Large sample properties for estimators based on the order statistics approach in auctions

Konrad Menzel, Paolo Morganti

    Research output: Contribution to journalArticlepeer-review


    For symmetric auctions, there is a close relationship between distributions of order statistics of bidders' valuations and observable bids that is often used to estimate or bound the valuation distribution, optimal reserve price, and other quantities of interest nonparametrically. However, we show that the functional mapping from distributions of order statistics to their parent distribution is, in general, not Lipschitz continuous and, therefore, introduces an irregularity into the estimation problem. More specifically, we derive the optimal rate for nonparametric point estimation of, and bounds for, the private value distribution, which is typically substantially slower than the regular root-n rate. We propose trimming rules for the nonparametric estimator that achieve that rate and derive the asymptotic distribution for a regularized estimator. We then demonstrate that policy parameters that depend on the valuation distribution, including optimal reserve price and expected revenue, are irregularly identified when bidding data are incomplete. We also give rates for nonparametric estimation of descending bid auctions and strategic equivalents.

    Original languageEnglish (US)
    Pages (from-to)329-375
    Number of pages47
    JournalQuantitative Economics
    Issue number2
    StatePublished - Jul 2013


    • Bounds
    • Empirical auctions
    • Irregular identification
    • Order statistics
    • Uniform consistency

    ASJC Scopus subject areas

    • Economics and Econometrics


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