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Cheating with (Recursive) Models

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  • Kfir Eliaz
  • Ran Spiegler
  • Yair Weiss

Abstract

To what extent can agents with misspecified subjective models predict false correlations? We study an "analyst" who utilizes models that take the form of a recursive system of linear regression equations. The analyst fits each equation to minimize the sum of squared errors against an arbitrarily large sample. We characterize the maximal pairwise correlation that the analyst can predict given a generic objective covariance matrix, subject to the constraint that the estimated model does not distort the mean and variance of individual variables. We show that as the number of variables in the model grows, the false pairwise correlation can become arbitrarily close to one, regardless of the true correlation.

Suggested Citation

  • Kfir Eliaz & Ran Spiegler & Yair Weiss, 2019. "Cheating with (Recursive) Models," Papers 1911.01251, arXiv.org.
    • Handle: RePEc:arx:papers:1911.01251
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    References listed on IDEAS

    as
    1. Ignacio Esponda & Demian Pouzo, 2016. "Berk–Nash Equilibrium: A Framework for Modeling Agents With Misspecified Models," Econometrica, Econometric Society, vol. 84, pages 1093-1130, May.
    2. St'ephane Bonhomme & Martin Weidner, 2018. "Minimizing Sensitivity to Model Misspecification," Papers 1807.02161, arXiv.org, revised Oct 2021.
    3. Alfredo Di Tillio & Marco Ottaviani & Peter Norman Sørensen, 2017. "Persuasion Bias in Science: Can Economics Help?," Economic Journal, Royal Economic Society, vol. 127(605), pages 266-304, October.
    4. Pooya Molavi, 2019. "Macroeconomics with Learning and Misspecification: A General Theory and Applications," 2019 Meeting Papers 1584, Society for Economic Dynamics.
    5. Alfredo Di Tillio & Marco Ottaviani & Peter Norman Sørensen, 2017. "Persuasion Bias in Science: Can Economics Help?," Economic Journal, Royal Economic Society, vol. 127(605), pages 266-304, October.
    6. Ignacio Esponda & Demian Pouzo, 2016. "Berk–Nash Equilibrium: A Framework for Modeling Agents With Misspecified Models," Econometrica, Econometric Society, vol. 84, pages 1093-1130, May.
    7. Ran Spiegler, 2017. "“Data Monkeys”: A Procedural Model of Extrapolation from Partial Statistics," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 84(4), pages 1818-1841.
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