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

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  • 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
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    References listed on IDEAS

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    1. Matthew Gentry & Tong Li, 2014. "Identification in Auctions With Selective Entry," Econometrica, Econometric Society, vol. 82(1), pages 315-344, January.
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    8. 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.
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    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. Zincenko, Federico, 2024. "Estimation and inference of seller’s expected revenue in first-price auctions," Journal of Econometrics, Elsevier, vol. 241(1).
    3. Joris Pinkse & Karl Schurter, 2019. "Estimation of Auction Models with Shape Restrictions," Papers 1912.07466, arXiv.org.
    4. Haitian Xie, 2023. "Grenander-type Density Estimation under Myerson Regularity," Papers 2305.09052, arXiv.org.

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