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Affiliation and Dependence in Economic Models

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  • Luciano I. de Castro
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    Abstract

    Affiliation has been a prominent assumption in the study of economic models with statistical dependence. Despite its large number of applications, especially in auction theory, affiliation has limitations that are important to be aware of. This paper shows that affiliation is a restrictive condition and the intuition usually given for its adoption may be misleading. Also, other usual justifications for affiliation are not compelling. Moreover, some implications of affiliation do not generalize to other definitions of positive dependence. These results show the need to consider alternatives to affiliation. The results of this paper suggest new directions for the study of dependence in economics. The main result classifies economic models of information and proves the existence of a minimally informative random variable that makes types conditionally independent. If this variable is known, then all results that are valid under independence are also valid for these models with statistically dependent types. Complementing this result, we describe a method to study general forms of dependence using grid distributions, which are distributions whose densities are constant in squares. This method allows a comprehensive investigation on the revenue ranking of auctions under general dependence.

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    Bibliographic Info

    Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1479.

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    Date of creation: 30 Sep 2009
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    Handle: RePEc:nwu:cmsems:1479

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    Related research

    Keywords: affiliation; positive dependence; statistical dependence of types; conditional independence; de Finetti’s theorem; minimally informative random variable; auctions; pure strategy equilibrium; revenue ranking;

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    1. Hubbard, Timothy P. & Li, Tong & Paarsch, Harry J., 2011. "Semiparametric Estimation in Models of First-Price, Sealed-Bid Auctions with Affiliation," CEI Working Paper Series 2010-10, Center for Economic Institutions, Institute of Economic Research, Hitotsubashi University.
    2. Monteiro, Paulo Klinger & Moreira, Humberto, 2006. "First-price auctions without affiliation," Economics Letters, Elsevier, vol. 91(1), pages 1-7, April.
    3. Olivier Gossner & Ehud Kalai & Robert Weber, 2009. "Information Independence and Common Knowledge," Econometrica, Econometric Society, vol. 77(4), pages 1317-1328, 07.
    4. Paul Klemperer, 2004. "Auctions: Theory and Practice," Economics Papers 2004-W09, Economics Group, Nuffield College, University of Oxford.
    5. Bergin, James, 2001. "Common Knowledge with Monotone Statistics," Econometrica, Econometric Society, vol. 69(5), pages 1315-32, September.
    6. Luciano I. de Castro, 2007. "Affiliation, equilibrium existence and the revenue ranking of auctions," Economics Working Papers we074622, Universidad Carlos III, Departamento de Economía.
    7. Van Zandt, Timothy & Vives, Xavier, 2007. "Monotone equilibria in Bayesian games of strategic complementarities," Journal of Economic Theory, Elsevier, vol. 134(1), pages 339-360, May.
    8. Castro, Luciano I. De & Paarsch, Harry J., 2009. "Testing Affiliation in Private-values Models of First-price Auctions Using Grid Distributions," CEI Working Paper Series 2009-11, Center for Economic Institutions, Institute of Economic Research, Hitotsubashi University.
    9. John McMillan, 1994. "Selling Spectrum Rights," Journal of Economic Perspectives, American Economic Association, vol. 8(3), pages 145-162, Summer.
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