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Competing Models

Author

Listed:
  • José Luis Montiel Olea

    (Columbia University)

  • Pietro Ortoleva

    (Princeton University)

  • Mallesh Pai

    (Rice University)

  • Andrea Prat

    (Columbia University)

Abstract
Different agents compete to predict a variable of interest related to a set of covariates via an unknown data generating process. All agents are Bayesian, but may consider different subsets of covariates to make their prediction. After observing a common dataset, who has the highest confidence in her predictive ability? We characterize it and show that it crucially depends on the size of the dataset. With small data, typically it is an agent using a model that is small-dimensional, in the sense of considering fewer covariates than the true data generating process. With big data, it is instead typically large-dimensional, possibly using more variables than the true model. These features are reminiscent of model selection techniques used in statistics and machine learning. However, here model selection does not emerge normatively, but positively as the outcome of competition between standard Bayesian decision makers. The theory is applied to auctions of assets where bidders observe the same information but hold different priors.

Suggested Citation

  • José Luis Montiel Olea & Pietro Ortoleva & Mallesh Pai & Andrea Prat, 2021. "Competing Models," Working Papers 2021-89, Princeton University. Economics Department..
    • Handle: RePEc:pri:econom:2021-89
    as

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    File URL: https://arxiv.org/pdf/1907.03809.pdf
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    References listed on IDEAS

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    More about this item

    Keywords

    Models. Low-dimensional Model; High-dimensional Model;

    JEL classification:

    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General

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