Identification and Estimation in a Third-Price Auction Model

Andrea Enache, and Jean-Pierre Florens


The first novelty of this paper is that we show global identification of the private values distribution in a sealed-bid third-price auction model using a fully nonparametric methodology. The second novelty of the paper comes from the study of the identification and estimation of the model using a quantile approach. We consider an i.i.d. private values environment with risk-averse bidders. In the first place, we consider the case where the risk-aversion parameter is known. We show that the speed of convergence in process of our nonparametric estimator produces at the root-n parametric rate and we explain the intuition behind this apparently surprising result. Next, we consider that the risk-aversion parameter is unknown and we locally identify it using exogenous variation in the number of participants. We extend our procedure to the case where we observe only the bids corresponding to the transaction prices, and we generalize the model so as to account for the presence of exogenous variables. The methodological toolbox used to analyse identification of the third-price auction model can be employed in the study of other games of incomplete information. Our results are interesting also from a policy perspective,as some authors recommend the use of the third-price auction format for certain Internet auctions. Moreover, we contribute to the econometric literature on auctions using a quantile approach.


structural nonparametric estimation; nonlinear inverse problems; global identification; functional convergence of estimators; third-price auction mode;

JEL codes

  • C40: General
  • C73: Stochastic and Dynamic Games • Evolutionary Games • Repeated Games


Andrea Enache, and Jean-Pierre Florens, Identification and Estimation in a Third-Price Auction Model, Econometric Theory, vol. 36, n. 3, June 2020, pp. 386–409.

Published in

Econometric Theory, vol. 36, n. 3, June 2020, pp. 386–409