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Learning generates Long Memory

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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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File URL: http://hal-essec.archives-ouvertes.fr/docs/00/66/10/12/PDF/WP1113.pdf
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Paper provided by ESSEC Research Center, ESSEC Business School in its series ESSEC Working Papers with number WP1113.

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Length: 55 pages
Date of creation: 24 Nov 2011
Handle: RePEc:ebg:essewp:dr-11013
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ESSEC Research Center, BP 105, 95021 Cergy, France

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