Matthew L. Gentry

Identification in Auctions with Selective Entry

This paper considers nonparametric identification of a two-stage entry and bidding game we call the Affiliated-Signal (AS) model. This model assumes that potential bidders have private values, observe signals of their values prior to entry, and then choose whether to undertake a costly entry process, but imposes only minimal structure on the relationship between signals and values. It thereby nests a wide range of entry processes, including in particular the Samuelson (1985) and Levin and Smith (1994) models as special cases. Working within the AS model, we map variation in factors affecting entry behavior (potential competition or entry costs) into identified bounds on model fundamentals. These bounds are constructive, collapse to point identification when available entry variation is continuous, and can readily be refined to produce the pointwise sharp identified set. We then extend our core results to accommodate nonseparable unobserved auction-level heterogeneity and potential endogeneity of entry shifters, thereby establishing a formal identification framework for structural analysis of auctions with selective entry.

Entry and Competition in Takeover Auctions

We estimate the degree of uncertainty faced by potential bidders in takeover auctions and quantify how it affects prices in auctions and negotiations. The high degree of uncertainty revealed by our structural estimation encourages entry in auctions but reduces a target’s bargaining power in negotiations. In the aggregate, auctions and negotiations produce similar prices, even though auctions are preferred in takeover markets with high uncertainty, while the reverse is true for negotiations. Firm characteristics predict pre-entry uncertainty and thus are informative about the relative performance of auctions and negotiations for individual targets.

Auctions with selective entry

We consider auctions with entry based on a general analytical framework we call the Arbitrarily Selective (AS) model. We characterize symmetric equilibrium in a broad class of standard auctions within this framework, in the process extending the classic revenue equivalence results of Myerson (1981), Riley and Samuelson (1981) and Levin and Smith (1994) to environments with endogenous and arbitrarily selective entry. We also explore the relationship between revenue maximization and efficiency, showing that a revenue maximizing seller will typically employ both higher-than-efficient reservation prices and higher-than-efficient entry fees.

Displays, Sales, and In-Store Search in Retail Markets

This paper develops and estimates a structural model of differentiated-products demand in an environment with in-store displays and costly consumer price search. This investigation is motivated by two stylized facts on retail markets. First, the prevalence of retail “sales” means that relative prices in most product categories vary substantially from week to week. Second, quantities sold often respond at least as much to changes in relative locations (in-store displays) as to changes in relative prices. The model proposed here incorporates both effects: sale-induced price variation provides a reason to search, and displays convey information about prevailing prices. This model is then applied to store-level data on laundry detergent purchases, using short-run price fluctuation to recover preference parameters and short-run display fluctuations to recover search parameters. The resulting structural estimates suggest that information frictions have substantial effects on purchase outcomes, with roughly 52 percent of consumers having positive search costs and a mean search cost of roughly

Structural Econometrics of Auctions: A Review

1.68 among this sub-population. I further explore the potential relationship between consumer search and demand analysis, and find that accounting for displays and other promotions substantially lowers elasticity estimates.

Identification and Inference in First-Price Auctions with Risk-Averse Bidders and Selective Entry

We review the literature concerned with the structural econometrics of observational data from auctions, discussing the problems that have been solved and highlighting those that remain unsolved as well as suggesting areas for future research. Where appropriate, we discuss different modeling choices as well as the fragility or robustness of different methods.

On Monotone Strategy Equilibria in Simultaneous Auctions for Complementary Goods

We study identification and estimation in first-price auctions with risk averse bidders and selective entry, building on a flexible entry and bidding framework we call the Affiliated Signal with Risk Aversion (AS-RA) model. This framework extends the AS model of Gentry and Li (2014) to accommodate arbitrary bidder risk aversion, thereby nesting a variety of standard models as special cases. It poses, however, a unique methodological challenge – existing results on identification with risk aversion fail in the presence of selection, while the selection-robust bounds of Gentry and Li (2014) fail in the presence of risk aversion. Motivated by this problem, we translate excludable variation in potential competition into identified sets for AS-RA primitives under various classes of restrictions on the model. We show that a single parametric restriction – on the copula governing selection into entry – is typically sufficient to restore point identification of all primitives. In contrast, a parametric form for utility yields point identification of the utility function but only partial identification of remaining primitives. Finally, we outline a simple semiparametric estimator combining Constant Relative Risk Aversion utility with a parametric signal-value copula. Simulation evidence suggests that this estimator performs very well even in small samples, underscoring the practical value of our identification results.

Preferences and Performance in Simultaneous First-Price Auctions: A Structural Analysis

We explore existence and properties of equilibrium when N>1 bidders compete for L>1 objects via simultaneous but separate auctions. Bidders have private combinatorial valuations over all sets of objects they could win, and objects are complements in the sense that these valuations are supermodular in the set of objects won. We provide a novel partial order on types under which best replies are monotone, and demonstrate that Bayesian Nash equilibria which are monotone with respect to this partial order exist on any finite bid lattice. We apply this result to show existence of monotone Bayesian Nash equilibria in continuous bid spaces when a single global bidder competes for L objects against many local bidders who bid for single objects only, highlighting the step in this extension which fails with multiple global bidders. We therefore instead consider an alternative equilibrium with endogenous tie-breaking building on Jackson, Simon, Swinkels and Zame (2002), and demonstrate that this exists in general. Finally, we explore efficiency in simultaneous auctions with symmetric bidders, establishing novel sufficient conditions under which inefficiency in expectation approaches zero as the number of bidders increases.

A new class of asymptotically efficient estimators for moment condition models

Motivated by the empirical prevalence of simultaneous bidding across a wide range of auction markets, we develop and estimate a structural model of strategic interaction in simultaneous first-price auctions when objects are heterogeneous and bidders have preferences over combinations. In this model, bidders have stochastic private valuations for each object and stable incremental preferences over combinations, nesting the standard separable model as the special case when incremental preferences over combinations are zero. We establish non-parametric identification of primitives in this model under standard exclusion restrictions, providing a basis for both estimation and testing of preferences over combinations. We then apply our model to data on Michigan Department of Transportation (MDOT) highway procurement auctions, quantifying the magnitude of cost synergies and evaluating the performance of the simultaneous first-price mechanism in the MDOT marketplace.Motivated by the empirical prevalence of simultaneous bidding across a wide range of auction markets, we develop and estimate a structural model of strategic interaction in simultaneous first-price auctions when objects are heterogeneous and bidders have preferences over combinations. We begin by proposing a general theoretical model of bidding in simultaneous first price auctions, exploring properties of best responses and existence of equilibrium within this environment. We then specialize this model to an empirical framework in which bidders have stochastic private valuations for each object and stable incremental preferences over combinations; this immediately reduces to the standard separable model when incremental preferences over combinations are zero. We establish non-parametric identification of the resulting model under standard exclusion restrictions, thereby providing a basis for both testing on and estimation of preferences over combinations. We then apply our model to data on Michigan Department of Transportation highway procurement auctions, we quantify the magnitude of cost synergies and assess possible efficiency losses arising from simultaneous bidding in this market. ∗We are grateful to Philip Haile, Ken Hendricks, Paul Klemperer, and Balazs Szentes for their comments and insight. We also thank seminar participants at the University of Wisconsin (Madison), the University of Zurich, University of Leuven, Cardiff University, Oxford University, Cornell University, the University of East Anglia, and Universitie Paris 1 for helpful discussion. †London School of Economics, m.l.gentry@lse.ac.uk ‡London School of Economics, t.komarova@lse.ac.uk §London School of Economics and CEPR, p.schiraldi@lse.ac.uk