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Nonparametric Identification inAsymmetricSecond-Price Auctions: A New Approach

Author

Listed:
  • Tatiana Komorova
Abstract
This paper proposes an approach to proving nonparametric identification fordistributions of bidders' values in asymmetric second-price auctions. I consider thecase when bidders have independent private values and the only available datapertain to the winner's identity and the transaction price. My proof of identificationis constructive and is based on establishing the existence and uniqueness of asolution to the system of non-linear differential equations that describesrelationships between unknown distribution functions and observable functions.The proof is conducted in two logical steps. First, I prove the existence anduniqueness of a local solution. Then I describe a method that extends this localsolution to the whole support.This paper delivers other interesting results. I show how this approach can beapplied to obtain identification in more general auction settings, for instance, inauctions with stochastic number of bidders or weaker support conditions.Furthermore, I demonstrate that my results can be extended to generalizedcompeting risks models. Moreover, contrary to results in classical competing risks(Roy model), I show that in this generalized class of models it is possible to obtainimplications that can be used to check whether the risks in a model are dependent.Finally, I provide a sieve minimum distance estimator and show that it consistentlyestimates the underlying valuation distribution of interest.

Suggested Citation

  • Tatiana Komorova, 2009. "Nonparametric Identification inAsymmetricSecond-Price Auctions: A New Approach," STICERD - Econometrics Paper Series 545, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    • Handle: RePEc:cep:stiecm:545
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    References listed on IDEAS

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    1. A. Banerji & J.V. Meenakshi, 2004. "Buyer Collusion and Efficiency of Government Intervention in Wheat Markets in Northern India: An Asymmetric Structural Auctions Analysis," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 86(1), pages 236-253.
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    3. Brendstrup, Bjarne & Paarsch, Harry J., 2007. "Semiparametric identification and estimation in multi-object, English auctions," Journal of Econometrics, Elsevier, vol. 141(1), pages 84-108, November.
    4. Emmanuel Guerre & Isabelle Perrigne & Quang Vuong, 2009. "Nonparametric Identification of Risk Aversion in First-Price Auctions Under Exclusion Restrictions," Econometrica, Econometric Society, vol. 77(4), pages 1193-1227, July.
    5. 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.
    6. Krishna, Vijay, 2009. "Auction Theory," Elsevier Monographs, Elsevier, edition 2, number 9780123745071.
    7. 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.
    8. Meenakshi, J.V. & Banerji, A., 2005. "The unsupportable support price: an analysis of collusion and government intervention in paddy auction markets in North India," Journal of Development Economics, Elsevier, vol. 76(2), pages 377-403, April.
    9. 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.
    10. Harstad, Ronald M. & Kagel, John H. & Levin, Dan, 1990. "Equilibrium bid functions for auctions with an uncertain number of bidders," Economics Letters, Elsevier, vol. 33(1), pages 35-40, May.
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