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Proxy variables and feedback effects in decision making

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  • Clyde, Alexander

Abstract

When using data, an analyst often only has access to proxies of the true variables. I propose a framework that models decision makers who naively assume potentially noisy proxy variables are perfect measurements. Due to feedback from choices into data, a notion of equilibrium is required to close the model. I illustrate the concept with applications to policing/crime and market entry. In these applications, we see that very small imperfections in the proxy variable can lead to large distortions in beliefs. I show that the set of strategies that can arise as equilibria with arbitrarily close to perfect measurement coincides with a version of Self-Confirming Equilibrium.

Suggested Citation

  • Clyde, Alexander, 2025. "Proxy variables and feedback effects in decision making," Games and Economic Behavior, Elsevier, vol. 153(C), pages 408-429.
    • Handle: RePEc:eee:gamebe:v:153:y:2025:i:c:p:408-429
    DOI: 10.1016/j.geb.2025.07.008
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    References listed on IDEAS

    as
    1. Yuval Salant & Josh Cherry, 2020. "Statistical Inference in Games," Econometrica, Econometric Society, vol. 88(4), pages 1725-1752, July.
    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. Jehiel, Philippe & Koessler, Frédéric, 2008. "Revisiting games of incomplete information with analogy-based expectations," Games and Economic Behavior, Elsevier, vol. 62(2), pages 533-557, March.
    4. Mathew L. A. Hayward & Dean A. Shepherd & Dale Griffin, 2006. "A Hubris Theory of Entrepreneurship," Management Science, INFORMS, vol. 52(2), pages 160-172, February.
    5. Dekel, Eddie & Fudenberg, Drew & Levine, David K., 2004. "Learning to play Bayesian games," Games and Economic Behavior, Elsevier, vol. 46(2), pages 282-303, February.
    6. Ran Spiegler, 2016. "Bayesian Networks and Boundedly Rational Expectations," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 131(3), pages 1243-1290.
    7. Eliaz, Kfir & Spiegler, Ran & Thysen, Heidi C., 2021. "Strategic interpretations," Journal of Economic Theory, Elsevier, vol. 192(C).
    8. Fudenberg, Drew & Kamada, Yuichiro, 2018. "Rationalizable partition-confirmed equilibrium with heterogeneous beliefs," Games and Economic Behavior, Elsevier, vol. 109(C), pages 364-381.
    9. Philippe Jehiel, 2018. "Investment Strategy and Selection Bias: An Equilibrium Perspective on Overoptimism," American Economic Review, American Economic Association, vol. 108(6), pages 1582-1597, June.
    10. Ulrike Malmendier & Geoffrey Tate, 2005. "CEO Overconfidence and Corporate Investment," Journal of Finance, American Finance Association, vol. 60(6), pages 2661-2700, December.
    11. Mira Frick & Ryota Iijima & Yuhta Ishii, 2020. "Misinterpreting Others and the Fragility of Social Learning," Econometrica, Econometric Society, vol. 88(6), pages 2281-2328, November.
    12. John Haltiwanger, 2015. "Job Creation, Job Destruction, and Productivity Growth: The Role of Young Businesses," Annual Review of Economics, Annual Reviews, vol. 7(1), pages 341-358, August.
    13. Drew Fudenberg & David K. Levine, 2006. "Superstition and Rational Learning," American Economic Review, American Economic Association, vol. 96(3), pages 630-651, June.
    14. , & ,, 2008. "Contagion through learning," Theoretical Economics, Econometric Society, vol. 3(4), December.
    15. Emi Nakamura & Jón Steinsson, 2013. "Price Rigidity: Microeconomic Evidence and Macroeconomic Implications," Annual Review of Economics, Annual Reviews, vol. 5(1), pages 133-163, May.
    16. Pierpaolo Battigalli & Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci, 2015. "Self-Confirming Equilibrium and Model Uncertainty," American Economic Review, American Economic Association, vol. 105(2), pages 646-677, February.
    17. Susanne Schennach, 2022. "Measurement Systems," Journal of Economic Literature, American Economic Association, vol. 60(4), pages 1223-1263, December.
    18. Ran Spiegler, 2020. "Can Agents with Causal Misperceptions be Systematically Fooled?," Journal of the European Economic Association, European Economic Association, vol. 18(2), pages 583-617.
    19. Fudenberg, Drew & Levine, David K, 1993. "Self-Confirming Equilibrium," Econometrica, Econometric Society, vol. 61(3), pages 523-545, May.
    20. James Heckman, 2013. "Sample selection bias as a specification error," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 31(3), pages 129-137.
    21. Jehiel, Philippe, 2005. "Analogy-based expectation equilibrium," Journal of Economic Theory, Elsevier, vol. 123(2), pages 81-104, August.
    22. Drew Fudenberg & Kevin He, 2018. "Learning and Type Compatibility in Signaling Games," Econometrica, Econometric Society, vol. 86(4), pages 1215-1255, July.
    23. Elliot Lipnowski & Evan Sadler, 2019. "Peer‐Confirming Equilibrium," Econometrica, Econometric Society, vol. 87(2), pages 567-591, March.
    24. Patil, Sanket & Salant, Yuval, 2024. "Optimal sample sizes and statistical decision rules," Theoretical Economics, Econometric Society, vol. 19(2), May.
    25. Aaron Chalfin & Justin McCrary, 2018. "Are U.S. Cities Underpoliced? Theory and Evidence," The Review of Economics and Statistics, MIT Press, vol. 100(1), pages 167-186, March.
    26. Osborne, Martin J. & Rubinstein, Ariel, 2003. "Sampling equilibrium, with an application to strategic voting," Games and Economic Behavior, Elsevier, vol. 45(2), pages 434-441, November.
    27. , & ,, 2015. "Rationalizable partition-confirmed equilibrium," Theoretical Economics, Econometric Society, vol. 10(3), September.
    28. Spiegler, Ran, 2021. "Modeling players with random “data access”," Journal of Economic Theory, Elsevier, vol. 198(C).
    29. Duarte Gonc{c}alves, 2022. "Sequential Sampling Equilibrium," Papers 2212.07725, arXiv.org, revised Nov 2023.
    30. Schumacher, Heiner & Thysen, Heidi Christina, 2022. "Equilibrium contracts and boundedly rational expectations," Theoretical Economics, Econometric Society, vol. 17(1), January.
    31. Ignacio Esponda & Demian Pouzo, 2017. "Conditional Retrospective Voting in Large Elections," American Economic Journal: Microeconomics, American Economic Association, vol. 9(2), pages 54-75, May.
    32. Kfir Eliaz & Ran Spiegler, 2020. "A Model of Competing Narratives," American Economic Review, American Economic Association, vol. 110(12), pages 3786-3816, December.
    33. Battigalli, P. & Francetich, A. & Lanzani, G. & Marinacci, M., 2019. "Learning and self-confirming long-run biases," Journal of Economic Theory, Elsevier, vol. 183(C), pages 740-785.
    34. J. Tetlow, Robert & von zur Muehlen, Peter, 2001. "Robust monetary policy with misspecified models: Does model uncertainty always call for attenuated policy?," Journal of Economic Dynamics and Control, Elsevier, vol. 25(6-7), pages 911-949, June.
    35. Cooper, Arnold C. & Woo, Carolyn Y. & Dunkelberg, William C., 1988. "Entrepreneurs' perceived chances for success," Journal of Business Venturing, Elsevier, vol. 3(2), pages 97-108.
    36. Drew Fudenberg & Giacomo Lanzani & Philipp Strack, 2024. "Selective-Memory Equilibrium," Journal of Political Economy, University of Chicago Press, vol. 132(12), pages 3978-4020.
    37. Diane Coyle, 2015. "GDP: A Brief but Affectionate History (Revised and Expanded Edition)," Economics Books, Princeton University Press, edition 2, number 10598, December.
    38. Paul Heidhues & Botond Kőszegi & Philipp Strack, 2018. "Unrealistic Expectations and Misguided Learning," Econometrica, Econometric Society, vol. 86(4), pages 1159-1214, July.
    39. J. Aislinn Bohren & Daniel N. Hauser, 2021. "Learning With Heterogeneous Misspecified Models: Characterization and Robustness," Econometrica, Econometric Society, vol. 89(6), pages 3025-3077, November.
    40. Osborne, Martin J & Rubinstein, Ariel, 1998. "Games with Procedurally Rational Players," American Economic Review, American Economic Association, vol. 88(4), pages 834-847, September.
    41. Ignacio Esponda, 2008. "Behavioral Equilibrium in Economies with Adverse Selection," American Economic Review, American Economic Association, vol. 98(4), pages 1269-1291, September.
    42. Drew Fudenberg & Giacomo Lanzani & Philipp Strack, 2021. "Limit Points of Endogenous Misspecified Learning," Econometrica, Econometric Society, vol. 89(3), pages 1065-1098, May.
    43. Bohren, Aislinn & Hauser, Daniel, 2017. "Learning with Heterogeneous Misspecified Models: Characterization and Robustness," CEPR Discussion Papers 12036, C.E.P.R. Discussion Papers.
    44. J. Aislinn Bohren & Daniel N. Hauser, 2024. "Behavioral Foundations of Model Misspecification," PIER Working Paper Archive 24-032, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
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    JEL classification:

    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making

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