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Title:Affiliation and dependence in economic models PDF Logo
Authors:de Castro, Luciano I.
Issue Date:2009
Series/Report no.:Discussion Paper, Center for Mathematical Studies in Economics and Management Science 1479
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.
Subjects:affiliation
positive dependence
statistical dependence of types
conditional independence
de Finetti's theorem
minimally informative random variable
auctions
pure strategy equilibrium
revenue ranking
JEL:C62
C72
D44
D82
Document Type:Working Paper
Appears in Collections:Discussion Papers, Kellogg School of Management, Northwestern University

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