Partial Identification of the Valuation Distribution in Sequential English Auctions

2026-05-14

AI Summary

This study addresses the challenge of identifying private value distributions in sequential English auctions, where bidders’ strategic waiting for future opportunities violates the static auction assumption that opponents should not be allowed to win at beatable prices. To overcome this, the paper introduces a novel dynamic opportunity cost constraint and develops a nonparametric partial identification framework that avoids solving for dynamic equilibria. It further proposes a new estimator based on moment condition inversion, which effectively pools auction data with varying numbers of bidders and mitigates the instability of order-statistic methods in finite samples. Empirical application to Korean wholesale used-car and Cars and Bids online auction data yields informative bounds on bidder valuations. Counterfactual analysis reveals that the option to wait reduces first-round revenue by 8–11%, while increasing the number of effective bidders from 8 to 20 boosts seller revenue by 40–65%.

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.

Problem

• sequential auctions
• valuation distribution
• partial identification
• English auctions
• opportunity cost

Innovation

• sequential auctions
• partial identification
• dynamic opportunity cost
• moment-condition inversion
• nonparametric bounds