Identification and Estimation in a Third-Price Auction Model

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 a 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.Although the model is globally identified, we also present the functional local approach, which is useful when the model is not globally tractable. This is the case when one searches to identify also the risk-aversion parameter. Moreover there is a recent interest of local treatment of nonparametric models. Using the exogenous variation in the number of participants we are able to achieve the local identification of the unknown risk-aversion parameter. Not only this methodology is more rigorous, but it can also be applied for different types of games, which involve complicated nonlinear inverse problems.We extend our procedure to the case where we observe only the bids corresponding to the transaction prices and we generalize the model as to account for the presence of exogenous variables.The methodological toolbox used for analyzing local and global identification of the third-price auction model can be employed in the study of other games of incomplete information. Moreover, our results are interesting also from a policy perspective, as some authors recommend the use of the third-price auction format for some Internet auctions.