Estimation in English auctions with unobserved heterogeneity

Abstract

We propose a framework for identification and estimation of a private values model with unobserved heterogeneity from bid data in English auctions, using variation in the number of bidders across auctions, and extend the framework to settings where the number of bidders is not cleanly observed in each auction. We illustrate our method on data from eBay Motors auctions. We find that unobserved heterogeneity is important, accounting for two thirds of price variation after controlling for observables, and that welfare measures would be dramatically misestimated if unobserved heterogeneity were ignored.

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

“…Two recent papers, Mbakop (2017) and Luo and Xiao (2019), obtained identification arguments for ascending auctions with unobserved heterogeneity by exploiting cases where the econometrician observes more than two bids. Hernández, Quint, and Turansick (2020) used an alternative argument that allows for both unobserved heterogeneity and for some forms of limited information about the number of bidders, such as it being partially observed or the econometrician observing auctions under at least two different known probability distributions for the number of bidders 5…”

“…Two recent papers, Mbakop (2017) and Luo and Xiao (2019), obtained identification arguments for ascending auctions with unobserved heterogeneity by exploiting cases where the econometrician observes more than two bids. Hernández, Quint, and Turansick (2020) used an alternative argument that allows for both unobserved heterogeneity and for some forms of limited information about the number of bidders, such as it being partially observed or the econometrician observing auctions under at least two different known probability distributions for the number of bidders. 5 Our application contributes to a small literature on digital rights management and copyright infringement (e.g., Stallman (1997), Liu, Safavi-Naini, and Sheppard (2003), Walker (2003), Von Lohmann (2004) and the literature on piracy and copyright enforcement more broadly (Harbaugh and Khemka (2010)).…”

Identification of Auction Models Using Order Statistics

“…5 Two random bids are required in each auction, and UH is restricted to have a separable structure on bidder valuation. Hernández et al (2020) achieves point identification using English auction models with additively separable UH, as-suming piecewise real analytic density functions and using variations in the number of bidders across auctions. We focus on finite UH, which does not directly extend to the deconvolution approach.…”

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.…”

“…This situation results in auction-level unobserved heterogeneity (UH), which leads to inaccurate estimates of bidder value distributions and, therefore, misleading policy implications. For instance, Hernández et al (2020) finds that UH accounts for two-thirds of price variation after controlling for information provided in the eBay Motors auctions, and that ignoring this feature would dramatically mis-estimate the welfare measures. The existing literature adapts measurement error approaches to tackle such an issue.…”