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Learning from ambiguous and misspecified models

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  • Marinacci, Massimo
  • Massari, Filippo

Abstract

We model inter-temporal ambiguity as the scenario in which a Bayesian learner holds more than one prior distribution over a set of models and provide sufficient conditions for ambiguity to fade away because of learning. Our conditions apply to most learning environments: iid and non-iid model-classes, well-specified and misspecified model-classes/prior support pairs. We show that ambiguity fades away if the empirical evidence supports a set of models with identical predictions, a condition much weaker than learning the truth.

Suggested Citation

  • Marinacci, Massimo & Massari, Filippo, 2019. "Learning from ambiguous and misspecified models," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 144-149.
    • Handle: RePEc:eee:mateco:v:84:y:2019:i:c:p:144-149
    DOI: 10.1016/j.jmateco.2019.07.012
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    References listed on IDEAS

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    1. Larry G. Epstein & Martin Schneider, 2007. "Learning Under Ambiguity," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 74(4), pages 1275-1303.
    2. Epstein, Larry G. & Schneider, Martin, 2003. "Recursive multiple-priors," Journal of Economic Theory, Elsevier, vol. 113(1), pages 1-31, November.
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    5. Massari, Filippo, 2017. "Markets with heterogeneous beliefs: A necessary and sufficient condition for a trader to vanish," Journal of Economic Dynamics and Control, Elsevier, vol. 78(C), pages 190-205.
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    7. Ehud Lehrer & Rann Smorodinsky, 1996. "Compatible Measures and Merging," Mathematics of Operations Research, INFORMS, vol. 21(3), pages 697-706, August.
    8. Filippo Massari, 2013. "Comment on If You're so Smart, Why Aren't You Rich? Belief Selection in Complete and Incomplete Markets," Econometrica, Econometric Society, vol. 81(2), pages 849-851, March.
    9. Massimo Marinacci, 2002. "Learning from ambiguous urns," Statistical Papers, Springer, vol. 43(1), pages 143-151, January.
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    Cited by:

    1. Cinfrignini, Andrea & Petturiti, Davide & Vantaggi, Barbara, 2023. "Dynamic bid–ask pricing under Dempster-Shafer uncertainty," Journal of Mathematical Economics, Elsevier, vol. 107(C).
    2. Dindo, Pietro & Massari, Filippo, 2020. "The wisdom of the crowd in dynamic economies," Theoretical Economics, Econometric Society, vol. 15(4), November.
    3. Bottazzi, Giulio & Giachini, Daniele & Ottaviani, Matteo, 2023. "Market selection and learning under model misspecification," Journal of Economic Dynamics and Control, Elsevier, vol. 156(C).
    4. Xiaoyu Cheng, 2022. "Robust Data-Driven Decisions Under Model Uncertainty," Papers 2205.04573, arXiv.org.
    5. Gemayel, Roland & Preda, Alex, 2021. "Performance and learning in an ambiguous environment: A study of cryptocurrency traders," International Review of Financial Analysis, Elsevier, vol. 77(C).
    6. Massari, Filippo & Newton, Jonathan, 2020. "When does ambiguity fade away?," Economics Letters, Elsevier, vol. 194(C).
    7. Daniele Giachini, 2021. "Rationality and asset prices under belief heterogeneity," Journal of Evolutionary Economics, Springer, vol. 31(1), pages 207-233, January.
    8. Chen, Jaden Yang, 2022. "Biased learning under ambiguous information," Journal of Economic Theory, Elsevier, vol. 203(C).
    9. Larry G. Epstein & Shaolin Ji, 2017. "Optimal Learning and Ellsberg’s Urns," Boston University - Department of Economics - Working Papers Series WP2017-010, Boston University - Department of Economics.
    10. Larry G. Epstein & Shaolin Ji, 2022. "Optimal Learning Under Robustness and Time-Consistency," Operations Research, INFORMS, vol. 70(3), pages 1317-1329, May.

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