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Bounds on Revenue Distributions in Counterfactual Auctions with Reserve Prices

  • Xun Tang

    ()

    (Department of Economics, University of Pennsylvania)

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    In first-price auctions with interdependent bidder values, the distributions of private signals and values cannot be uniquely recovered from bids in Bayesian Nash equilibria. Non-identification invalidates structural analyses that rely on the exact knowledge of model primitives. In this paper I introduce tight, informative bounds on the distribution of revenues in counterfactual first-price and second-price auctions with binding reserve prices. These robust bounds are identified from distributions of equilibrium bids in first-price auctions under minimal restrictions where I allow for affiliated signals and both private and common-value paradigms. The bounds can be used to compare auction formats and to select optimal reserve prices. I propose consistent nonparametric estimators of the bounds. I extend the approach to account for observed heterogeneity across auctions, as well as binding reserve prices in the data. I use a recent data of 6,721 first-price auctions of U.S. municipal bonds to estimate bounds on counterfactual revenue distributions. I then bound optimal reserve prices for sellers with various risk attitudes.

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    File URL: http://economics.sas.upenn.edu/system/files/working-papers/08-042.pdf
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    Paper provided by Penn Institute for Economic Research, Department of Economics, University of Pennsylvania in its series PIER Working Paper Archive with number 08-042.

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    Length: 85 pages
    Date of creation: 02 Sep 2008
    Date of revision:
    Handle: RePEc:pen:papers:08-042
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    1. Guido Imbens & Charles F. Manski, 2003. "Confidence intervals for partially identified parameters," CeMMAP working papers CWP09/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. Paul Klemperer, 1999. "Auction Theory: A Guide to the Literature," Economics Series Working Papers 1999-W12, University of Oxford, Department of Economics.
    3. Philip A. Haile & Han Hong & Matthew Shum, 2004. "Nonparametric Tests for Common Values in First-Price Sealed-Bid Auctions," Working Papers 2004.149, Fondazione Eni Enrico Mattei.
    4. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
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    6. Hong, Han & Shum, Matthew, 2002. "Increasing Competition and the Winner's Curse: Evidence from Procurement," Review of Economic Studies, Wiley Blackwell, vol. 69(4), pages 871-98, October.
    7. Matthew Shum, 2000. "Nonparametric Tests for Common Values," Econometric Society World Congress 2000 Contributed Papers 1598, Econometric Society.
    8. 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 329-55, Summer.
    9. Li, Tong & Perrigne, Isabelle & Vuong, Quang, 2000. "Conditionally independent private information in OCS wildcat auctions," Journal of Econometrics, Elsevier, vol. 98(1), pages 129-161, September.
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    11. Guerre, E. & Perrigne, I. & Vuong, Q., 1995. "Nonparametric Estimation of First-Price Auctions," Papers 9504, Southern California - Department of Economics.
    12. Paarsch, Harry J., 1997. "Deriving an estimate of the optimal reserve price: An application to British Columbian timber sales," Journal of Econometrics, Elsevier, vol. 78(2), pages 333-357, June.
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    15. McAdams, David, 2007. "Uniqueness in symmetric first-price auctions with affiliation," Journal of Economic Theory, Elsevier, vol. 136(1), pages 144-166, September.
    16. Athey, Susan & Haile, Philip A., 2007. "Nonparametric Approaches to Auctions," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 60 Elsevier.
    17. McAfee, R Preston & McMillan, John, 1987. "Auctions and Bidding," Journal of Economic Literature, American Economic Association, vol. 25(2), pages 699-738, June.
    18. Hendricks, Ken & Porter, Robert H., 2007. "An Empirical Perspective on Auctions," Handbook of Industrial Organization, Elsevier.
    19. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-30, November.
    20. Alexander W. Butler, 2008. "Distance Still Matters: Evidence from Municipal Bond Underwriting," Review of Financial Studies, Society for Financial Studies, vol. 21(2), pages 763-784, April.
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