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Nonparametric Identification and Estimation of Multi-Unit, Sequential, Oral, Ascending-Price Auctions With Asymmetric Bidders

Author

Listed:
  • Harry J. Paarsch

    (Department of Economics, University of Iowa)

  • Bjarne Brendstrup

    (Department of Economics, University of Aarhus)

Abstract

Within the independent private-values paradigm, we derive the data-generating process of the winning bid for the last unit sold at multi-unit sequential English auctions when bidder valuations are draws from different distributions; i.e., in the presence of asymmetries. When the identity of the winner as well as the number of units won by each bidder in previous stages of the auction are observed, we demonstrate nonparametric identification and then propose two estimation strategies, one based on the empirical distribution function of winning bids for the last unit sold and the other based on approximation methods using orthogonal polynomials. We apply our methods to daily data from fish auctions held in Grenå, Denmark. For single-unit supply, we use our estimates to compare the revenues a seller could expect to earn were a Dutch auction employed instead.

Suggested Citation

  • Harry J. Paarsch & Bjarne Brendstrup, 2004. "Nonparametric Identification and Estimation of Multi-Unit, Sequential, Oral, Ascending-Price Auctions With Asymmetric Bidders," Working Papers 2004.11, Fondazione Eni Enrico Mattei.
  • Handle: RePEc:fem:femwpa:2004.11
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    References listed on IDEAS

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    1. 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.
    2. Mireia Jofre-Bonet & Martin Pesendorfer, 2003. "Estimation of a Dynamic Auction Game," Econometrica, Econometric Society, vol. 71(5), pages 1443-1489, September.
    3. Ashenfelter, Orley, 1989. "How Auctions Work for Wine and Art," Journal of Economic Perspectives, American Economic Association, vol. 3(3), pages 23-36, Summer.
    4. Eric Maskin & John Riley, 2000. "Asymmetric Auctions," Review of Economic Studies, Oxford University Press, vol. 67(3), pages 413-438.
    5. Krishna, Vijay, 2009. "Auction Theory," Elsevier Monographs, Elsevier, edition 2, number 9780123745071.
    6. Michael Peters, 1997. "A Competitive Distribution of Auctions," Review of Economic Studies, Oxford University Press, vol. 64(1), pages 97-123.
    7. Susan Athey & Philip A. Haile, 2002. "Identification of Standard Auction Models," Econometrica, Econometric Society, vol. 70(6), pages 2107-2140, November.
    8. Donald, Stephen G. & Paarsch, Harry J., 2002. "Superconsistent estimation and inference in structural econometric models using extreme order statistics," Journal of Econometrics, Elsevier, vol. 109(2), pages 305-340, August.
    9. Gallant, A Ronald & Nychka, Douglas W, 1987. "Semi-nonparametric Maximum Likelihood Estimation," Econometrica, Econometric Society, vol. 55(2), pages 363-390, March.
    10. Eastwood, Brian J. & Gallant, A. Ronald, 1991. "Adaptive Rules for Seminonparametric Estimators That Achieve Asymptotic Normality," Econometric Theory, Cambridge University Press, vol. 7(03), pages 307-340, September.
    11. Xiaohong Chen & Xiaotong Shen, 1998. "Sieve Extremum Estimates for Weakly Dependent Data," Econometrica, Econometric Society, vol. 66(2), pages 289-314, March.
    12. Laffont, Jean-Jacques & Ossard, Herve & Vuong, Quang, 1995. "Econometrics of First-Price Auctions," Econometrica, Econometric Society, vol. 63(4), pages 953-980, July.
    13. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
    14. Lebrun, Bernard, 1999. "First Price Auctions in the Asymmetric N Bidder Case," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(1), pages 125-142, February.
    15. Robert J. Weber, 1981. "Multiple-Object Auctions," Discussion Papers 496, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    16. repec:cup:etheor:v:7:y:1991:i:3:p:307-40 is not listed on IDEAS
    17. Philip A. Haile & Elie Tamer, 2003. "Inference with an Incomplete Model of English Auctions," Journal of Political Economy, University of Chicago Press, vol. 111(1), pages 1-51, February.
    18. Guerre, E. & Perrigne, I. & Vuong, Q., 1995. "Nonparametric Estimation of First-Price Auctions," Papers 9504, Southern California - Department of Economics.
    19. Donald, Stephen G & Paarsch, Harry J, 1993. "Piecewise Pseudo-maximum Likelihood Estimation in Empirical Models of Auctions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 34(1), pages 121-148, February.
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    Cited by:

    1. Susan Athey & Jonathan Levin & Enrique Seira, 2004. "Comparing Open and Sealed Bid Auctions: Theory and Evidence from Timber Auctions," Levine's Bibliography 122247000000000524, UCLA Department of Economics.
    2. Harry J. Paarsch & Bjarne Brendstrup, 2004. "Nonparametric Estimation of Dutch and First-Price, Sealed-Bid Auction Models with Asymmetric Bidders," Econometric Society 2004 North American Summer Meetings 39, Econometric Society.

    More about this item

    Keywords

    Asymmetric; Multi-unit; Sequential; Oral; Ascending-price fish auctions; Dutch auctions; Nonparametric identification and estimation;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance
    • Q22 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - Fishery

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