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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. As an application, we consider the problem of inference on the optimal reserve price.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 5899.

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Date of creation: Oct 2006
Date of revision: 02 Mar 2006
Handle: RePEc:pra:mprapa:5899

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

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References

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  1. Elliott, Graham & Muller, Ulrich K., 2007. "Confidence sets for the date of a single break in linear time series regressions," Journal of Econometrics, Elsevier, Elsevier, vol. 141(2), pages 1196-1218, December.
  2. Guerre, E. & Perrigne, I. & Vuong, Q., 1995. "Nonparametric Estimation of First-Price Auctions," Papers, Southern California - Department of Economics 9504, Southern California - Department of Economics.
  3. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, Cambridge University Press, number 9780521355643.
  4. Newey, Whitney K., 1994. "Kernel Estimation of Partial Means and a General Variance Estimator," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 10(02), pages 1-21, June.
  5. Rosa L. Matzkin, 1999. "Nonparametric Estimation of Nonadditive Random Functions," Working Papers 38, Universidad de San Andres, Departamento de Economia, revised Sep 2001.
  6. Philip A. Haile & Han Hong & Matthew Shum, 2003. "Nonparametric Tests for Common Values in First-Price Sealed-Bid Auctions," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1445, Cowles Foundation for Research in Economics, Yale University.
  7. Philip A. Haile & Elie Tamer, 2003. "Inference with an Incomplete Model of English Auctions," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 111(1), pages 1-51, February.
  8. Paarsch, Harry J., 1997. "Deriving an estimate of the optimal reserve price: An application to British Columbian timber sales," Journal of Econometrics, Elsevier, Elsevier, vol. 78(2), pages 333-357, June.
  9. Emmanuel Guerre & Isabelle Perrigne & Quang Vuong, 2009. "Nonparametric Identification of Risk Aversion in First-Price Auctions Under Exclusion Restrictions," Econometrica, Econometric Society, Econometric Society, vol. 77(4), pages 1193-1227, 07.
  10. Emmanuel Guerre & Isabelle Perrigne & Quang Vuong, 2000. "Optimal Nonparametric Estimation of First-Price Auctions," Econometrica, Econometric Society, Econometric Society, vol. 68(3), pages 525-574, May.
  11. Marmer, Vadim & Shneyerov, Artyom, 2009. "Supplement to "Quantile-Based Nonparametric Inference for First-Price Auctions"," Microeconomics.ca working papers, Vancouver School of Economics vadim_marmer-2009-61, Vancouver School of Economics, revised 09 Sep 2010.
  12. Marmer, Vadim & Shneyerov, Artyom, 2006. "Quantile-Based Nonparametric Inference for First-Price Auctions," MPRA Paper 5899, University Library of Munich, Germany, revised 02 Mar 2006.
  13. Matt Shum & Phil Haile & Han Hong, 2003. "Nonparametric Tests for Common Values in First-Price Auctions," Economics Working Paper Archive, The Johns Hopkins University,Department of Economics 501, The Johns Hopkins University,Department of Economics.
  14. Athey, Susan & Haile, Philip A., 2007. "Nonparametric Approaches to Auctions," Handbook of Econometrics, Elsevier, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 60 Elsevier.
  15. repec:cup:cbooks:9780521496032 is not listed on IDEAS
  16. 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, American Statistical Association, vol. 21(1), pages 53-64, January.
  17. 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, American Statistical Association, vol. 26, pages 423-434.
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Citations

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Cited by:
  1. Marmer, Vadim & Shneyerov, Artyom, 2008. "Quantile-Based Nonparametric Inference for First-Price Auctions," Microeconomics.ca working papers, Vancouver School of Economics marmer-08-01-17-12-16-12, Vancouver School of Economics, revised 16 May 2013.
  2. Marmer, Vadim & Shneyerov, Artyom & Xu, Pai, 2007. "What Model for Entry in First-Price Auctions? A Nonparametric Approach," Microeconomics.ca working papers, Vancouver School of Economics marmer-07-11-22-02-26-44, Vancouver School of Economics, revised 18 Feb 2011.
  3. 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, Cambridge University Press, vol. 28(01), pages 87-129, February.

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