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Semiparametric Estimation of First-Price Auction Models

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  • Aryal, Gaurab
  • Gabrielli, Maria F.
  • Vuong, Quang

Abstract

We propose a semiparametric estimator within the class of indirect methods. Specifically, we model private valuations through a set of conditional moment restrictions. Our econometric model calls for a two step procedure. In the first step we recover a sample of pseudo private values while using a Local Polynomial Estimator. In the second step we use a GMM procedure to obtain an estimate for the parameter of interest. The proposed semiparametric estimator is shown to have desirable statistical properties namely, it is consistent and has an asymptotic normal distribution. Moreover, the estimator attains the parametric rate of convergence.

Suggested Citation

  • Aryal, Gaurab & Gabrielli, Maria F. & Vuong, Quang, 2014. "Semiparametric Estimation of First-Price Auction Models," MPRA Paper 57340, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:57340
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    References listed on IDEAS

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    1. Isabelle Perrigne & Quang Vuong, 1999. "Structural Econometrics of First-price Auctions: A Survey of Methods," Canadian Journal of Agricultural Economics/Revue canadienne d'agroeconomie, Canadian Agricultural Economics Society/Societe canadienne d'agroeconomie, vol. 47(3), pages 203-223, November.
    2. Paarsch, Harry J., 1992. "Deciding between the common and private value paradigms in empirical models of auctions," Journal of Econometrics, Elsevier, vol. 51(1-2), pages 191-215.
    3. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    4. Lavergne, Pascal & Vuong, Quang H, 1996. "Nonparametric Selection of Regressors: The Nonnested Case," Econometrica, Econometric Society, vol. 64(1), pages 207-219, January.
    5. Bernard Elyakime & Jean-Jacques Laffont & Patrice Loisel & Quang Vuong, 1994. "First-Price Sealed-Bid Auctions with Secret Reservation Prices," Annals of Economics and Statistics, GENES, issue 34, pages 71-114.
    6. McAfee, R. Preston & McMillan, John, 1987. "Auctions with entry," Economics Letters, Elsevier, vol. 23(4), pages 343-347.
    7. Krishna, Vijay, 2009. "Auction Theory," Elsevier Monographs, Elsevier, edition 2, number 9780123745071, December.
    8. Chunrong Ai & Xiaohong Chen, 2003. "Efficient Estimation of Models with Conditional Moment Restrictions Containing Unknown Functions," Econometrica, Econometric Society, vol. 71(6), pages 1795-1843, November.
    9. McAfee, R. Preston & McMillan, John, 1987. "Auctions with a stochastic number of bidders," Journal of Economic Theory, Elsevier, vol. 43(1), pages 1-19, October.
    10. Tong Li & Isabelle Perrigne, 2003. "Timber Sale Auctions with Random Reserve Prices," The Review of Economics and Statistics, MIT Press, vol. 85(1), pages 189-200, February.
    11. Harry J. Paarsch & Han Hong, 2006. "An Introduction to the Structural Econometrics of Auction Data," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262162350, December.
    12. McAfee, R Preston & McMillan, John, 1987. "Auctions and Bidding," Journal of Economic Literature, American Economic Association, vol. 25(2), pages 699-738, June.
    13. Bo E. Honoré & Ekaterini Kyriazidou, 2000. "Panel Data Discrete Choice Models with Lagged Dependent Variables," Econometrica, Econometric Society, vol. 68(4), pages 839-874, July.
    14. 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. Aryal, Gaurab & Gabrielli, Maria F., 2012. "Is Collusion Proof Auction Expensive? Estimates from Highway Procurements," MPRA Paper 57353, University Library of Munich, Germany, revised 19 Feb 2014.

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    More about this item

    Keywords

    Auctions; Structural Approach; Semiparametric Estimator; Local Polynomial; GMM.;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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