Partial Identification of the Valuation Distribution in Sequential English Auctions

TL;DR

This paper develops a method to nonparametrically bound bidder valuations in sequential English auctions, accounting for bidder waiting behavior, and applies it to real-world auction data.

Contribution

It introduces a dynamic opportunity-cost restriction and a novel estimator that handles heterogeneous auction data without solving dynamic equilibria.

Findings

Waiting options reduce first-period revenue by 8-11% in Korean auctions.

Increasing bidders from 8 to 20 boosts seller revenue by 40-65%.

Maximin reserve prices vary significantly across vehicle clusters.

Abstract

This paper extends the incomplete model of Haile and Tamer (2003) from static English auctions to sequential English auctions. Because bidders may wait for future opportunities, the static condition that bidders do not let rivals win at beatable prices need not hold. We replace it with a dynamic opportunity-cost restriction, yielding nonparametric valuation bounds without solving a dynamic equilibrium. Sharp bounds are also characterized. We propose a novel moment-condition inversion estimator that pools auctions with heterogeneous bidder counts, mitigating finite-sample instability of order statistics approaches and admitting analytical standard errors and smooth confidence intervals. Applications to Korean wholesale used-car auctions and Cars and Bids online auctions deliver informative bounds. Counterfactual analyses show that the option to wait lowers first-period revenue by 8--11% in the Korean market, that increasing effective competition from 8 to 20 serious bidders in Cars and Bids raises seller revenue by 40--65%, and that maximin reserve prices vary substantially across vehicle clusters.