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Learning, Large Deviations and Rare Events

  • Jess Benhabib
  • Chetan Dave

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.

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File URL: http://www.nber.org/papers/w16816.pdf
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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 16816.

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Date of creation: Feb 2011
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Publication status: published as 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), July.
Handle: RePEc:nbr:nberwo:16816
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