Identification in ascending auctions, with an application to digital rights management

Abstract

This study provides new identification and estimation results for ascending (traditional English or online) auctions with unobserved auction‐level heterogeneity and an unknown number of bidders. When the seller's reserve price and two order statistics of bids are observed, we derive conditions under which the distributions of buyer valuations, unobserved heterogeneity, and number of participants are point identified. We also derive conditions for point identification in cases where reserve prices are binding and present general conditions for partial identification. We propose a nonparametric maximum likelihood approach for estimation and inference. We apply our approach to the online market for used iPhones and analyze the effects of recent regulatory changes banning consumers from circumventing digital rights management technologies used to lock phones to service providers. We find that buyer valuations for unlocked phones dropped by 39% on average after the unlocking ban took effect, from $231.30 to $141.50.

Identification of Auction Models Using Order Statistics

“…11 We build on Song (2004), which considers online English auctions with unobserved competition. Related to our result, Freyberger and Larsen (2017) studies the problem in the classical setting (i.e., separable and continuous UH) using reserve price and two order statistics of bids; without identifying the value distributions, Coey et al (2021) focuses on identification of the optimal reserve price using two order statistics in a general setting. Our approach uses two consecutive order statistics with an instrument, and achieves point identification under nonseparable and finite UH.…”

“…Kim and Lee (2014) applies the identification results of Song (2004) to wholesale used-car auctions in Korea, for which only a small subset of bids is observable (due to the ascending auction format). Freyberger and Larsen (2017) studies eBay auctions for used iPhones with auction-specific UH and an unknown number of bidders. The issue of correlated order statistics is circumvented using observed reserve prices, returning the identification problem to its standard form.…”

“…The earliest approach to allow for UH in auctions exploits an auxiliary variable that is monotone in UH. See, e.g.,Campo et al (2003) and.2 For instance,Kim and Lee (2014) observes the second, third, and fourth highest bids in ascending used-car auctions Freyberger and Larsen (2017). uses the second and third order statistics of bids in eBay auctions for used iPhones.3 For instance, three apparent low bids in all auctions since 1999 are one-click downloadable on the California DOT website.…”

Order Statistics Approaches to Unobserved Heterogeneity in Auctions

“…In the framework of additively separable continuous UH, Hernández et al (2020) achieves point identification using English auction models, assuming piecewise real analytic density functions and using variations in the number of bidders across auctions; Freyberger and Larsen (2022) provides identification results for ascending auctions, relying on reserve prices and two order statistics of bids. Cho et al (2022) studies deconvolution using two order statistics.…”

Secret reserve prices by uninformed sellers

“…1111 For ascending auctions, Freyberger and Larsen (2019) show that secret reserve prices can help identify the distribution of unobserved heterogeneity and values when the number of bidders is unknown. …”