Identification in ascending auctions under limited information, with an application to absentee bidding

Abstract

This paper presents new identification results for ascending auctions when the number of bidders is unknown. The identification results exploit insights from the statistics literature about the stochastic ordering of sample spacings. In an incomplete model with a shape restriction on the latent value distribution, sample spacings are shown to set-identify the expected bidder surplus and seller revenues. The method is illustrated by estimating informative bounds on policy-relevant counterfactuals in a small sample of Sotheby's wine auctions with absentee bidding. Results indicate that Sotheby's restricts the full exploitation of the exclusion principle of optimal reserve prices by imposing a binding cap on the maximum reserve price, forcing some sellers to set too low reserves. Sellers with lower-valued wines benefit the most (up to 16.7%) from relaxing the constraint by adopting a reserve price rule equal to 105% of the current cap.

Keywords: JEL codes: C01, C46, C57, D44, L1 Ascending auctions, order statistics, shape restriction, identification, exclusion principle, absentee bidding, wine auctions

JEL Classification: D44, C01, C46, C57