Empirical Models of Auctions

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

Empirical Models of Auctions

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.

Nonparametric Identification of Multinomial Choice Demand Models with Heterogeneous Consumers

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

Identification in a Class of Nonparametric Simultaneous Equations Models

We consider identification in a class of nonseparable nonparametric simultaneous equations models introduced by Matzkin (2008). These models combine standard exclusion restrictions with a requirement that each structural error enter through a "residual index" function. We provide constructive proofs of identification under several sets of conditions, demonstrating tradeoffs between restrictions on the support of the instruments, restrictions on the joint distribution of the structural errors, and restrictions on the form of the residual index function.Simultaneous equations, Nonseparable models, Nonparametric identification

Identification of a Heterogeneous Generalized Regression Model with Group Effects

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

On the Empirical Content of Quantal Response Equilibrium

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

Nonparametric Tests for Common Values at First-Price Sealed-Bid Auctions

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.

On the Empirical Content of Quantal Response Equilibrium

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

Nonparametric Tests for Common Values in First-Price Sealed-Bid Auctions

We develop tests for common values at first-price sealed-bid auctions. Our tests are nonparametric, require observations 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 bidderis 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

Unobserved Heterogeneity in Auctions

A common concern in the empirical study of auctions is the likely presence of auction-specific factors that are common knowledge among bidders but unobserved to the econometrician. Such unobserved heterogeneity confounds attempts to uncover the underlying structure of demand and information, typically a primary feature of interest in an auction market. Unobserved heterogeneity presents a particular challenge in first-price auctions, where identification arguments rely on the econometrician’s ability to reconstruct from observables the conditional probabilities that entered each bidder’s equilibrium optimization problem; when bidders condition on unobservables, it is not obvious that this is possible. Here we discuss several approaches to identification developed in recent work on first-price auctions with unobserved heterogeneity. Despite the special challenges of this setting, all of the approaches build on insights developed in other areas of econometrics, including those on control functions, measurement error, and mixture models. Because each strategy relies on different combinations of model restrictions, technical assumptions, and data requirements, their relative attractiveness will vary with the application. However, this varied menu of results suggests both a type of robustness of identifiability and the potential for expanding the frontier with additional work