Testing affiliation in private-values models of first-price auctions   using grid distributions
  Within the private-values paradigm, we construct a tractable empirical model of equilibrium behavior at first-price auctions when bidders' valuations are potentially dependent, but not necessarily affiliated. We develop a test of affiliation and apply our framework to data from low-price, sealed-bid auctions held by the Department of Transportation in the State of Michigan to procure road-resurfacing services: we do not reject the hypothesis of affiliation in cost signals. 
Luciano I. de Castro, Harry J. Paarsch
stat.AP