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Quantile-Based Nonparametric Inference for First-Price Auctions

  • Marmer, Vadim
  • Shneyerov, Artyom

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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File URL: https://mpra.ub.uni-muenchen.de/5899/2/MPRA_paper_5899.pdf
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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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  1. Newey, W.K., 1992. "Kernel Estimation of Partial Means and a General Variance Estimator," Working papers 93-3, Massachusetts Institute of Technology (MIT), Department of Economics.
  2. 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, 07.
  3. 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.
  4. Philip A. Haile & Han Hong & Matthew Shum, 2004. "Nonparametric Tests for Common Values in First-Price Sealed-Bid Auctions," Working Papers 2004.149, Fondazione Eni Enrico Mattei.
  5. Haile,P.A. & Tamer,E.T., 2000. "Inference with an incomplete model of English auctions," Working papers 18, Wisconsin Madison - Social Systems.
  6. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521586115, June.
  7. 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.
  8. Elliott, Graham & Muller, Ulrich K., 2004. "Confidence Sets for the Date of a Single Break in Linear Time Series Regressions," University of California at San Diego, Economics Working Paper Series qt9hf4j4c2, Department of Economics, UC San Diego.
  9. Rosa L. Matzkin, 1999. "Nonparametric Estimation of Nonadditive Random Functions," Working Papers 38, Universidad de San Andres, Departamento de Economia, revised Sep 2001.
  10. 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.
  11. 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.
  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. Emmanuel Guerre & Isabelle Perrigne & Quang Vuong, 2000. "Optimal Nonparametric Estimation of First-Price Auctions," Econometrica, Econometric Society, vol. 68(3), pages 525-574, May.
  14. Guerre, E. & Perrigne, I. & Vuong, Q., 1995. "Nonparametric Estimation of First-Price Auctions," Papers 9504, Southern California - Department of Economics.
  15. 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.
  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, vol. 21(1), pages 53-64, January.
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