Identification of Auction Models Using Order Statistics

78 Pages Posted: 8 Jun 2020 Last revised: 17 Jul 2020

See all articles by Yao Luo

Yao Luo

University of Toronto - Department of Economics

Ruli Xiao

Indiana University; Indiana University

Date Written: July 16, 2020


Auction data often contain information on only the most competitive bids as opposed to all bids. The usual measurement error approaches to unobserved heterogeneity are inapplicable due to dependence among order statistics. We bridge this gap by providing a set of positive results. First, we show that symmetric auctions are identifiable using three consecutive order statistics or two consecutive ones with an instrument. Second, we introduce competition intensity, i.e., the number of bidders, as additional unobserved heterogeneity. Third, we extend our results to asymmetric auctions. Lastly, we apply our methods to U.S. Forest Service timber auctions and find that ignoring unobserved heterogeneity reduces both bidder and auctioneer surplus.

Keywords: Asymmetric Auction, Unobserved Competition, Multidimensional Unobserved Heterogeneity, Consecutive Order Statistics, Finite Mixture, Data Truncation

JEL Classification: C14, D44

Suggested Citation

Luo, Yao and Xiao, Ruli and Xiao, Ruli, Identification of Auction Models Using Order Statistics (July 16, 2020). Available at SSRN: or

Yao Luo

University of Toronto - Department of Economics ( email )

150 St. George Street
Toronto, Ontario M5S3G7

Ruli Xiao (Contact Author)

Indiana University ( email )

Wylie Hall
Bloomington, IN 47405-6620
United States

Indiana University ( email )

100 S Woodlawn Ave
Bloomington, IN 47405
United States

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