Identification of First-Price Auctions with Non-separable Unobserved Heterogeneity ∗

We propose a novel methodology for identification of first-price auctions, when bidders’ private valuations are independent conditional on one-dimensional unobserved heterogeneity. We extend the existing literature (Li and Vuong (1998), Krasnokutskaya (2011)) by allowing the unobserved heterogeneity to be nonseparable from bidders ’ valuations. Our central identifying assumption is that the distribution of bidder values is increasing in the state. When the state-space is finite, such monotonicity implies the completeness conditions needed for identification. When the state-space is continuous, we also provide some new sufficient conditions which ensure that completeness holds. Further, we extend our approach to the conditionally independent private values model of Li, Perrigne, and Vuong (2000), as well as to unobserved heterogeneity settings in which the implicit reserve price or the cost of bidding varies across auctions.