Inference with an Incomplete Model of English Auctions

Abstract

Standard models of English auctions abstract from actual practice by assuming that bidders continuously affirm their willingness to pay as the price rises exogenously. We show that one need not rely on these models to make useful inferences on the latent demand structure at private value English auctions. Weak implications of rational bidding provide sufficient structure to nonparametrically bound the distribution of bidder valuations and the optimal reserve price, based on observed bids. If auctions and/or bidders differ in observable characteristics, our approach also yields bounds on parameters characterizing the effects of observables on valuations. Whenever observed bids are consistent with the standard model, the identified bounds collapse to the true distribution (or parameters) of interest. Throughout, we propose estimators that consistently estimate the identified features. We conduct a number of Monte Carlo experiments and apply our methods to data from U.S. Forest Service timber auctions in order to assess reserve price policy.