Nonparametric inference on counterfactuals in first-price auctions

In a classical model of the first-price sealed-bid auction with independent private
values, we develop nonparametric estimators for several policy-relevant targets, such as
the bidder’s surplus and auctioneer’s revenue under counterfactual reserve prices, with
the corresponding optimal nonparametric rate of convergence achieved. Motivated by
the linearity of these targets in the quantile function of bidders’ values, we derive
its Bahadur-Kiefer expansion, which carries towards the construction of valid uniform
confidence bands via undersmoothing. This allows to test complex hypotheses, such as
the optimality of reserve prices.