Nonparametric Identification inAsymmetricSecond-Price Auctions: A New Approach

Tatiana Komorova

STICERD - Econometrics Paper Series from Suntory and Toyota International Centres for Economics and Related Disciplines, LSE

Abstract: This paper proposes an approach to proving nonparametric identification fordistributions of bidders' values in asymmetric second-price auctions. I consider thecase when bidders have independent private values and the only available datapertain to the winner's identity and the transaction price. My proof of identificationis constructive and is based on establishing the existence and uniqueness of asolution to the system of non-linear differential equations that describesrelationships between unknown distribution functions and observable functions.The proof is conducted in two logical steps. First, I prove the existence anduniqueness of a local solution. Then I describe a method that extends this localsolution to the whole support.This paper delivers other interesting results. I show how this approach can beapplied to obtain identification in more general auction settings, for instance, inauctions with stochastic number of bidders or weaker support conditions.Furthermore, I demonstrate that my results can be extended to generalizedcompeting risks models. Moreover, contrary to results in classical competing risks(Roy model), I show that in this generalized class of models it is possible to obtainimplications that can be used to check whether the risks in a model are dependent.Finally, I provide a sieve minimum distance estimator and show that it consistentlyestimates the underlying valuation distribution of interest.

Date: 2009-10
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