IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1909.12974.html
   My bibliography  Save this paper

Monotonicity-Constrained Nonparametric Estimation and Inference for First-Price Auctions

Author

Listed:
  • Jun Ma
  • Vadim Marmer
  • Artyom Shneyerov
  • Pai Xu

Abstract

We propose a new nonparametric estimator for first-price auctions with independent private values that imposes the monotonicity constraint on the estimated inverse bidding strategy. We show that our estimator has a smaller asymptotic variance than that of Guerre, Perrigne and Vuong's (2000) estimator. In addition to establishing pointwise asymptotic normality of our estimator, we provide a bootstrap-based approach to constructing uniform confidence bands for the density function of latent valuations.

Suggested Citation

  • Jun Ma & Vadim Marmer & Artyom Shneyerov & Pai Xu, 2019. "Monotonicity-Constrained Nonparametric Estimation and Inference for First-Price Auctions," Papers 1909.12974, arXiv.org.
    • Handle: RePEc:arx:papers:1909.12974
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1909.12974
    File Function: Latest version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Matthew Gentry & Tong Li, 2014. "Identification in Auctions With Selective Entry," Econometrica, Econometric Society, vol. 82(1), pages 315-344, January.
    2. Emmanuel Guerre & Isabelle Perrigne & Quang Vuong, 2000. "Optimal Nonparametric Estimation of First-Price Auctions," Econometrica, Econometric Society, vol. 68(3), pages 525-574, May.
    3. V. Chernozhukov & I. Fernández-Val & A. Galichon, 2009. "Improving point and interval estimators of monotone functions by rearrangement," Biometrika, Biometrika Trust, vol. 96(3), pages 559-575.
    4. 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.
    5. 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.
    6. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037, Decembrie.
    7. Tong Li & Xiaoyong Zheng, 2009. "Entry and Competition Effects in First-Price Auctions: Theory and Evidence from Procurement Auctions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 76(4), pages 1397-1429.
    8. Nianqing Liu & Yao Luo, 2017. "A Nonparametric Test For Comparing Valuation Distributions In First‐Price Auctions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 58, pages 857-888, August.
    9. Susan Athey & Jonathan Levin & Enrique Seira, 2011. "Comparing open and Sealed Bid Auctions: Evidence from Timber Auctions," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 126(1), pages 207-257.
    10. Daniel J. Henderson & Christopher F. Parmeter, 2009. "Imposing economic constraints in nonparametric regression: survey, implementation, and extension," Advances in Econometrics, in: Nonparametric Econometric Methods, pages 433-469, Emerald Group Publishing Limited.
    11. 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.
    12. Chernozhukov, Victor & Chetverikov, Denis & Kato, Kengo, 2016. "Empirical and multiplier bootstraps for suprema of empirical processes of increasing complexity, and related Gaussian couplings," Stochastic Processes and their Applications, Elsevier, vol. 126(12), pages 3632-3651.
    13. 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.
    14. Marmer, Vadim & Shneyerov, Artyom, 2012. "Quantile-based nonparametric inference for first-price auctions," Journal of Econometrics, Elsevier, vol. 167(2), pages 345-357.
    15. 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.
    16. 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.
    17. Jales, Hugo & Ma, Jun & Yu, Zhengfei, 2017. "Optimal bandwidth selection for local linear estimation of discontinuity in density," Economics Letters, Elsevier, vol. 153(C), pages 23-27.
    18. Jun Ma & Hugo Jales & Zhengfei Yu, 2020. "Minimum Contrast Empirical Likelihood Inference of Discontinuity in Density," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(4), pages 934-950, October.
    19. Henderson, Daniel J. & List, John A. & Millimet, Daniel L. & Parmeter, Christopher F. & Price, Michael K., 2012. "Empirical implementation of nonparametric first-price auction models," Journal of Econometrics, Elsevier, vol. 168(1), pages 17-28.
    20. Kenneth Hendricks & Joris Pinkse & Robert H. Porter, 2003. "Empirical Implications of Equilibrium Bidding in First-Price, Symmetric, Common Value Auctions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 70(1), pages 115-145.
    21. 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.
    22. Hendricks, Ken & Porter, Robert H., 2007. "An Empirical Perspective on Auctions," Handbook of Industrial Organization, in: Mark Armstrong & Robert Porter (ed.), Handbook of Industrial Organization, edition 1, volume 3, chapter 32, pages 2073-2143, Elsevier.
    23. Brent R. Hickman & Timothy P. Hubbard, 2015. "Replacing Sample Trimming with Boundary Correction in Nonparametric Estimation of First‐Price Auctions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(5), pages 739-762, August.
    24. 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.
    25. Mark Armstrong & Robert Porter (ed.), 2007. "Handbook of Industrial Organization," Handbook of Industrial Organization, Elsevier, edition 1, volume 3, number 1.
    26. Elena Krasnokutskaya, 2011. "Identification and Estimation of Auction Models with Unobserved Heterogeneity," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 78(1), pages 293-327.
    27. Nathalie Gimenes, 2017. "Econometrics of Ascending Auctions by Quantile Regression," The Review of Economics and Statistics, MIT Press, vol. 99(5), pages 944-953, December.
    28. 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.
    29. Gentry, Matthew L. & Hubbard, Timothy P. & Nekipelov, Denis & Paarsch, Harry J., 2018. "Structural Econometrics of Auctions: A Review," Foundations and Trends(R) in Econometrics, now publishers, vol. 9(2-4), pages 79-302, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Enache, Andreea & Florens, Jean-Pierre & Sbai, Erwann, 2023. "A functional estimation approach to the first-price auction models," Journal of Econometrics, Elsevier, vol. 235(2), pages 1564-1588.
    2. Joris Pinkse & Karl Schurter, 2019. "Estimation of Auction Models with Shape Restrictions," Papers 1912.07466, arXiv.org.
    3. Haitian Xie, 2023. "Grenander-type Density Estimation under Myerson Regularity," Papers 2305.09052, arXiv.org.
    4. Zincenko, Federico, 2024. "Estimation and inference of seller’s expected revenue in first-price auctions," Journal of Econometrics, Elsevier, vol. 241(1).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Philip A Haile & Yuichi Kitamura, 2019. "Unobserved heterogeneity in auctions," The Econometrics Journal, Royal Economic Society, vol. 22(1), pages 1-19.
    3. Gimenes, Nathalie & Guerre, Emmanuel, 2022. "Quantile regression methods for first-price auctions," Journal of Econometrics, Elsevier, vol. 226(2), pages 224-247.
    4. 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.
    5. Hickman Brent R. & Hubbard Timothy P. & Sağlam Yiğit, 2012. "Structural Econometric Methods in Auctions: A Guide to the Literature," Journal of Econometric Methods, De Gruyter, vol. 1(1), pages 67-106, August.
    6. Hickman Brent R. & Hubbard Timothy P. & Sağlam Yiğit, 2012. "Structural Econometric Methods in Auctions: A Guide to the Literature," Journal of Econometric Methods, De Gruyter, vol. 1(1), pages 67-106, August.
    7. Joris Pinkse & Karl Schurter, 2019. "Estimation of Auction Models with Shape Restrictions," Papers 1912.07466, arXiv.org.
    8. Emmanuel Guerre & Yao Luo, 2019. "Nonparametric Identification of First-Price Auction with Unobserved Competition: A Density Discontinuity Framework," Papers 1908.05476, arXiv.org, revised Dec 2024.
    9. Marmer, Vadim & Shneyerov, Artyom, 2012. "Quantile-based nonparametric inference for first-price auctions," Journal of Econometrics, Elsevier, vol. 167(2), pages 345-357.
    10. 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.
    11. Matthew Gentry & Tong Li & Jingfeng Lu, 2015. "Identification and estimation in first-price auctions with risk-averse bidders and selective entry," CeMMAP working papers CWP16/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    12. Giovanni Compiani & Philip Haile & Marcelo Sant’Anna, 2020. "Common Values, Unobserved Heterogeneity, and Endogenous Entry in US Offshore Oil Lease Auctions," Journal of Political Economy, University of Chicago Press, vol. 128(10), pages 3872-3912.
    13. An, Yonghong & Hu, Yingyao & Shum, Matthew, 2010. "Estimating first-price auctions with an unknown number of bidders: A misclassification approach," Journal of Econometrics, Elsevier, vol. 157(2), pages 328-341, August.
    14. Zincenko, Federico, 2018. "Nonparametric estimation of first-price auctions with risk-averse bidders," Journal of Econometrics, Elsevier, vol. 205(2), pages 303-335.
    15. Nathalie Gimenes & Emmanuel Guerre, 2019. "Nonparametric identification of an interdependent value model with buyer covariates from first-price auction bids," Papers 1910.10646, arXiv.org.
    16. repec:vuw:vuwscr:19224 is not listed on IDEAS
    17. Fang, Hanming & Tang, Xun, 2014. "Inference of bidders’ risk attitudes in ascending auctions with endogenous entry," Journal of Econometrics, Elsevier, vol. 180(2), pages 198-216.
    18. 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.
    19. Gimenes, Nathalie & Guerre, Emmanuel, 2020. "Nonparametric identification of an interdependent value model with buyer covariates from first-price auction bids," Journal of Econometrics, Elsevier, vol. 219(1), pages 1-18.
    20. Sağlam, Yiğit, 2012. "Structural Econometric Methods in Auctions: A Guide to the Literature," Working Paper Series 19224, Victoria University of Wellington, The New Zealand Institute for the Study of Competition and Regulation.
    21. Nathalie Gimenes, 2014. "Econometrics of Ascending Auctions by Quantile Regression," Working Papers, Department of Economics 2014_25, University of São Paulo (FEA-USP).

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1909.12974. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.