Identification in the Roy Model with an Application to Auctions

The paper presents conditions for non-parametric identification of a joint distribution when the marginal distributions are identified and the joint distribution is partially identified. Specifically, the paper considers the problem of estimating a J-dimensional Roy Model and shows that the joint distribution is identified up to an approximation. The paper extends Heckman and Honore (1990) by providing an additional identification result with reasonable data requirements and without strong parametric assumptions. The result is applied to private value sealed bid auctions where bidders face competing auctions for substitutes, such as in auction platforms like eBay or Google Adwords. ∗Thanks to Matthew Chesnes, Ian Gale, Hiro Kasahara, Kyoo il Kim, Greg Lewis, Rob McMillan, Chris Metcalf, Katja Seim, Art Shneyerov, Jeff Wooldridge, Robert Zeithammer, David Zimmer, participants at the 2009 IIOC, Wisconsin, Minnesota, DOJ, Cornell Johnson School, as well as the many others that I have talked to about this question. I am also grateful to an anonymous reviewer who pointed to the connection between the auction problem and the Roy model. The views expressed in this article are those of the author and do not necessarily reflect those of the Federal Trade Commission. All remaining errors are my own.