IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2106.13856.html
   My bibliography  Save this paper

Nonparametric inference on counterfactuals in first-price auctions

Author

Listed:
  • Pasha Andreyanov
  • Grigory Franguridi

Abstract

In a classical model of the first-price sealed-bid auction with independent private values, we develop nonparametric estimators for several policy-relevant targets, such as the bidder's surplus and auctioneer's revenue under counterfactual reserve prices. Motivated by the linearity of these targets in the quantile function of bidders' values, we propose an estimator of the latter and derive its Bahadur-Kiefer expansion. This makes it possible to construct uniform confidence bands and test complex hypotheses about the auction design. Using the data on U.S. Forest Service timber auctions, we test whether setting zero reserve prices in these auctions was revenue maximizing.

Suggested Citation

  • Pasha Andreyanov & Grigory Franguridi, 2021. "Nonparametric inference on counterfactuals in first-price auctions," Papers 2106.13856, arXiv.org, revised Oct 2024.
    • Handle: RePEc:arx:papers:2106.13856
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2106.13856
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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. M. Jones, 1992. "Estimating densities, quantiles, quantile densities and density quantiles," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 44(4), pages 721-727, December.
    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, vol. 28(1), pages 87-129, February.
    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. Loertscher, Simon & Marx, Leslie M., 2020. "Asymptotically optimal prior-free clock auctions," Journal of Economic Theory, Elsevier, vol. 187(C).
    6. 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.
    7. 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.
    8. M. C. Jones & H. W. Lotwick, 1984. "A Remark on Algorithm as 176. Kernel Density Estimation Using the Fast Fourier Transform," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 33(1), pages 120-122, March.
    9. Li, Tong & Perrigne, Isabelle & Vuong, Quang, 2000. "Conditionally independent private information in OCS wildcat auctions," Journal of Econometrics, Elsevier, vol. 98(1), pages 129-161, September.
    10. Harry J. Paarsch & Han Hong, 2006. "An Introduction to the Structural Econometrics of Auction Data," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262162350, December.
    11. Victor Chernozhukov & Denis Chetverikov & Kengo Kato, 2012. "Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors," Papers 1212.6906, arXiv.org, revised Jan 2018.
    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. Isabelle Perrigne & Quang Vuong, 2019. "Econometrics of Auctions and Nonlinear Pricing," Annual Review of Economics, Annual Reviews, vol. 11(1), pages 27-54, August.
    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. 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.
    16. Welsh, A. H., 1988. "Asymptotically efficient estimation of the sparsity function at a point," Statistics & Probability Letters, Elsevier, vol. 6(6), pages 427-432, May.
    17. Ingraham Allan T, 2005. "A Test for Collusion between a Bidder and an Auctioneer in Sealed-Bid Auctions," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 4(1), pages 1-32, September.
    18. Falk, Michael, 1986. "On the estimation of the quantile density function," Statistics & Probability Letters, Elsevier, vol. 4(2), pages 69-73, March.
    19. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
    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. Grigory Franguridi, 2022. "Bias correction and uniform inference for the quantile density function," Papers 2207.09004, arXiv.org.

    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. Gimenes, Nathalie & Guerre, Emmanuel, 2022. "Quantile regression methods for first-price auctions," Journal of Econometrics, Elsevier, vol. 226(2), pages 224-247.
    2. 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.
    3. 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.
    4. 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.
    5. Zincenko, Federico, 2018. "Nonparametric estimation of first-price auctions with risk-averse bidders," Journal of Econometrics, Elsevier, vol. 205(2), pages 303-335.
    6. 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.
    7. 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.
    8. Joris Pinkse & Karl Schurter, 2019. "Estimation of Auction Models with Shape Restrictions," Papers 1912.07466, arXiv.org.
    9. 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.
    10. 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.
    11. Philip A Haile & Yuichi Kitamura, 2019. "Unobserved heterogeneity in auctions," The Econometrics Journal, Royal Economic Society, vol. 22(1), pages 1-19.
    12. 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.
    13. Jiaming Mao & Jingzhi Xu, 2020. "Ensemble Learning with Statistical and Structural Models," Papers 2006.05308, arXiv.org.
    14. Zincenko, Federico, 2024. "Estimation and inference of seller’s expected revenue in first-price auctions," Journal of Econometrics, Elsevier, vol. 241(1).
    15. Zhang, Yu Yvette, 2022. "Nonparametric estimation of first price auctions via density–quantile function," Economics Letters, Elsevier, vol. 216(C).
    16. Lu Ji & Tong Li, 2008. "Multi-round procurement auctions with secret reserve prices: theory and evidence," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(7), pages 897-923.
    17. Lamy, Laurent, 2012. "The econometrics of auctions with asymmetric anonymous bidders," Journal of Econometrics, Elsevier, vol. 167(1), pages 113-132.
    18. 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.
    19. Brasil, Eric Universo Rodrigues & Postali, Fernando Antonio Slaibe, 2014. "Informational rents in oil and gas concession auctions in Brazil," Energy Economics, Elsevier, vol. 46(C), pages 93-101.
    20. Marmer, Vadim & Shneyerov, Artyom, 2012. "Quantile-based nonparametric inference for first-price auctions," Journal of Econometrics, Elsevier, vol. 167(2), pages 345-357.

    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:2106.13856. 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.