Incomplete English auction models with heterogeneity

This paper studies identification and estimation of the distribution of bidder valuations in an incomplete model of English auctions. As in Haile and Tamer (2003) bidders are assumed to (i) bid no more than their valuations and (ii) never let an opponent win at a price they are willing to beat. Unlike the model studied by Haile and Tamer (2003), the requirement of independent private values is dropped, enabling the use of these restrictions on bidder behavior with affiliated private values, for example through the presence of auction specific unobservable heterogeneity. In addition, a semiparametric index restriction on the effect of auction-specific observable heterogeneity is incorporated, which, relative to nonparametric methods, can be helpful in alleviating the curse of dimensionality with a moderate or large number of covariates. The identification analysis employs results from Chesher and Rosen (2017) to characterize identified sets for bidder valuation distributions and functionals thereof.