Inference for First-Price Auctions with Guerre, Perrigne, and Vuong's Estimator

TL;DR

This paper establishes the asymptotic properties of the GPV estimator for valuation densities in first-price auctions, providing methods for valid inference including confidence intervals and bands.

Contribution

It proves the asymptotic normality of the GPV estimator and introduces practical variance estimation and bootstrap methods for inference.

Findings

Asymptotic normality of the GPV estimator is established.

Valid bootstrap confidence intervals for the valuation density are developed.

Uniform confidence bands are constructed using Gaussian approximation.

Abstract

We consider inference on the probability density of valuations in the first-price sealed-bid auctions model within the independent private value paradigm. We show the asymptotic normality of the two-step nonparametric estimator of Guerre, Perrigne, and Vuong (2000) (GPV), and propose an easily implementable and consistent estimator of the asymptotic variance. We prove the validity of the pointwise percentile bootstrap confidence intervals based on the GPV estimator. Lastly, we use the intermediate Gaussian approximation approach to construct bootstrap-based asymptotically valid uniform confidence bands for the density of the valuations.