A Nonparametric Test of Exogenous Participation in First-Price Auctions

This paper proposes a nonparametric test of exogenous participation in first-price auctions. Exogenous participation means that the valuation distribution does not depend on the number of bidders. Our test is motivated by the fact that two valuation distributions are the same if and only if their generalized Lorenz curves are the same. Our method avoids estimating unobserved valuations and does not require smooth estimation of bid density. We show that our test is consistent against all fixed alternatives and has power against root-n local alternatives. Monte Carlo experiments show that our test performs well in finite samples. We implement our method on data from the U.S. Forest Service timber auctions. We also discuss how our test can be adapted to other testing problems in auctions.