This paper proposes a general approach and a computationally convenient estimation procedure for the structural analysis of auction data. Considering first-price sealed-bid auction models within the independent private value paradigm, we show that the underlying distribution of bidders' private values is identified from observed bids and the number of actual bidders without any parametric assumptions. Using the theory of minimax, we establish the best rate of uniform convergence at which the latent density of private values can be estimated nonparametrically from available data. We then propose a two-step kernel-based estimator that converges at the optimal rate.

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SUMMARYCollusion and heterogeneity across firms may introduce asymmetry in bidding games. A major difficulty in asymmetric auctions is that the Bayesian Nash equilibrium strategies are solutions of an intractable system of differential equations. We propose a simple method for estimating asymmetric first-price auctions with affiliated private values. Considering two types of bidders, we show that these differential equations can be rewritten using the observed bid distribution. We establish the identification of the model, characterize its theoretical restrictions, and propose a two-step non-parametric estimation procedure for estimating the private value distributions. An empirical analysis of joint bidding in OCS auctions is provided.

price sealed-bid auctions. The model allows for bidders' individual efficiencies and opportunity costs, while permitting dependence among bidders' private values through affiliation. We establish the nonparametric identification of the APV model, characterize its theoretical restrictions, and propose a computationally convenient and consistent two-step nonparametric estimation procedure for estimating the joint private value distribution from observed bids. Using simulated bid data we provide a step by step guide on how to implement our procedure and show the good behavior of our estimator in small samples.