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Semi-nonparametric estimation of independently and identically repeated first-price auctions via an integrated simulated moments method

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  • Bierens, Herman J.
  • Song, Hosin

Abstract

In this paper we propose to estimate the value distribution of independently and identically repeated first-price auctions directly via a semi-nonparametric integrated simulated moments sieve approach. Given a candidate value distribution function in a sieve space, we simulate bids according to the equilibrium bid function involved. We take the difference of the empirical characteristic functions of the actual and simulated bids as the moment function. The objective function is then the integral of the squared moment function over an interval. Minimizing this integral to the distribution functions in the sieve space involved and letting the sieve order increase to infinity with the sample size then yields a uniformly consistent semi-nonparametric estimator of the actual value distribution. Also, we propose an integrated moment test for the validity of the first-price auction model, and an data-driven method for the choice of the sieve order. Finally, we conduct a few numerical experiments to check the performance of our approach.

Suggested Citation

  • Bierens, Herman J. & Song, Hosin, 2012. "Semi-nonparametric estimation of independently and identically repeated first-price auctions via an integrated simulated moments method," Journal of Econometrics, Elsevier, vol. 168(1), pages 108-119.
    • Handle: RePEc:eee:econom:v:168:y:2012:i:1:p:108-119
    DOI: 10.1016/j.jeconom.2011.09.012
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    Cited by:

    1. Yu Zhu, 2020. "Inference in nonparametric/semiparametric moment equality models with shape restrictions," Quantitative Economics, Econometric Society, vol. 11(2), pages 609-636, May.
    2. 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.
    3. Joris Pinkse & Karl Schurter, 2019. "Estimation of Auction Models with Shape Restrictions," Papers 1912.07466, arXiv.org.
    4. JoonHwan Cho & Yao Luo & Ruli Xiao, 2024. "Deconvolution from two order statistics," Papers 2403.17777, arXiv.org.
    5. Jean-Jacques Forneron, 2019. "A Sieve-SMM Estimator for Dynamic Models," Papers 1902.01456, arXiv.org, revised Jan 2023.
    6. JoonHwan Cho & Yao Luo & Ruli Xiao, 2022. "Deconvolution from Two Order Statistics," Working Papers tecipa-739, University of Toronto, Department of Economics.
    7. 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.

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    More about this item

    Keywords

    First-price auctions; Semi-nonparametric estimation; Sieve estimation; Empirical characteristic functions; Simulated moments; Legendre polynomials; Integrated moment test;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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