Quantile-Based Nonparametric Inference for First-Price Auctions

We propose a quantile-based nonparametric approach to inference on the probability density function (PDF) of the private values in …rst-price sealedbid auctions with independent private values. Our method of inference is based on a fully nonparametric kernel-based estimator of the quantiles and PDF of observable bids. Our estimator attains the optimal rate of Guerre, Perrigne, and Vuong (2000), and is also asymptotically normal with the appropriate choice of the bandwidth. As an application, we consider the problem of inference on the optimal reserve price. Keywords: First-price auctions, independent private values, nonparametric estimation, kernel estimation, quantiles, optimal reserve price. 1 Introduction Following the seminal article of Guerre, Perrigne, and Vuong (2000), GPV hereafter, there has been an enormous interest in nonparametric approaches to auctions.1 By removing the need to impose tight functional form assumptions, the nonparametric approach provides a more ‡exible framework for estimation and inference. Moreover, We thank Don Andrews for helpful comments. Pai Xu provided excellent research assistance. The …rst author gratefully acknowledges the research support of the Social Sciences and Humanities Research Council of Canada under grant number 410-2007-1998. 1See a recent survey by Athey and Haile (2005).