Nonparametric Identification of First-Price Auction with Unobserved Competition: A Density Discontinuity Framework

Emmanuel Guerre and Yao Luo

Working Papers from University of Toronto, Department of Economics

Abstract: We consider nonparametric identification of independent private value first-price auction models, in which the analyst only observes winning bids. Our benchmark model assumes an exogenous number of bidders N. We show that, if the bidders observe N, the resulting discontinuities in the winning bid density can be used to identify the distribution of N. The private value distribution can be nonparametrically identified in a second step. This extends, under testable identification conditions, to the case where N is a number of potential buyers, who bid with some unknown probability. Identification also holds in presence of additive unobserved heterogeneity drawn from some parametric distributions.

Keywords: Auction models; unobserved competition; nonparametric identification; density discontinuities; bidder uncertainty; unobserved heterogeneity (search for similar items in EconPapers)
JEL-codes: C14 C57 D44 (search for similar items in EconPapers)
Pages: Unknown pages
Date: 2026-09-24
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