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Identification of Auction Models Using Order Statistics


  • Yao Luo
  • Ruli Xiao


Auction data often fail to record all bids or all relevant factors that shift bidder values. In this paper, we study the identification of auction models with unobserved heterogeneity (UH) using multiple order statistics of bids. Classical measurement error approaches require multiple independent measurements. Order statistics, by definition, are dependent, rendering classical approaches inapplicable. First, we show that models with nonseparable finite UH is identifiable using three consecutive order statistics or two consecutive ones with an instrument. Second, two arbitrary order statistics identify the models if UH provides support variations. Third, models with separable continuous UH are identifiable using two consecutive order statistics under a weak restrictive stochastic dominance condition. Lastly, we apply our methods to U.S. Forest Service timber auctions and find evidence of UH.

Suggested Citation

  • Yao Luo & Ruli Xiao, 2019. "Identification of Auction Models Using Order Statistics," Working Papers tecipa-630, University of Toronto, Department of Economics.
  • Handle: RePEc:tor:tecipa:tecipa-630

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    References listed on IDEAS

    1. Quang Vuong & Sandra Campo & Isabelle Perrigne, 2003. "Asymmetry in first-price auctions with affiliated private values," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(2), pages 179-207.
    2. Philip A. Haile, 2001. "Auctions with Resale Markets: An Application to U.S. Forest Service Timber Sales," American Economic Review, American Economic Association, vol. 91(3), pages 399-427, June.
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    More about this item


    Unobserved Heterogeneity; Measurement Error; Finite Mixture; Multiplicative Separability; Support Variations; Deconvolution;

    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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