Nonparametric inference on counterfactuals in first-price auctions

Abstract

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. Motivated by the linearity of these targets in the quantile function of bidders' values, we propose an estimator of the latter and derive its Bahadur-Kiefer expansion. This makes it possible to construct uniform confidence bands and test complex hypotheses about the auction design. Using the data on U.S. Forest Service timber auctions, we test whether setting zero reserve prices in these auctions was revenue maximizing.