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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

In the independent private values framework for first-price auctions, we propose a new nonparametric estimator of the probability density of latent valuations 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 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.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:emetrv:v:40:y:2021:i:10:p:944-982
    DOI: 10.1080/07474938.2021.1889198
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    Cited by:

    1. Joris Pinkse & Karl Schurter, 2019. "Estimation of Auction Models with Shape Restrictions," Papers 1912.07466, arXiv.org.
    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. 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).

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