Inference with an Incomplete Model of English Auctions

Standard models of English auctions abstract from actual practice by assuming that bidders continuously affirm their willingness to pay as the price rises exogenously. This creates a significant mismatch between the bids envisioned in theory and those observed in practice, limiting the usefulness of the theory as a basis for a structural econometric model. We show that one often can obtain tight bounds on the structural objects of interest without resorting to dubious identifying assumptions based on existing models. Very weak assumptions provide sufficient structure to enable nonparameteric identification of bounds on the distribution of bidder valuations and the optimal reserve price. When auctions differ in observable characteristics, bounds on parameters of a semiparametric model can also be identified. We apply our estimation approach to data from U.S. Forest Service timber auctions.