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Quantile regression methods for first-price auctions

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  • Nathalie Gimenes
  • Emmanuel Guerre

Abstract

The paper proposes a quantile-regression inference framework for first-price auctions with symmetric risk-neutral bidders under the independent private-value paradigm. It is first shown that a private-value quantile regression generates a quantile regression for the bids. The private-value quantile regression can be easily estimated from the bid quantile regression and its derivative with respect to the quantile level. This also allows to test for various specification or exogeneity null hypothesis using the observed bids in a simple way. A new local polynomial technique is proposed to estimate the latter over the whole quantile level interval. Plug-in estimation of functionals is also considered, as needed for the expected revenue or the case of CRRA risk-averse bidders, which is amenable to our framework. A quantile-regression analysis to USFS timber is found more appropriate than the homogenized-bid methodology and illustrates the contribution of each explanatory variables to the private-value distribution. Linear interactive sieve extensions are proposed and studied in the Appendices.

Suggested Citation

  • Nathalie Gimenes & Emmanuel Guerre, 2019. "Quantile regression methods for first-price auctions," Papers 1909.05542, arXiv.org, revised Sep 2020.
    • Handle: RePEc:arx:papers:1909.05542
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Jayeeta Bhattacharya & Nathalie Gimenes & Emmanuel Guerre, 2019. "Semiparametric Quantile Models for Ascending Auctions with Asymmetric Bidders," Papers 1911.13063, arXiv.org, revised Sep 2020.
    2. 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.
    3. Jayeeta Bhattacharya, 2020. "Quantile regression with generated dependent variable and covariates," Papers 2012.13614, arXiv.org.
    4. Joris Pinkse & Karl Schurter, 2019. "Estimation of Auction Models with Shape Restrictions," Papers 1912.07466, arXiv.org.

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