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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
  • Bjarne Brendstrup

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, oral, ascending-price 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 a semi-nonparametric estimation strategy based on approximation methods using orthogonal polynomials. We apply our estimator to daily data from fish auctions held in Grenaa, 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 Econometric Society in its series Econometric Society 2004 Latin American Meetings with number 2.

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Date of creation: 11 Aug 2004
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Handle: RePEc:ecm:latm04:2

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Keywords: nonparametric identification; semi-nonparametric estimation; asymmetric; sequential; English auction;

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References

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  1. 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.
  2. Paul Milgrom & Robert J. Weber, 1981. "A Theory of Auctions and Competitive Bidding," Discussion Papers 447R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  3. Maskin, Eric & Riley, John, 2000. "Asymmetric Auctions," Review of Economic Studies, Wiley Blackwell, vol. 67(3), pages 413-38, July.
  4. Athey,S. & Haile,P.A., 2000. "Identification of standard auction models," Working papers 13, Wisconsin Madison - Social Systems.
  5. Xiaohong Chen & Xiaotong Shen, 1998. "Sieve Extremum Estimates for Weakly Dependent Data," Econometrica, Econometric Society, vol. 66(2), pages 289-314, March.
  6. 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.
  7. Michael Peters, 1995. "A Competitive Distribution of Auctions," Working Papers peters-95-03, University of Toronto, Department of Economics.
  8. Mireia Jofre-Bonet & Martin Pesendorfer, 2001. "Estimation of a Dynamic Auction Game," NBER Working Papers 8626, National Bureau of Economic Research, Inc.
  9. Laffont, Jean-Jacques & Ossard, Herve & Vuong, Quang, 1995. "Econometrics of First-Price Auctions," Econometrica, Econometric Society, vol. 63(4), pages 953-80, July.
  10. repec:cup:etheor:v:7:y:1991:i:3:p:307-40 is not listed on IDEAS
  11. Ashenfelter, Orley, 1989. "How Auctions Work for Wine and Art," Journal of Economic Perspectives, American Economic Association, vol. 3(3), pages 23-36, Summer.
  12. Gallant, A Ronald & Nychka, Douglas W, 1987. "Semi-nonparametric Maximum Likelihood Estimation," Econometrica, Econometric Society, vol. 55(2), pages 363-90, March.
  13. Philip Haile, 2000. "Inference with an Incomplete Model of English Auctions," Econometric Society World Congress 2000 Contributed Papers 1546, Econometric Society.
  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 125-42, February.
  15. 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.
  16. Guerre, E. & Perrigne, I. & Vuong, Q., 1995. "Nonparametric Estimation of First-Price Auctions," Papers 9504, Southern California - Department of Economics.
  17. Robert J. Weber, 1981. "Multiple-Object Auctions," Discussion Papers 496, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  18. 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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Cited by:
  1. Jonathan Levin & Susan Athey & Enrique Seira, 2004. "Comparing Open and Sealed Bid Auctions: Theory and Evidence from Timber Auctions," Working Papers 2004.142, Fondazione Eni Enrico Mattei.
  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.

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