Identi cation and Estimation of First-Price Auctions Without Assuming Correct Beliefs

This paper studies identi cation and estimation of rst-price auctions, without assuming that the bidders have correct beliefs about the distribution of valuations. Identi cation is achieved through an exclusion restriction and a common support assumption for the belief and the valuation distribution. The identi cation result yields a closed form for the inverse bid function, which suggests two-step estimators for the valuation distribution and the belief. We derive the asymptotic properties of the estimators and conduct a Monte Carlo study. Robustness to biased beliefs comes at the cost of a moderate e ciency loss compared to Guerre, Perrigne, and Vuong (2000). We apply the method to US Forest Service timber auctions and nd that the bidders underestimate their winning probability, which leads to overbidding.