While English auctions are the most common in practice, their rules typically lack sufficient structure to yield a tractable theoretical model without significant abstractions. Rather than relying on one stylized model to provide an exact interpretation of the data, we explore an incomplete model based on two simple assumptions: bidders neither bid more than their valuations nor let an opponent win at a price they would be willing to beat. Focusing on the symmetric independent private values paradigm, we show that this limited structure enables construction of informative bounds on the distribution function char-acterizing bidder demand, on the optimal reserve price, and on the effects of observable covariates on bidder valuations. If the standard theoretical model happens to be the true model, our bounds collapse to the true features of interest. In contrast, when the true data-gen-erating process deviates in seemingly small ways from that implied by equilibrium in the standard theoretical model, existing methods can yield misleading results that need not even lie within our bounds. We report results from Monte Carlo experiments illustrating the perform-ance of our approach and comparing it to others. We apply our ap-

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We present new identification results for models of first-price, second-price, ascending (English), and descending (Dutch) auctions. We analyze a general specification of the latent demand and information structure, nesting as special cases the pure private values and pure common values models, and allowing both ex ante symmetric and asymmetric bidders. We address identification of a series of nested models and derive testable restrictions that enable discrimination between models on the basis of observed data. The simplest model–that of symmetric independent private values–is nonparametrically identified even if only the transaction price from each auction is observed. For more complex models, identification and testable restrictions are obtained when additional information of one or more of the following types is available: (i) the identity of the winning bidder or other bidders, (ii) one or more bids in addition to the transaction price; (iii) exogenous variation in the number of bidders; (iv) bidder-specific covariates; (v) auction-specific covariates. While many private values (PV) models are nonparametrically

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We study entry and bidding patterns in sealed bid and open auctions with heterogeneous bidders. Using data from U.S. Forest Service timber auctions, we document a set of systematic e¤ects of auction format: sealed bid auctions attract more small bidders, shift the allocation towards these bidders, and can also generate higher revenue. We propose a model, which extends the theory of private value auctions with heterogeneous bidders to capture participation decisions, that can account for these qualititive e¤ects of auction format. We then calibrate the model using parameters estimated from the data and show that the model can explain the quantitative e¤ects as well. Finally, we use the model to provide an assessment of bidder competitiveness, which has important consequences for auction choice. We thank Phil Haile, Guido Imbens, Richard Levin, Paul Milgrom, and Ilya Segal for helpful suggestions, and Jerry Hausman for advice at the early stages of this project. We are especially grateful to Rob Porter for providing detailed and insightful comments on an earlier draft of the

We develop a nonparametric approach that allows one to discriminate among alter-native models of entry in …rst-price auctions. Three models of entry are considered: Levin and Smith (1994), Samuelson (1985), and a new model in which the informa-tion received at the entry stage is imperfectly correlated with valuations. We derive testable restrictions that these three models impose on the quantiles of active bidders valuations, and develop nonparametric tests of these restrictions. We implement the tests on a dataset of highway procurement auctions in Oklahoma. Depending on the project size, we …nd no support for the Samuelson model, some support for the Levin and Smith model, and somewhat more support for the new model. 1

This paper studies the nonparametric identification of the first-price auction model with risk averse bidders within the private value paradigm. First, we show that the benchmark model is nonindentified from observed bids. We also derive the restrictions imposed by the model on observables and show that these restrictions are weak. Second, we establish the nonparametric identification of the bidders ’ utility function under exclusion restrictions. Our primary exclusion restriction takes the form of an exogenous bidders ’ participation, leading to a latent distribution of private values that is independent of the number of bidders. The key idea is to exploit the property that the bid distribution varies with the number of bidders while the private value distribution does not. We then extend these results to endogenous bidders ’ participation when the exclusion restriction takes the form of instruments that do not affect the bidders ’ private value distribution. Though derived for a benchmark model, our results extend to more general cases such as a binding reserve price, affiliated private values, and asymmetric bidders. Last, possible estimation methods are proposed.

In many procurement auctions, the bidders ’ unobserved costs depend both on a common shock and on idiosyncratic private information. Assuming a multiplicative structure, I derive sufficient conditions under which the model is identified and propose a nonparametric estimation procedure which results in uniformly consistent estimators of the cost components ’ distributions. The estimation procedure is applied to data from Michigan highway procurement auctions. Private information is estimated to account for 34 % of the variation in bidders ’ costs. It is shown that accounting for unobserved auction heterogeneity has important implications for the evaluation of the distribution of rents, efficiency, and optimal auction design.

The existence of collusion and heterogeneity across firms is known to introduce some asymmetry in bidding games. A major difficulty when considering asymmetric auctions is that the equilibrium strategies are solutions of an intractable system of differential equations. This paper proposes a simple method for estimating asymmetric first-price auctions within the affiliated private values (APV) paradigm. Specifically, we consider two types of bidders and derive the differential equations characterizing the Bayesian Nash equilibrium strategies. We show that these differential equations can be rewritten using the distribution of observed bids.

Abstract. We study entry and bidding patterns in sealed bid and open auctions. Using data from U.S. Forest Service timber auctions, we document a set of systematic e¤ects: sealed bid auctions attract more small bidders, shift the allocation towards these bidders, and can also generate higher revenue. A private value auction model with endogenous participation can account for these qualitative e¤ects of auction format. We estimate the model’s parameters and show that it can explain the quantitative e¤ects as well. We then use the model to assess bidder competitiveness, which has important consequences for auction design. We thank the editor Larry Katz and the referees for very helpful suggestions, and also Phil Haile, Jerry