Semiparametric Estimation of First-Price Auctions with Risk Averse Bidders*

This paper studies the identification and estimation of the first-price auction model with risk averse bidders within the private value paradigm. We show that the benchmark model is nonidentified in general from observed bids. We then consider various extensions including a binding reserve price, affiliation among private values and asymmetric bidders. In particular, we exploit heterogeneity across auctioned objects to establish semiparametric identification under a conditional quantile restriction and a parameterization of the bidders’ utility function. Next we propose a semiparametric method for estimating the corresponding auction model. This method involves several steps and allows to recover the parameter(s) of the utility function as well as the bidders’ private value distribution. We show that our semiparametric estimator of the utility function parameter(s) converges at the optimal rate, which is slower than the parametric one. The method is illustrated on U.S. Forest Service timber sales and a test of bidders’ risk neutrality is performed.