Learning, Large Deviations and Rare Events

46 Pages Posted: 28 Feb 2011

See all articles by Jess Benhabib

Jess Benhabib

New York University - Leonard N. Stern School of Business - Department of Economics; National Bureau of Economic Research (NBER)

Chetan Dave

New York University

Date Written: February 2011

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.

Suggested Citation

Benhabib, Jess and Dave, Chetan, Learning, Large Deviations and Rare Events (February 2011). NBER Working Paper No. w16816. Available at SSRN: https://ssrn.com/abstract=1770371

Jess Benhabib (Contact Author)

New York University - Leonard N. Stern School of Business - Department of Economics ( email )

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Chetan Dave

New York University ( email )

Department of Economics
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New York, NY 10012
United States

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