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Learning generates Long Memory

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Abstract

We consider a prototypical representative-agent forward-looking model, and study the low frequency variability of the data when the agent's beliefs about the model are updated through linear learning algorithms. We nd that learning in this context can generate strong persistence. The degree of persistence depends on the weights agents place on past observations when they update their beliefs, and on the magnitude of the feedback from expectations to the endogenous variable. When the learning algorithm is recursive least squares, long memory arises when the coefficient on expectations is sufficiently large. In algorithms with discounting, long memory provides a very good approximation to the low-frequency variability of the data. Hence long memory arises endogenously, due to the self-referential nature of the model, without any persistence in the exogenous shocks. This is distinctly di erent from the case of rational expectations, where the memory of the endogenous variable is determined exogenously. Finally, this property of learning is used to shed light on some well-known empirical puzzles.

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  • Chevillon, Guillaume & Mavroeidis, Sophocles, 2011. "Learning generates Long Memory," ESSEC Working Papers WP1113, ESSEC Research Center, ESSEC Business School.
  • Handle: RePEc:ebg:essewp:dr-11013
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    Cited by:

    1. Rambaccussing, Dooruj, 2015. "Modelling Housing Prices using a Present Value State Space Model," SIRE Discussion Papers 2015-32, Scottish Institute for Research in Economics (SIRE).
    2. Susanne M. Schennach, 2018. "Long Memory via Networking," Econometrica, Econometric Society, vol. 86(6), pages 2221-2248, November.
    3. Rambaccussing, Dooruj, 2015. "Modelling Housing Prices using a Present Value State Space Model," 2007 Annual Meeting, July 29-August 1, 2007, Portland, Oregon TN 2015-32, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    4. Chevillon, G. & Hecq, A.W. & Laurent, S.F.J.A., 2015. "Long memory through marginalization of large systems and hidden cross-section dependence," Research Memorandum 014, Maastricht University, Graduate School of Business and Economics (GSBE).
    5. Damjanovic, Tatiana & Girdėnas, Šarūnas & Liu, Keqing, 2015. "Stationarity of econometric learning with bounded memory and a predicted state variable," Economics Letters, Elsevier, vol. 130(C), pages 93-96.
    6. Gilles de Truchis & Florent Dubois, 2014. "Unbalanced Fractional Cointegration and the No-Arbitrage Condition on Commodity Markets," Working Papers halshs-01065775, HAL.

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    Keywords

    Learning; Long Memory; Persistence; Present-Value Models;
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