Quantile-Based Nonparametric Inference for First-Price Auctions

Abstract

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 et al. (2000), and is also asymptotically normal with the appropriate choice of the bandwidth.JEL Classi…cation: C14, D44

Replacing Sample Trimming with Boundary Correction in Nonparametric Estimation of First‐Price Auctions

“…Marmer and Shneyerov () propose a quantile‐based estimator which avoids explicit trimming because it directly maps the quantiles of the bid distribution into the quantiles of the private value distribution. However, their estimator is still subject to boundary effects because it uses a standard KDE and therefore cannot consistently estimate the 0th and 100th percentiles.…”

What Model for Entry in First-Price Auctions? A Nonparametric Approach

“…Following the approach of GPV, we show that the quantiles, Q * (τ |N ), can be nonparametrically identified in any SEM model if the number of potential bidders and all bids in each auction are observed. Our nonparametric tests and the estimation method are based on an asymptotically normal estimator of Q * (τ |N ) that we develop by following an approach similar to Marmer and Shneyerov (2012).…”

A Nonparametric Test for Comparing Valuation Distributions in First‐price Auctions

“…() shows that a bidder's value ( v ) can be expressed as an explicit function of the submitted bid ( b ), the bid PDF (), and the bid CDF () This equation can be rewritten in terms of the quantile functions of values and bids as where and are the α quantiles of the valuations and bids, respectively. Marmer and Shneyerov () used the well‐known formula to estimate . Haile et al.…”

“…Although our testing approach is new, we are not the first to use quantile‐based approaches in auctions. Marmer and Shneyerov () and Marmer et al. () proposed a quantile‐based estimator in first‐price auctions and a quantile‐based test for distinguishing different entry models, respectively.…”