Nonparametric estimation of first-price auctions with risk-averse bidders

This paper proposes nonparametric estimators for the bidders' utility function and density of private values in a first-price sealed-bid auction model with independent valuations. I study a setting with risk-averse bidders and adopt a fully nonparametric approach by not placing any restrictions on the shape of the utility function beyond regularity conditions. I propose a population criterion function that has a unique minimizer, which characterizes the utility function and density of private values. The resulting estimators emerge after replacing the population quantities by sample analogues. These estimators are uniformly consistent and their convergence rates are established. I further suggest an estimator for the optimal reserve price. Monte Carlo experiments show that the proposed estimators perform well in finite samples.