jet.2011.09.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0022053111001281
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jet.2011.09.001?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. Acharya, Viral V., 2009. "A theory of systemic risk and design of prudential bank regulation," Journal of Financial Stability, Elsevier, vol. 5(3), pages 224-255, September.
    3. Robert Shimer & Lones Smith, 2000. "Assortative Matching and Search," Econometrica, Econometric Society, vol. 68(2), pages 343-370, March.
    4. Hennessy, David A. & Lapan, Harvey E., 2003. "Definition of 'More Systematic Risk' With Some Welfare Implications, A," Staff General Research Papers Archive 10110, Iowa State University, Department of Economics.
    5. Gajdos, Thibault & Maurin, Eric, 2004. "Unequal uncertainties and uncertain inequalities: an axiomatic approach," Journal of Economic Theory, Elsevier, vol. 116(1), pages 93-118, May.
    6. Margaret Meyer & Bruno Strulovici, 2013. "The Supermodular Stochastic Ordering," Discussion Papers 1563, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    7. 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.
    8. Calvo-Armengol, Antoni & Jackson, Matthew O., 2007. "Networks in labor markets: Wage and employment dynamics and inequality," Journal of Economic Theory, Elsevier, vol. 132(1), pages 27-46, January.
    9. Bernard Caillaud & Jean Tirole, 2007. "Consensus Building: How to Persuade a Group," American Economic Review, American Economic Association, vol. 97(5), pages 1877-1900, December.
    10. A. B. Atkinson & F. Bourguignon, 1982. "The Comparison of Multi-Dimensioned Distributions of Economic Status," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 49(2), pages 183-201.
    11. 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.
    12. Joe, Harry, 1990. "Multivariate concordance," Journal of Multivariate Analysis, Elsevier, vol. 35(1), pages 12-30, October.
    13. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
    14. 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.
    15. Decancq, Koen, 2012. "Elementary multivariate rearrangements and stochastic dominance on a Fréchet class," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1450-1459.
    16. 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.
    17. 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.
    18. Andrea Galeotti & Sanjeev Goyal & Matthew O. Jackson & Fernando Vega-Redondo & Leeat Yariv, 2010. "Network Games," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 77(1), pages 218-244.
    19. Luciano I. de Castro, 2009. "Affiliation and Dependence in Economic Models," Discussion Papers 1479, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    20. 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.
    21. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    22. repec:cor:louvrp:-2425 is not listed on IDEAS
    23. R. Preston McAfee, 2002. "Coarse Matching," Econometrica, Econometric Society, vol. 70(5), pages 2025-2034, September.
    24. François Bourguignon & Satya R. Chakravarty, 2019. "The Measurement of Multidimensional Poverty," Themes in Economics, in: Satya R. Chakravarty (ed.), Poverty, Social Exclusion and Stochastic Dominance, pages 83-107, Springer.
    25. Margaret A. Meyer & Dilip Mookherjee, 1987. "Incentives, Compensation, and Social Welfare," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(2), pages 209-226.
    26. repec:bla:econom:v:70:y:2003:i:277:p:19-29 is not listed on IDEAS
    27. repec:bla:econom:v:70:y:2003:i:279:p:493-507 is not listed on IDEAS
    28. Ian Jewitt, 1987. "Risk Aversion and the Choice Between Risky Prospects: The Preservation of Comparative Statics Results," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(1), pages 73-85.
    29. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    30. Chew, Soo Hong & Sagi, Jacob S., 2012. "An inequality measure for stochastic allocations," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1517-1544.
    31. Raquel Fernández & Jordi Gali, 1999. "To Each According to …? Markets, Tournaments, and the Matching Problem with Borrowing Constraints," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(4), pages 799-824.
    32. 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.
    33. Donald M. Topkis, 1978. "Minimizing a Submodular Function on a Lattice," Operations Research, INFORMS, vol. 26(2), pages 305-321, April.
    34. Prat, Andrea, 2002. "Should a team be homogeneous?," European Economic Review, Elsevier, vol. 46(7), pages 1187-1207, July.
    35. 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.
    36. 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.
    37. Levy, Haim & Paroush, Jacob, 1974. "Toward multivariate efficiency criteria," Journal of Economic Theory, Elsevier, vol. 7(2), pages 129-142, February.
    38. 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.
    39. Syngjoo Choi & Douglas Gale & Shachar Kariv, 2005. "Learning in Networks: An Experimental Study," Levine's Bibliography 122247000000000044, UCLA Department of Economics.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Barney Hartman‐Glaser & Benjamin Hébert, 2020. "The Insurance Is the Lemon: Failing to Index Contracts," Journal of Finance, American Finance Association, vol. 75(1), pages 463-506, February.
    2. Carole Bernard & Christoph M. Rheinberger & Nicolas Treich, 2018. "Catastrophe Aversion and Risk Equity in an Interdependent World," Management Science, INFORMS, vol. 64(10), pages 4490-4504, October.
    3. 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.
    4. Mira Frick & Ryota Iijima & Yuhta Ishii, 2018. "Dispersed Behavior and Perceptions in Assortative Societies," Cowles Foundation Discussion Papers 2128R2, Cowles Foundation for Research in Economics, Yale University, revised Oct 2021.
    5. Amir, Rabah & Lazzati, Natalia, 2016. "Endogenous information acquisition in Bayesian games with strategic complementarities," Journal of Economic Theory, Elsevier, vol. 163(C), pages 684-698.
    6. Gajdos, Thibault & Weymark, John A., 2012. "Introduction to inequality and risk," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1313-1330.
    7. Christian Gollier, 2020. "Aversion to risk of regret and preference for positively skewed risks," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(4), pages 913-941, November.
    8. Andres Espitia, 2024. "Confidence and Organizations," CRC TR 224 Discussion Paper Series crctr224_2024_521, University of Bonn and University of Mannheim, Germany.
    9. Rene Kirkegaard, 2023. "Financial Constraints and Multivariate Incomplete Information in the Mixture Model of Contests," Working Papers 2402, University of Guelph, Department of Economics and Finance.
    10. Arieli, Itai & Babichenko, Yakov, 2019. "Private Bayesian persuasion," Journal of Economic Theory, Elsevier, vol. 182(C), pages 185-217.
    11. Christoffer Sonne-Schmidt & Finn Tarp & Lars Peter Østerdal, 2016. "Ordinal Bivariate Inequality: Concepts and Application to Child Deprivation in Mozambique," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 62(3), pages 559-573, September.
    12. Gollier, Christian, 2016. "Gamma discounters are short-termist," Journal of Public Economics, Elsevier, vol. 142(C), pages 83-90.
    13. Chollete, Lorán & de la Peña, Victor & Klass, Michael, 2023. "The price of independence in a model with unknown dependence," Mathematical Social Sciences, Elsevier, vol. 123(C), pages 51-58.
    14. Christoffer Sonne-Schmidt & Finn Tarp & Lars Peter Østerdal, 2013. "Ordinal Multidimensional Inequality," WIDER Working Paper Series wp-2013-097, World Institute for Development Economic Research (UNU-WIDER).
    15. Decancq, Koen, 2012. "Elementary multivariate rearrangements and stochastic dominance on a Fréchet class," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1450-1459.
    16. Dertwinkel-Kalt, Markus & Ebert, Sebastian & Köster, Mats, 2023. "On correlated lotteries in economic applications," Journal of Economic Behavior & Organization, Elsevier, vol. 215(C), pages 292-306.
    17. Sonne-Schmidt, Christoffer & Tarp, Finn & Østerdal, Lars Peter, 2013. "Ordinal Multidimensional Inequality," WIDER Working Paper Series 097, World Institute for Development Economic Research (UNU-WIDER).
    18. He, Wei & Li, Jiangtao, 2022. "Correlation-robust auction design," Journal of Economic Theory, Elsevier, vol. 200(C).
    19. Margaret Meyer & Bruno Strulovici, 2013. "The Supermodular Stochastic Ordering," Discussion Papers 1563, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    20. Guy Kaplanski & Haim Levy, 2017. "Envy and Altruism: Contrasting Bivariate and Univariate Prospect Preferences," Scandinavian Journal of Economics, Wiley Blackwell, vol. 119(2), pages 457-483, April.
    21. Awaya, Yu & Do, Jihwan, 2022. "Incentives under equal-pay constraint and subjective peer evaluation," Games and Economic Behavior, Elsevier, vol. 135(C), pages 41-59.
    22. Francesco Andreoli & Claudio Zoli, 2020. "From unidimensional to multidimensional inequality: a review," METRON, Springer;Sapienza Università di Roma, vol. 78(1), pages 5-42, April.
    23. Dorinel Bastide & St'ephane Cr'epey, 2024. "Provisions and Economic Capital for Credit Losses," Papers 2401.07728, arXiv.org, revised Jan 2024.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Meyer, Margaret & Strulovici, Bruno, 2013. "The Supermodular Stochastic Ordering," CEPR Discussion Papers 9486, C.E.P.R. Discussion Papers.
    2. Margaret Meyer & Bruno Strulovici, 2013. "Beyond Correlation: Measuring Interdependence Through Complementarities," Economics Series Working Papers 655, University of Oxford, Department of Economics.
    3. Gajdos, Thibault & Weymark, John A., 2012. "Introduction to inequality and risk," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1313-1330.
    4. Kobus, Martyna & Kurek, Radosław, 2018. "Copula-based measurement of interdependence for discrete distributions," Journal of Mathematical Economics, Elsevier, vol. 79(C), pages 27-39.
    5. Francesco Andreoli & Claudio Zoli, 2020. "From unidimensional to multidimensional inequality: a review," METRON, Springer;Sapienza Università di Roma, vol. 78(1), pages 5-42, April.
    6. Aaberge, Rolf & Peluso, Eugenio & Sigstad, Henrik, 2019. "The dual approach for measuring multidimensional deprivation: Theory and empirical evidence," Journal of Public Economics, Elsevier, vol. 177(C), pages 1-1.
    7. Koen Decancq, 2020. "Measuring cumulative deprivation and affluence based on the diagonal dependence diagram," METRON, Springer;Sapienza Università di Roma, vol. 78(2), pages 103-117, August.
    8. Thibault Gajdos & John Weymark, 2005. "Multidimensional generalized Gini indices," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(3), pages 471-496, October.
    9. Rolf Aaberge & Eugenio Peluso & Henrik Sigstad, 2015. "The dual approach for measuring. Multidimesional deprivation and poverty," Discussion Papers 820, Statistics Norway, Research Department.
    10. 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.
    11. Cesar Calvo & Stefan Dercon, 2013. "Vulnerability to individual and aggregate poverty," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(4), pages 721-740, October.
    12. Rolf Aaberge & Andrea Brandolini, 2014. "Multidimensional poverty and inequality," Temi di discussione (Economic working papers) 976, Bank of Italy, Economic Research and International Relations Area.
    13. Rolf Aaberge & Eugenio Peluso, 2011. "A Counting Approach for Measuring Multidimensional Deprivation," Working Papers 07/2011, University of Verona, Department of Economics.
    14. Suman Seth, 2013. "A class of distribution and association sensitive multidimensional welfare indices," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 11(2), pages 133-162, June.
    15. Croci Angelini, Elisabetta & Michelangeli, Alessandra, 2012. "Axiomatic measurement of multidimensional well-being inequality: Some distributional questions," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 41(5), pages 548-557.
    16. Christoffer Sonne-Schmidt & Finn Tarp & Lars Peter Østerdal, 2016. "Ordinal Bivariate Inequality: Concepts and Application to Child Deprivation in Mozambique," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 62(3), pages 559-573, September.
    17. Magdalou, Brice, 2021. "A model of social welfare improving transfers," Journal of Economic Theory, Elsevier, vol. 196(C).
    18. Christoph Heinzel, 2014. "Term structure of discount rates under multivariate s-ordered consumption growth," Working Papers SMART 14-01, INRAE UMR SMART.
    19. Koen Decancq & María Ana Lugo, 2009. "Measuring inequality of well-being with a correlation-sensitive multidimensional Gini index," Working Papers 124, ECINEQ, Society for the Study of Economic Inequality.
    20. Galichon, Alfred & Henry, Marc, 2012. "Dual theory of choice with multivariate risks," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1501-1516.

    More about this item

    Keywords

    Dependence ordering; Stochastic orders; Supermodularity; Weak association; Concordance;
    All these keywords.

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. 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.

    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 CitEc recognized a bibliographic reference but did not link an item in RePEc 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622869 .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.