Learning,large deviations and rare events |
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| Institution: | 1. New York University, Department of Economics, 19 W. 4th Street, 6FL, New York, NY 10012, USA;2. New York University (Abu Dhabi), PO Box 903, New York, NY 10276, USA;1. Faculty of Civil Engineering, Slovak University of Technology, Radlinského 11, 813 68 Bratislava, Slovakia;2. UTIA CAS, Pod Vodárenskou vě?í 4, 182 08 Prague, Czech Republic;3. School of Sciences, Communication University of China, Beijing 100024, China;4. Singidunum University, 11000 Belgrade, Serbia;5. Óbuda University, H-1034 Budapest, Hungary;1. Boston University, United States;2. Korea Advanced Institute of Science and Technology, South Korea |
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| Abstract: | We examine the role of generalized stochastic gradient constant gain (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, driven by sequences of consistently low or consistently high shocks and then apply our model to the canonical asset pricing framework. We demonstrate that the tails of the stationary distribution of the price–dividend ratio will follow a power law. |
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| Keywords: | Adaptive learning Large deviations Fat tails Asset prices |
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