Identification of the Joint Value Distribution from Auction Data

This paper presents results showing sufficient conditions for identifying the joint distribution of valuations for differentiated products using secondprice auction data. That is, the paper suggests methods for estimating the cross-elasticity of demand between products using on-line auction data. The paper shows that observed choice can be combined with information on order statistics to estimate part of the joint distribution. It further shows that the copula function can be nonparametrically identified and thus the complete joint value distribution is nonparametrically identified. The results are generalized to cases where the exact number of bidders is unobserved, the exact choices are unobserved and where bidders are heterogenous. ∗Thanks to Hiro Kasahara, Kyoo il Kim, Rob McMillan, Katja Seim, Art Shneyerov, Jeff Wooldridge, Robert Zeithammer, David Zimmer, participants at the 2009 IIOC and the University of Wisconsin IO Seminar and the many other that I have talked to about this question. Note that this paper does not necessarily represent the views of the Commission or any individual Commissioners. All remaining errors are my own.