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Nonparametric estimation of first-price auctions with risk-averse bidders

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  • Zincenko, Federico

Abstract

This paper proposes nonparametric estimators for the bidders’ utility function and density of private values in a first-price sealed-bid auction model with independent valuations. I study a setting with risk-averse bidders and adopt a fully nonparametric approach by not placing any restrictions on the shape of the utility function beyond regularity conditions. I propose a population criterion function that has a unique minimizer, which characterizes the utility function and density of private values. The resulting estimators emerge after replacing the population quantities by sample analogues. These estimators are uniformly consistent and their convergence rates are established. I further suggest an estimator for the optimal reserve price. Monte Carlo experiments show that the proposed estimators perform well in finite samples.

Suggested Citation

  • Zincenko, Federico, 2018. "Nonparametric estimation of first-price auctions with risk-averse bidders," Journal of Econometrics, Elsevier, vol. 205(2), pages 303-335.
    • Handle: RePEc:eee:econom:v:205:y:2018:i:2:p:303-335
    DOI: 10.1016/j.jeconom.2018.03.015
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    Cited by:

    1. Federico Zincenko, 2023. "Nonparametric estimation of conditional densities by generalized random forests," Papers 2309.13251, arXiv.org, revised Mar 2025.
    2. Zhang, Yu Yvette, 2022. "Nonparametric estimation of first price auctions via density–quantile function," Economics Letters, Elsevier, vol. 216(C).
    3. Nathalie Gimenes & Tonghui Qi & Sorawoot Srisuma, 2025. "Identification and Estimation of Seller Risk Aversion in Ascending Auctions," Papers 2509.19945, arXiv.org.
    4. Gimenes, Nathalie & Guerre, Emmanuel, 2022. "Quantile regression methods for first-price auctions," Journal of Econometrics, Elsevier, vol. 226(2), pages 224-247.
    5. Luo, Yao, 2020. "Unobserved heterogeneity in auctions under restricted stochastic dominance," Journal of Econometrics, Elsevier, vol. 216(2), pages 354-374.
    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. Matthew Gentry & Tong Li & Jingfeng Lu, 2015. "Identification and estimation in first-price auctions with risk-averse bidders and selective entry," CeMMAP working papers 16/15, Institute for Fiscal Studies.
    8. 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.
    9. Kim, Dong-Hyuk & Ratan, Anmol, 2022. "Disentangling risk aversion and loss aversion in first-price auctions: An empirical approach," European Economic Review, Elsevier, vol. 150(C).
    10. Dong Li & Luya Wang & Ximing Wu, 2021. "Bayesian estimation of bidding process and bidder’s preference under shape restrictions," Empirical Economics, Springer, vol. 60(1), pages 157-176, January.
    11. Xiaohong Chen & Matthew Gentry & Tong Li & Jingfeng Lu, 2020. "Identification and Inference in First-Price Auctions with Risk Averse Bidders and Selective Entry," Cowles Foundation Discussion Papers 2257, Cowles Foundation for Research in Economics, Yale University.
    12. Grundl, Serafin & Zhu, Yu, 2024. "Two results on auctions with endogenous entry," Economics Letters, Elsevier, vol. 234(C).
    13. Zhang, Yu Yvette, 2017. "A shape constrained estimator of bidding function of first-price sealed-bid auctions," Economics Letters, Elsevier, vol. 150(C), pages 67-72.
    14. 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.
    15. Zincenko, Federico, 2024. "Estimation and inference of seller’s expected revenue in first-price auctions," Journal of Econometrics, Elsevier, vol. 241(1).
    16. Grundl, Serafin & Zhu, Yu, 2019. "Identification and estimation of risk aversion in first-price auctions with unobserved auction heterogeneity," Journal of Econometrics, Elsevier, vol. 210(2), pages 363-378.
    17. Enache, Andreea & Florens, Jean-Pierre, 2020. "Identification And Estimation In A Third-Price Auction Model," Econometric Theory, Cambridge University Press, vol. 36(3), pages 386-409, June.
    18. Enache, Andreea & Florens, Jean-Pierre, 2019. "Identification and Estimation in a Third-Price Auction Model," TSE Working Papers 19-989, Toulouse School of Economics (TSE).

    More about this item

    Keywords

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    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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