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Learning, Large Deviations and Rare Events

Author

Listed:
  • Jess Benhabib

    (NYU)

  • Chetan Dave

    (NYU)

Abstract

We examine the role of generalized constant gain stochastic gradient (SGCG) learning in generating large deviations of an endogenous variable from its rational expectations value. We show analytically that these large deviations can occur with a frequency associated with a fat tailed distribution even though the model is driven by thin tailed exogenous stochastic processes. We characterize these large deviations that are driven by sequences of consistently low or consistently high shocks. We then apply our model to the canonical asset-pricing model. We demonstrate that the tails of the stationary distribution of the price-dividend ratio will follow a power law. (Copyright: Elsevier)

Suggested Citation

  • Jess Benhabib & Chetan Dave, 2014. "Learning, Large Deviations and Rare Events," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 17(3), pages 367-382, July.
    • Handle: RePEc:red:issued:12-17
    DOI: 10.1016/j.red.2013.09.004
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    Cited by:

    1. In-Koo Cho & Kenneth Kasa, 2017. "Gresham's Law of Model Averaging," American Economic Review, American Economic Association, vol. 107(11), pages 3589-3616, November.
    2. Koulovatianos, Christos & Wieland, Volker, 2011. "Asset pricing under rational learning about rare disasters," IMFS Working Paper Series 46, Goethe University Frankfurt, Institute for Monetary and Financial Stability (IMFS).
    3. Dave, Chetan & Tsang, Kwok Ping, 2014. "Recursive preferences, learning and large deviations," Economics Letters, Elsevier, vol. 124(3), pages 329-334.
    4. Dave, Chetan & Malik, Samreen, 2017. "A tale of fat tails," European Economic Review, Elsevier, vol. 100(C), pages 293-317.
    5. Lianfeng Song & Hongxia Wang & Huanshui Zhang & Hongdan Li, 2023. "Rational Expectations Models with Multiplicative Noise," Journal of Optimization Theory and Applications, Springer, vol. 199(1), pages 233-257, October.
    6. Chetan Dave & Scott J. Dressler & Samreen Malik, 2022. "A Cautionary Tale of Fat Tails," Villanova School of Business Department of Economics and Statistics Working Paper Series 53, Villanova School of Business Department of Economics and Statistics.
    7. Dave, Chetan & Sorge, Marco M., 2020. "Sunspot-driven fat tails: A note," Economics Letters, Elsevier, vol. 193(C).
    8. Kamihigashi, Takashi & Stachurski, John, 2016. "Seeking ergodicity in dynamic economies," Journal of Economic Theory, Elsevier, vol. 163(C), pages 900-924.
    9. Dave, Chetan & Sorge, Marco, 2020. "Equilibrium Indeterminacy and Extreme Outcomes: A Fat Sunspot Ta(i)l(e)," Working Papers 2020-12, University of Alberta, Department of Economics.
    10. Takashi Kamihigashiw & John Stachurski, 2014. "Seeking Ergodicity in Dynamic Economies," Working Papers 2014-402, Department of Research, Ipag Business School.
    11. Christian Di Pietro & Mariafortuna Pietroluongo & Marco M. Sorge, 2023. "Stochastic Ordering of Stationary Distributions of Linear Recurrences: Further Results and Economic Applications," Economies, MDPI, vol. 11(4), pages 1-10, April.
    12. Dave, Chetan & Sorge, Marco M., 2021. "Equilibrium indeterminacy and sunspot tales," European Economic Review, Elsevier, vol. 140(C).
    13. Michele Berardi, 2020. "A probabilistic interpretation of the constant gain learning algorithm," Bulletin of Economic Research, Wiley Blackwell, vol. 72(4), pages 393-403, October.
    14. Chevillon, Guillaume & Mavroeidis, Sophocles, 2018. "Perpetual learning and apparent long memory," Journal of Economic Dynamics and Control, Elsevier, vol. 90(C), pages 343-365.
    15. Dave, Chetan & Sorge, Marco, 2023. "Fat Tailed DSGE Models: A Survey and New Results," Working Papers 2023-3, University of Alberta, Department of Economics.
    16. Gandré, Pauline, 2020. "US stock prices and recency-biased learning in the run-up to the Global Financial Crisis and its aftermath," Journal of International Money and Finance, Elsevier, vol. 104(C).

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    More about this item

    Keywords

    Adaptive learning; Large deviations; Fat tails; Asset prices;
    All these keywords.

    JEL classification:

    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations

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