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Abstract:
We present new identification results for models of first-price, second-price, ascending (English), and descending (Dutch) auctions. We analyze a general specification of bidders' preferences and the underlying 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 such models and propose strategies for discriminating between them on the basis of observed data. In the simplest case, the symmetric independent private values model is nonparametrically identified even if only the transaction price from each auction is observed. For more complex models, we provide conditions for identification and testing when additional information of one of the following types is available: (i) one or more bids in addition to the transaction price; (ii) exogenous variation in the number of bidders; (iii) bidder-specific covariates that shift the distribution of valuations; (iv) the ex post realization of the value of the object sold. Our results include new tests that distinguish between private and common values models.

Auctions, nonparametric identification and testing, private values, common values, asymmetric bidders, unobserved bids, order statistics

Abstract:
The quantal response equilibrium (QRE) notion of McKelvey and Palfrey (1995) has recently attracted considerable attention, due in part to its widely documented ability to rationalize observed behavior in games played by experimental subjects. However, even with strong a priori restrictions on unobservables, QRE imposes no falsifiable restrictions: it can rationalize any distribution of behavior in any normal form game. After demonstrating this, we discuss several approaches to testing QRE under additional maintained assumptions.

Quantal response equilibrium, Falsifiability, Testable restrictions, Regular quantal response equilibrium, Rank-cumulative probabilities, Block-Marschak polynomials

Abstract:
The quantal response equilibrium (QRE) notion of McKelvey and Palfrey (1995) has recently attracted considerable attention, due largely to its widely documented ability to rationalize observed behavior in games played by experimental subjects. We show that this ability to fit the data, as typically measured in this literature, is uninformative. Without a priori distributional assumptions, a QRE can match any distribution of behavior by each player in any normal form game. We discuss approaches that might be taken to provide valid empirical evaluation of the QRE and discuss its potential value as an approximating empirical structure.

quantal response equilibrium, testable restrictions, comparative statics

Abstract:
Many important economic questions arising in auctions can be answered only with knowledge of the underlying primitive distributions governing bidder demand and information. An active literature has developed aiming to estimate these primitives by exploiting restrictions from economic theory as part of the econometric model used to interpret auction data. We review some highlights of this recent literature, focusing on identification and empirical applications. We describe three insights that underlie much of the recent methodological progress in this area and discuss some of the ways these insights have been extended to richer models allowing more convincing empirical applications. We discuss several recent empirical studies using these methods to address a range of important economic questions.

Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.

Abstract:
Many important economic questions arising in auctions can be answered only with knowledge of the underlying primitive distributions governing bidder demand and information. An active literature has developed aiming to estimate these primitives by exploiting restrictions from economic theory as part of the econometric model used to interpret auction data. We review some highlights of this recent literature, focusing on identification and empirical applications. We describe three insights that underlie much of the recent methodological progress in this area and discuss some of the ways these insights have been extended to richer models allowing more convincing empirical applications. We discuss several recent empirical studies using these methods to address a range of important economic questions.

Auctions, identification, estimation, testing

Abstract:
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 characterizing 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-generating 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 performance of our approach and comparing it to others. We apply our approach to U.S. Forest Service timber auctions to evaluate reserve price policy.

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.

English auctions, incomplete models, nonparametric identification and estimation, bounds analysis, timber auctions

Abstract:
This paper studies auctions held before bidders are sure of the values they place on the object for sale, leaving potential gains to subsequent resale trade. While important insights from models of auctions without resale carry over, equilibrium bidding can be fundamentally altered by the endogeneity of valuations and the informational linkages between primary and secondary markets. As a result, models ignoring resale may often misguide policy and interpretation of bidding data. Furthermore, results regarding players' incentives to signal through their bids, the effects of resale on auction revenues, an d revenue comparisons between standard auctions depend on the structure of the secondary market.

Abstract:
We develop tests for common values at first-price sealed-bid auctions. Our tests are nonparametric, require observation only of the bids submitted at each auction, and are based on the fact that the "winner's curse" arises only in common values auctions. The tests build on recently developed methods for using observed bids to estimate each bidder's conditional expectation of the value of winning the auction. Equilibrium behavior implies that in a private values auction these expectations are invariant to the number of opponents each bidder faces, while with common values they are decreasing in the number of opponents. This distinction forms the basis of our tests. We consider both exogenous and endogenous variation in the number of bidders. Monte Carlo experiments show that our tests can perform well in samples of moderate sizes. We apply our tests to two different types of U.S. Forest Service timber auctions. For unit-price ("scaled") sales often argued to fit a private values model, our tests consistently fail to find evidence of common values. For "lumpsum" sales, where a priori arguments for common values appear stronger, our tests yield mixed evidence against the private values hypothesis.

First-price auctions, Common values, Private values, Nonparametric testing, Winner's curse, Stochastic dominance, Endogenous participation, Timber auctions

Abstract:
We characterize the set of perfect Bayesian equilibria in symmetric separating strategies in Milgrom and Weber's (1982) model of English auctions. There is a continuum of such equilibria. The equilibrium derived by Milgrom and Weber is that in which bids are maximal. Only in the case of pure private values does a restriction to weakly undominated strategies select a unique equilibrium. This has important implications for empirical studies of English auctions, particularly outside the pure private values paradigm.

Abstract:
We develop tests for common values at first-price sealed-bid auctions. Our tests are nonparametric, require observation only of the bids submitted at each auction, and are based on the fact that the 'winner's curse' arises only in common values auctions. The tests build on recently developed methods for using observed bids to estimate each bidder's conditional expectation of the value of winning the auction. Equilibrium behavior implies that in a private values auction these expectations are invariant to the number of opponents each bidder faces, while with common values they are decreasing in the number of opponents. This distinction forms the basis of our tests. We consider both exogenous and endogenous variation in the number of bidders. Monte Carlo experiments show that our tests can perform well in samples of moderate sizes. We apply our tests to two different types of U.S. Forest Service timber auctions. For unit-price ('scaled') sales often argued to fit a private values model, our tests consistently fail to find evidence of common values. For 'lumpsum' sales, where a priori arguments for common values appear stronger, our tests yield mixed evidence against the private values hypothesis.

Abstract:
We consider identification in a "generalized regression model" (Han, 1987) for panel settings in which each observation can be associated with a "group" whose members are subject to a common unobserved shock. Common examples of groups include markets, schools or cities. The model is fully nonparametric and allows for the endogeneity of group-specific observables, which might include prices, policies, and/or treatments. The model features heterogeneous responses to observables and unobservables, and arbitrary heteroskedasticity. We provide sufficient conditions for full identification of the model, as well as weaker conditions sufficient for identification of the latent group effects and the distribution of outcomes conditional on covariates and the group effect.

nonparametric identification, binary choice, threshold crossing, censored regression, proportional hazard model

Abstract:
We consider identification of nonparametric random utility models of multinomial choice using "micro data," i.e., observation of the characteristics and choices of individual consumers. Our model of preferences nests random coefficients discrete choice models widely used in practice with parametric functional form and distributional assumptions. However, the model is nonparametric and distribution free. It allows choice-specific unobservables, endogenous choice characteristics, unknown heteroskedasticity, and high-dimensional correlated taste shocks. Under standard "large support" and instrumental variables assumptions, we show identifiability of the random utility model. We demonstrate robustness of these results to relaxation of the large support condition and show that when it is replaced with a weaker "common choice probability" condition, the demand structure is still identified. We show that key maintained hypotheses are testable.

Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.

Abstract:
We consider identification of nonparametric random utility models of multinomial choice using 'micro data,' i.e., observation of the characteristics and choices of individual consumers. Our model of preferences nests random coefficients discrete choice models widely used in practice with parametric functional form and distributional assumptions. However, the model is nonparametric and distribution free. It allows choice-specific unobservables, endogenous choice characteristics, unknown heteroskedasticity, and high-dimensional correlated taste shocks. Under standard 'large support' and instrumental variables assumptions, we show identifiability of the random utility model. We demonstrate robustness of these results to relaxation of the large support condition and show that when it is replaced with a weaker 'common choice probability' condition, the demand structure is still identified. We show that key maintained hypotheses are testable.

Nonparametric identification, Discrete choice demand, Differentiated products