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

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  • 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.

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Bibliographic Info

Paper provided by Fondazione Eni Enrico Mattei in its series Working Papers with number 2004.11.

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Date of creation: Jan 2004
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Handle: RePEc:fem:femwpa:2004.11

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

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References

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  1. 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 125-42, February.
  2. Michael Peters, 1995. "A Competitive Distribution of Auctions," Working Papers peters-95-03, University of Toronto, Department of Economics.
  3. Guerre, E. & Perrigne, I. & Vuong, Q., 1995. "Nonparametric Estimation of First-Price Auctions," Papers 9504, Southern California - Department of Economics.
  4. Laffont, Jean-Jacques & Ossard, Hervé & Vuong, Quang, 1991. "Econometrics of First-Price Auctions," IDEI Working Papers 7, Institut d'Économie Industrielle (IDEI), Toulouse.
  5. 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.
  6. repec:cup:etheor:v:7:y:1991:i:3:p:307-40 is not listed on IDEAS
  7. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
  8. 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.
  9. Mireia Jofre-Bonet & Martin Pesendorfer, 2001. "Estimation of a Dynamic Auction Game," NBER Working Papers 8626, National Bureau of Economic Research, Inc.
  10. Athey,S. & Haile,P.A., 2000. "Identification of standard auction models," Working papers 13, Wisconsin Madison - Social Systems.
  11. 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.
  12. 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 121-48, February.
  13. Xiaohong Chen & Xiaotong Shen, 1998. "Sieve Extremum Estimates for Weakly Dependent Data," Econometrica, Econometric Society, vol. 66(2), pages 289-314, March.
  14. Robert J. Weber, 1981. "Multiple-Object Auctions," Discussion Papers 496, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  15. Ashenfelter, Orley, 1989. "How Auctions Work for Wine and Art," Journal of Economic Perspectives, American Economic Association, vol. 3(3), pages 23-36, Summer.
  16. Maskin, Eric & Riley, John, 2000. "Asymmetric Auctions," Review of Economic Studies, Wiley Blackwell, vol. 67(3), pages 413-38, July.
  17. Haile,P.A. & Tamer,E.T., 2000. "Inference with an incomplete model of English auctions," Working papers 18, Wisconsin Madison - Social Systems.
  18. Gallant, A Ronald & Nychka, Douglas W, 1987. "Semi-nonparametric Maximum Likelihood Estimation," Econometrica, Econometric Society, vol. 55(2), pages 363-90, March.
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Cited by:
  1. 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.
  2. Susan Athey, 2005. "Comparing Open and Sealed Bid Auctions: Theory and Evidence from Timber Auctions," Theory workshop papers 658612000000000098, UCLA Department of Economics.

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