Extreme Value Theory and Auction Models

Abstract

The objective of this article is to develop a parametric approach to estimating auctions with incomplete data using Extreme Value Theory (EVT).  The methodology is mainly theoretical: we first review that, when only transaction prices can be observed, the distribution of private valuations is irregularly identified. The sample bias produced by nonparametric estimators will affect all functionals of practical interest.  We provide simulations for a best-case scenario and a worst-case scenario.  Our results show that, compared to nonparametric approaches, the approximation of such functionals developed using EVT produces more accurate results, is easy to compute, and does not require strong assumptions about the unobserved distribution of bidders' valuations.  It is recommended that financial operators working with auctions use this parametric approach when facing incomplete datasets.  Given the difficult nature of the analysis, this work does not provide large sample properties for the proposed estimators and recommends the use of bootstrapping.  This article contributes originally to the literature of structural estimation of auction models providing a useful and robust parametric approximation.