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Nonparametric estimation of first price auctions via density–quantile function

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  • Zhang, Yu Yvette

Abstract

We propose a nonparametric estimator of bidders’ value function based on a kernel estimator of the density–quantile function of bids in first price auctions. This estimator provides certain advantage over the conventional approach that relies on the distribution/density ratio of the bids. We use a boundary-adaptive kernel for boundary bias correction and propose a practical method of bandwidth selection. Our numerical experiments demonstrate good performance of the proposed method in the estimation of first price auctions with risk neutral and risk averse bidders.

Suggested Citation

  • Zhang, Yu Yvette, 2022. "Nonparametric estimation of first price auctions via density–quantile function," Economics Letters, Elsevier, vol. 216(C).
    • Handle: RePEc:eee:ecolet:v:216:y:2022:i:c:s0165176522001604
    DOI: 10.1016/j.econlet.2022.110560
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    References listed on IDEAS

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    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. 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.
    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.
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    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. Kim, Dong-Hyuk, 2015. "Nonparametric estimation of utility function in first-price sealed-bid auctions," Economics Letters, Elsevier, vol. 126(C), pages 101-106.
    7. Jingfeng Lu & Isabelle Perrigne, 2008. "Estimating risk aversion from ascending and sealed-bid auctions: the case of timber auction data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(7), pages 871-896.
    8. 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.
    9. Gimenes, Nathalie & Guerre, Emmanuel, 2022. "Quantile regression methods for first-price auctions," Journal of Econometrics, Elsevier, vol. 226(2), pages 224-247.
    10. Emmanuel Guerre & Isabelle Perrigne & Quang Vuong, 2009. "Nonparametric Identification of Risk Aversion in First-Price Auctions Under Exclusion Restrictions," Econometrica, Econometric Society, vol. 77(4), pages 1193-1227, July.
    11. 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.
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