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Bounds on Revenue Distributions in Counterfactual Auctions with Reserve Prices


  • Xun Tang

    () (Department of Economics, University of Pennsylvania)


In first-price auctions with interdependent bidder values, the distributions of private signals and values cannot be uniquely recovered from bids in Bayesian Nash equilibria. Non-identification invalidates structural analyses that rely on the exact knowledge of model primitives. In this paper I introduce tight, informative bounds on the distribution of revenues in counterfactual first-price and second-price auctions with binding reserve prices. These robust bounds are identified from distributions of equilibrium bids in first-price auctions under minimal restrictions where I allow for affiliated signals and both private and common-value paradigms. The bounds can be used to compare auction formats and to select optimal reserve prices. I propose consistent nonparametric estimators of the bounds. I extend the approach to account for observed heterogeneity across auctions, as well as binding reserve prices in the data. I use a recent data of 6,721 first-price auctions of U.S. municipal bonds to estimate bounds on counterfactual revenue distributions. I then bound optimal reserve prices for sellers with various risk attitudes.

Suggested Citation

  • Xun Tang, 2008. "Bounds on Revenue Distributions in Counterfactual Auctions with Reserve Prices," PIER Working Paper Archive 08-042, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  • Handle: RePEc:pen:papers:08-042

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    References listed on IDEAS

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    More about this item


    Empirical auctions; interdependent values; affiliated signals; partial identification; bounds; counter factual revenues; nonparametric estimation; municipal bonds;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C81 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Methodology for Collecting, Estimating, and Organizing Microeconomic Data; Data Access
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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