Affiliation and Dependence in Economic Models
AbstractAffiliation 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 InfoPaper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1479.
Date of creation: 30 Sep 2009
Date of revision:
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Postal: Center for Mathematical Studies in Economics and Management Science, Northwestern University, 580 Jacobs Center, 2001 Sheridan Road, Evanston, IL 60208-2014
Web page: http://www.kellogg.northwestern.edu/research/math/
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Find related papers by JEL classification:
- C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
- D44 - Microeconomics - - Market Structure and Pricing - - - Auctions
- D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
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