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Semiparametric Estimation of First-Price Auction Models

Author

Listed:
  • Gaurab Aryal
  • Maria Florencia Gabrielli
  • Quang Vuong

Abstract

We propose a semiparametric method to estimate the density of private values in first-price auctions. Specifically, we model private values through a set of conditional moment restrictions and use a two-step procedure. In the first step we recover a sample of pseudo private values using Local Polynomial Estimator. In the second step we use a GMM procedure to estimate the parameter(s) of interest. We show that the proposed semiparametric estimator is consistent, has an asymptotic normal distribution, and attains the parametric ("root-n") rate of convergence.

Suggested Citation

  • Gaurab Aryal & Maria Florencia Gabrielli & Quang Vuong, 2014. "Semiparametric Estimation of First-Price Auction Models," Papers 1407.7140, arXiv.org, revised Jun 2015.
    • Handle: RePEc:arx:papers:1407.7140
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    References listed on IDEAS

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    1. Emmanuel Guerre & Isabelle Perrigne & Quang Vuong, 2000. "Optimal Nonparametric Estimation of First-Price Auctions," Econometrica, Econometric Society, vol. 68(3), pages 525-574, May.
    2. 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.
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    6. 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.
    7. 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.
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    9. 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.
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    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 121-148, February.
    13. 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.
    14. Elodie Guerre & I. Perrigne & Q.H. Vuong, 2000. "Optimal nonparametric estimation of first-price auctions [[Estimation nonparamétrique optimale des enchères au premier prix]]," Post-Print hal-02697497, HAL.
    15. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
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    17. 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.
    18. McAfee, R. Preston & McMillan, John, 1987. "Auctions with entry," Economics Letters, Elsevier, vol. 23(4), pages 343-347.
    19. P. Lavergne & Q.H. Vuong, 1996. "Nonparametric selection of regressors : the nonnested case [[Sélection non paramétrique de régresseurs : le cas de régressions non emboîtées]]," Post-Print hal-02689500, HAL.
    20. 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.
    21. Manski, Charles F., 1985. "Semiparametric analysis of discrete response : Asymptotic properties of the maximum score estimator," Journal of Econometrics, Elsevier, vol. 27(3), pages 313-333, March.
    22. Laffont, Jean-Jacques & Vuong, Quang, 1996. "Structural Analysis of Auction Data," American Economic Review, American Economic Association, vol. 86(2), pages 414-420, May.
    23. 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.
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    Cited by:

    1. Gaurab Aryal & Maria Florencia Gabrielli, 2023. "Is Collusion-proof Procurement Expensive?," Working Papers 248, Red Nacional de Investigadores en Economía (RedNIE).
    2. Gabrielli, M. Florencia & Willington, Manuel, 2023. "Estimating damages from bidding rings in first-price auctions," Economic Modelling, Elsevier, vol. 126(C).
    3. 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.
    4. Gaurab Aryal & Maria F. Gabrielli, 2015. "Is Collusion-Proof Procurement Expensive?," Papers 1508.05353, arXiv.org, revised Nov 2020.

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    More about this item

    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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