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Quantile-Based Nonparametric Inference for First-Price Auctions

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  • Marmer, Vadim
  • Shneyerov, Artyom

Abstract

We propose a quantile-based nonparametric approach to inference on the probability density function (PDF) of the private values in first-price sealed-bid auctions with independent private values. Our method of inference is based on a fully nonparametric kernel-based estimator of the quantiles and PDF of observable bids. Our estimator attains the optimal rate of Guerre, Perrigne, and Vuong (2000), and is also asymptotically normal with the appropriate choice of the bandwidth.

Suggested Citation

  • Marmer, Vadim & Shneyerov, Artyom, 2008. "Quantile-Based Nonparametric Inference for First-Price Auctions," Microeconomics.ca working papers marmer-08-01-17-12-16-12, Vancouver School of Economics, revised 16 May 2013.
  • Handle: RePEc:ubc:pmicro:marmer-08-01-17-12-16-12
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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. 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.
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    5. Philip A. Haile & Han Hong & Matthew Shum, 2003. "Nonparametric Tests for Common Values in First-Price Sealed-Bid Auctions," Cowles Foundation Discussion Papers 1445, Cowles Foundation for Research in Economics, Yale University.
    6. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643, May.
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    8. 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.
    9. Li, Qi & Racine, Jeffrey S, 2008. "Nonparametric Estimation of Conditional CDF and Quantile Functions With Mixed Categorical and Continuous Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 423-434.
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    11. Riley, John G & Samuelson, William F, 1981. "Optimal Auctions," American Economic Review, American Economic Association, vol. 71(3), pages 381-392, June.
    12. 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.
    13. Marmer, Vadim & Shneyerov, Artyom, 2012. "Quantile-based nonparametric inference for first-price auctions," Journal of Econometrics, Elsevier, vol. 167(2), pages 345-357.
    14. Tong Li & Isabelle Perrigne & Quang Vuong, 2002. "Structural Estimation of the Affliated Private Value Auction Model," RAND Journal of Economics, The RAND Corporation, vol. 33(2), pages 171-193, Summer.
    15. Newey, Whitney K., 1994. "Kernel Estimation of Partial Means and a General Variance Estimator," Econometric Theory, Cambridge University Press, vol. 10(2), pages 1-21, June.
    16. Marmer, Vadim & Shneyerov, Artyom, 2009. "Supplement to "Quantile-Based Nonparametric Inference for First-Price Auctions"," Microeconomics.ca working papers vadim_marmer-2009-61, Vancouver School of Economics, revised 09 Sep 2010.
    17. Rosa L. Matzkin, 2003. "Nonparametric Estimation of Nonadditive Random Functions," Econometrica, Econometric Society, vol. 71(5), pages 1339-1375, September.
    18. 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.
    19. Li, Tong & Perrigne, Isabelle & Vuong, Quang, 2003. "Semiparametric Estimation of the Optimal Reserve Price in First-Price Auctions," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(1), pages 53-64, January.
    20. Matt Shum & Phil Haile & Han Hong, 2003. "Nonparametric Tests for Common Values in First-Price Auctions," Economics Working Paper Archive 501, The Johns Hopkins University,Department of Economics.
    21. Guerre, E. & Perrigne, I. & Vuong, Q., 1995. "Nonparametric Estimation of First-Price Auctions," Papers 9504, Southern California - Department of Economics.
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    Citations

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    Cited by:

    1. Yao Luo & Isabelle Perrigne & Quang Vuong, 2018. "Structural Analysis of Nonlinear Pricing," Journal of Political Economy, University of Chicago Press, vol. 126(6), pages 2523-2568.
    2. Marmer, Vadim & Shneyerov, Artyom & Xu, Pai, 2013. "What model for entry in first-price auctions? A nonparametric approach," Journal of Econometrics, Elsevier, vol. 176(1), pages 46-58.
    3. Marmer, Vadim & Shneyerov, Artyom, 2012. "Quantile-based nonparametric inference for first-price auctions," Journal of Econometrics, Elsevier, vol. 167(2), pages 345-357.
    4. Zincenko, Federico, 2018. "Nonparametric estimation of first-price auctions with risk-averse bidders," Journal of Econometrics, Elsevier, vol. 205(2), pages 303-335.
    5. Ma, Jun & Marmer, Vadim & Shneyerov, Artyom, 2019. "Inference for first-price auctions with Guerre, Perrigne, and Vuong’s estimator," Journal of Econometrics, Elsevier, vol. 211(2), pages 507-538.
    6. Jun, Sung Jae & Zincenko, Federico, 2022. "Testing for risk aversion in first-price sealed-bid auctions," Journal of Econometrics, Elsevier, vol. 226(2), pages 295-320.
    7. Federico Zincenko, 2019. "Testing for Risk Aversion in First-Price Sealed-Bid Auctions," Working Paper 6641, Department of Economics, University of Pittsburgh.
    8. Jun Ma & Vadim Marmer & Artyom Shneyerov & Pai Xu, 2021. "Monotonicity-constrained nonparametric estimation and inference for first-price auctions," Econometric Reviews, Taylor & Francis Journals, vol. 40(10), pages 944-982, November.
    9. Luo, Yao, 2018. "Identification of participation constraints in contracts," Economics Letters, Elsevier, vol. 173(C), pages 84-87.
    10. Yao Luo & Yuanyuan Wan, 2018. "Integrated-Quantile-Based Estimation for First-Price Auction Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(1), pages 173-180, January.
    11. Enache, Andreea & Florens, Jean-Pierre, 2020. "Quantile Analysis of "Hazard-Rate" Game Models," TSE Working Papers 20-1117, Toulouse School of Economics (TSE).
    12. Guerre, Emmanuel & Sabbah, Camille, 2012. "Uniform Bias Study And Bahadur Representation For Local Polynomial Estimators Of The Conditional Quantile Function," Econometric Theory, Cambridge University Press, vol. 28(1), pages 87-129, February.
    13. Nathalie Gimenes, 2014. "Econometrics of Ascending Auctions by Quantile Regression," Working Papers, Department of Economics 2014_25, University of São Paulo (FEA-USP).
    14. Pasha Andreyanov & Grigory Franguridi, 2021. "Nonparametric inference on counterfactuals in first-price auctions," Papers 2106.13856, arXiv.org, revised Jun 2022.
    15. Andreea Enache & Jean-Pierre Florens, 2020. "Identification and Estimation in a Third-Price Auction Model," Post-Print hal-02929530, HAL.
    16. Joris Pinkse & Karl Schurter, 2019. "Estimation of Auction Models with Shape Restrictions," Papers 1912.07466, arXiv.org.
    17. Nianqing Liu & Yao Luo, 2014. "A Nonparametric Test of Exogenous Participation in First-Price Auctions," Working Papers tecipa-519, University of Toronto, Department of Economics.
    18. Rothe, Christoph & Wied, Dominik, 2020. "Estimating derivatives of function-valued parameters in a class of moment condition models," Journal of Econometrics, Elsevier, vol. 217(1), pages 1-19.
    19. Gimenes, Nathalie & Guerre, Emmanuel, 2022. "Quantile regression methods for first-price auctions," Journal of Econometrics, Elsevier, vol. 226(2), pages 224-247.
    20. Emmanuel Guerre & Camille Sabbah, 2009. "Uniform Bias Study and Bahadur Representation for Local Polynomial Estimators of the Conditional Quantile Function," Working Papers 648, Queen Mary University of London, School of Economics and Finance.
    21. Robert Clark & Decio Coviello & Jean-Fran�ois Gauthier & Art Shneyerov, 2018. "Bid Rigging and Entry Deterrence in Public Procurement: Evidence from an Investigation into Collusion and Corruption in Quebec," The Journal of Law, Economics, and Organization, Oxford University Press, vol. 34(3), pages 301-363.
    22. Florens, Jean-Pierre & Enache, Andreea & Sbaï, Erwann, 2021. "A Functional Estimation Approach to the First-Price Auction Models," TSE Working Papers 21-1264, Toulouse School of Economics (TSE).
    23. Zhang, Yu Yvette, 2017. "A shape constrained estimator of bidding function of first-price sealed-bid auctions," Economics Letters, Elsevier, vol. 150(C), pages 67-72.
    24. Enache, Andreea & Florens, Jean-Pierre, 2019. "Identification and Estimation in a Third-Price Auction Model," TSE Working Papers 19-989, Toulouse School of Economics (TSE).

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    More about this item

    Keywords

    First-price auctions; independent private values; nonparametric estimation; kernel estimation; quantiles; optimal reserve price;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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