IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1911.01251.html

Cheating with (Recursive) Models

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1911.01251
    File Function: Latest version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. St'ephane Bonhomme & Martin Weidner, 2018. "Minimizing Sensitivity to Model Misspecification," Papers 1807.02161, arXiv.org, revised Oct 2021.
    4. 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.
    5. Pooya Molavi, 2019. "Macroeconomics with Learning and Misspecification: A General Theory and Applications," 2019 Meeting Papers 1584, Society for Economic Dynamics.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Esponda, Ignacio & Pouzo, Demian & Yamamoto, Yuichi, 2021. "Asymptotic behavior of Bayesian learners with misspecified models," Journal of Economic Theory, Elsevier, vol. 195(C).
    2. Philippe Jehiel, 2022. "Analogy-Based Expectation Equilibrium and Related Concepts:Theory, Applications, and Beyond," Working Papers halshs-03735680, HAL.
    3. Kubler, Felix & Scheidegger, Simon, 2023. "Uniformly self-justified equilibria," Journal of Economic Theory, Elsevier, vol. 212(C).
    4. Fudenberg, Drew & Lanzani, Giacomo, 2023. "Which misspecifications persist?," Theoretical Economics, Econometric Society, vol. 18(3), July.
    5. J. Aislinn Bohren & Daniel N. Hauser, 2023. "Behavioral Foundations of Model Misspecification," PIER Working Paper Archive 23-007, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    6. Berman, Ron & Heller, Yuval, 2020. "Naive Analytics Equilibrium," MPRA Paper 103824, University Library of Munich, Germany.
    7. Steiner, Jakub & Netzer, Nick & Robson, Arthur & Kocourek, Pavel, 2021. "Endogenous Risk Attitudes," CEPR Discussion Papers 16190, C.E.P.R. Discussion Papers.
    8. Kevin He & Jonathan Libgober, 2025. "Misspecified learning and evolutionary stability," Papers 2509.16067, arXiv.org.
    9. Spiegler, Ran, 2018. "News and Archival Information in Games," CEPR Discussion Papers 12805, C.E.P.R. Discussion Papers.
    10. Yingkai Li & Harry Pei, 2020. "Misspecified Beliefs about Time Lags," Papers 2012.07238, arXiv.org.
    11. Andrew Ellis & Heidi Christina Thysen, 2021. "Subjective Causality in Choice," Papers 2106.05957, arXiv.org, revised Mar 2025.
    12. Karantounias, Anastasios G., 2023. "Doubts about the model and optimal policy," Journal of Economic Theory, Elsevier, vol. 210(C).
    13. Schipper, Burkhard C., 2021. "Discovery and equilibrium in games with unawareness," Journal of Economic Theory, Elsevier, vol. 198(C).
    14. Gamp, Tobias & Krähmer, Daniel, 2022. "Biased Beliefs in Search Markets," Rationality and Competition Discussion Paper Series 365, CRC TRR 190 Rationality and Competition.
    15. Bo Honoré & Thomas Jørgensen & Áureo de Paula, 2020. "The informativeness of estimation moments," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(7), pages 797-813, November.
    16. Yingkai Li & Aleksandrs Slivkins, 2022. "Exploration and Incentivizing Participation in Randomized Trials," Papers 2202.06191, arXiv.org, revised Jan 2026.
    17. Maximilian Blesch & Philipp Eisenhauer, 2021. "Robust decision-making under risk and ambiguity," Papers 2104.12573, arXiv.org, revised Oct 2021.
    18. Ashesh Rambachan & Jonathan Roth, 2020. "Design-Based Uncertainty for Quasi-Experiments," Papers 2008.00602, arXiv.org, revised Jun 2025.
    19. Marek Weretka & Daniel Quint, 2022. "Slope-takers in anonymous markets," GRAPE Working Papers 64, GRAPE Group for Research in Applied Economics.
    20. Stéphane Bonhomme & Martin Weidner, 2022. "Minimizing sensitivity to model misspecification," Quantitative Economics, Econometric Society, vol. 13(3), pages 907-954, July.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1911.01251. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.