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Inference in Auctions with Many Bidders Using Transaction Prices

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  • Federico A. Bugni
  • Yulong Wang

Abstract

This paper studies inference in first-price and second-price sealed-bid auctions with many bidders, using an asymptotic framework where the number of bidders increases while the number of auctions remains fixed. Our approach enables asymptotically exact inference on key features, such as the winner's expected utility, the seller's expected revenue, and the tail of the valuation distribution, using only transaction price data. Our simulations demonstrate the accuracy of the methods in finite samples. We apply our methods to Hong Kong vehicle license auctions, focusing on high-priced, single-letter plates. Other relevant applications include online and art auctions.

Suggested Citation

  • Federico A. Bugni & Yulong Wang, 2023. "Inference in Auctions with Many Bidders Using Transaction Prices," Papers 2311.09972, arXiv.org, revised Apr 2026.
    • Handle: RePEc:arx:papers:2311.09972
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    References listed on IDEAS

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    1. Tatiana Komarova, 2013. "A new approach to identifying generalized competing risks models with application to second‐price auctions," Quantitative Economics, Econometric Society, vol. 4(2), pages 269-328, July.
    2. Konrad Menzel & Paolo Morganti, 2013. "Large sample properties for estimators based on the order statistics approach in auctions," Quantitative Economics, Econometric Society, vol. 4(2), pages 329-375, July.
    3. Emmanuel Guerre & Yao Luo, 2019. "Nonparametric Identification of First-Price Auction with Unobserved Competition: A Density Discontinuity Framework," Papers 1908.05476, arXiv.org, revised Sep 2026.
    4. Bajari, Patrick & Hortacsu, Ali, 2003. "The Winner's Curse, Reserve Prices, and Endogenous Entry: Empirical Insights from eBay Auctions," RAND Journal of Economics, The RAND Corporation, vol. 34(2), pages 329-355, Summer.
    5. Tong Li, 2005. "Econometrics of first-price auctions with entry and binding reservation prices," Journal of Econometrics, Elsevier, vol. 126(1), pages 173-200, May.
    6. Andrés Aradillas‐López & Amit Gandhi & Daniel Quint, 2013. "Identification and Inference in Ascending Auctions With Correlated Private Values," Econometrica, Econometric Society, vol. 81(2), pages 489-534, March.
    7. Komarova, Tatiana, 2013. "A new approach to identifying generalized competing risks models with application to second-price auctions," LSE Research Online Documents on Economics 50245, London School of Economics and Political Science, LSE Library.
    8. Joachim Freyberger & Bradley J. Larsen, 2022. "Identification in ascending auctions, with an application to digital rights management," Quantitative Economics, Econometric Society, vol. 13(2), pages 505-543, May.
    9. An, Yonghong & Hu, Yingyao & Shum, Matthew, 2010. "Estimating first-price auctions with an unknown number of bidders: A misclassification approach," Journal of Econometrics, Elsevier, vol. 157(2), pages 328-341, August.
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