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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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    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. Marmer, Vadim & Shneyerov, Artyom, 2012. "Quantile-based nonparametric inference for first-price auctions," Journal of Econometrics, Elsevier, vol. 167(2), pages 345-357.
    3. Philip A. Haile & Han Hong & Matthew Shum, 2003. "Nonparametric Tests for Common Values at First-Price Sealed-Bid Auctions," NBER Working Papers 10105, National Bureau of Economic Research, Inc.
    4. Newey, Whitney K., 1994. "Kernel Estimation of Partial Means and a General Variance Estimator," Econometric Theory, Cambridge University Press, vol. 10(02), pages 1-21, June.
    5. 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.
    6. 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.
    7. Rosa L. Matzkin, 2003. "Nonparametric Estimation of Nonadditive Random Functions," Econometrica, Econometric Society, vol. 71(5), pages 1339-1375, September.
    8. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643, 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. Elliott, Graham & Muller, Ulrich K., 2007. "Confidence sets for the date of a single break in linear time series regressions," Journal of Econometrics, Elsevier, vol. 141(2), pages 1196-1218, December.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. Guerre, E. & Perrigne, I. & Vuong, Q., 1995. "Nonparametric Estimation of First-Price Auctions," Papers 9504, Southern California - Department of Economics.
    16. 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.
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    Citations

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    Cited by:

    1. Yao Luo & Isabelle Perrigne & Quang Vuong, 2014. "Structural Analysis of Nonlinear Pricing," Working Papers tecipa-518, University of Toronto, Department of Economics.
    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. Federico Zincenko, 2016. "Nonparametric Estimation of First-Price Auctions with Risk-Averse Bidders," Working Paper 5855, Department of Economics, University of Pittsburgh.
    5. 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(01), pages 87-129, February.
    6. Nathalie Gimenes, 2014. "Econometrics of Ascending Auctions by Quantile Regression," Working Papers, Department of Economics 2014_25, University of São Paulo (FEA-USP).
    7. Yao Luo & Yuanyuan Wan, 2015. "Integrated-quantile-based estimation for first price auction models," Working Papers tecipa-539, University of Toronto, Department of Economics.
    8. 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.
    9. Ma, Jun & Marmer, Vadim & Shneyerov, Artyom, 2016. "Inference for First-Price Auctions with Guerre, Perrigne, and Vuong's estimator," Microeconomics.ca working papers vadim_marmer-2016-4, Vancouver School of Economics, revised 17 Mar 2018.
    10. Robert Clark & decio Coviello & Jean-Francois Gauthier & Art Shneyerov, 2018. "Bid rigging and entry deterrence in public procurement: Evidence from an investigation into collusion and corruption in Quebec," Working Papers 1401, Queen's University, Department of Economics.
    11. 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.

    More about this item

    Keywords

    First-price auctions; independent private values; nonparametric estimation; kernel estimation; quantiles; optimal reserve price;

    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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