IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Log in (now much improved!) to save this paper

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.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://www.nber.org/papers/w16816.pdf
Download Restriction: no

Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 16816.

as
in new window

Length:
Date of creation: Feb 2011
Date of revision:
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
Note: EFG
Contact details of provider: Postal:
National Bureau of Economic Research, 1050 Massachusetts Avenue Cambridge, MA 02138, U.S.A.

Phone: 617-868-3900
Web page: http://www.nber.org
Email:


More information through EDIRC

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. Xavier Gabaix & Parameswaran Gopikrishnan & Vasiliki Plerou & H. Eugene Stanley, 2006. "Institutional Investors and Stock Market Volatility," The Quarterly Journal of Economics, Oxford University Press, vol. 121(2), pages 461-504.
  2. Bengt Holmström, 1999. "Managerial Incentive Problems: A Dynamic Perspective," Review of Economic Studies, Oxford University Press, vol. 66(1), pages 169-182.
  3. Volker Wieland & Christos Koulovatianos, 2011. "Asset Pricing under Rational Learning about Rare Disasters," 2011 Meeting Papers 1417, Society for Economic Dynamics.
  4. Eva Carceles Poveda & Chryssi Giannitsarou, 2006. "Asset pricing with adaptive learning," Computing in Economics and Finance 2006 25, Society for Computational Economics.
  5. George W. Evans & Seppo Honkapohja & Noah Williams, 2005. "Generalized Stochastic Gradient Learning," NBER Technical Working Papers 0317, National Bureau of Economic Research, Inc.
  6. Adam, Klaus & Marcet, Albert & Nicolini, Juan Pablo, 2012. "Stock Market Volatility and Learning," Working Papers 12-06, University of Mannheim, Department of Economics.
  7. Wiliam Branch & George W. Evans, . "Asset Return Dynamics and Learning," University of Oregon Economics Department Working Papers 2006-14, University of Oregon Economics Department.
  8. Martin L. Weitzman, 2007. "Subjective Expectations and Asset-Return Puzzles," American Economic Review, American Economic Association, vol. 97(4), pages 1102-1130, September.
  9. Bullard, James & Duffy, John, 2001. "Learning And Excess Volatility," Macroeconomic Dynamics, Cambridge University Press, vol. 5(02), pages 272-302, April.
  10. Thomas Sargent & Noah Williams & Tao Zha, 2004. "Shocks and Government Beliefs: The Rise and Fall of American Inflation," NBER Working Papers 10764, National Bureau of Economic Research, Inc.
  11. Robert J. Barro, 2009. "Rare Disasters, Asset Prices, and Welfare Costs," American Economic Review, American Economic Association, vol. 99(1), pages 243-64, March.
  12. Thomas J. Sargent & Noah Williams, 2003. "Impacts of priors on convergence and escapes from Nash inflation," FRB Atlanta Working Paper 2003-14, Federal Reserve Bank of Atlanta.
  13. Bengt Holmstrom, 1999. "Managerial Incentive Problems: A Dynamic Perspective," NBER Working Papers 6875, National Bureau of Economic Research, Inc.
  14. Chryssi Giannitsarou & Eva Carceles-Poveda, 2004. "Adaptive Learning in Practice," Computing in Economics and Finance 2004 271, Society for Computational Economics.
  15. Ghosh, Arka P. & Hay, Diana & Hirpara, Vivek & Rastegar, Reza & Roitershtein, Alexander & Schulteis, Ashley & Suh, Jiyeon, 2010. "Random linear recursions with dependent coefficients," Statistics & Probability Letters, Elsevier, vol. 80(21-22), pages 1597-1605, November.
  16. William Poole & Robert H. Rasche, 2002. "Flation," Review, Federal Reserve Bank of St. Louis, issue Nov, pages 1-6.
    • William Poole, 2002. "Flation," Speech 49, Federal Reserve Bank of St. Louis.
  17. Jess Benhabib, 2009. "A Note on Regime Switching, Monetary Policy, and Multiple Equilibria," NBER Working Papers 14770, National Bureau of Economic Research, Inc.
  18. Jess Benhabib & Alberto Bisin & Shenghao Zhu, 2011. "The Distribution of Wealth and Fiscal Policy in Economies With Finitely Lived Agents," Econometrica, Econometric Society, vol. 79(1), pages 123-157, 01.
  19. Cho, In-Koo & Sargent, Thomas J., 2000. "Escaping Nash inflation," Working Paper Series 0023, European Central Bank.
  20. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November.
  21. Allan Timmermann, 1996. "Excess Volatility and Predictability of Stock Prices in Autoregressive Dividend Models with Learning," Review of Economic Studies, Oxford University Press, vol. 63(4), pages 523-557.
  22. Allan G. Timmermann, 1993. "How Learning in Financial Markets Generates Excess Volatility and Predictability in Stock Prices," The Quarterly Journal of Economics, Oxford University Press, vol. 108(4), pages 1135-1145.
  23. Cogley, Timothy & Sargent, Thomas J., 2008. "The market price of risk and the equity premium: A legacy of the Great Depression?," Journal of Monetary Economics, Elsevier, vol. 55(3), pages 454-476, April.
  24. Adam, Klaus & Marcet, Albert, 2011. "Internal rationality, imperfect market knowledge and asset prices," Journal of Economic Theory, Elsevier, vol. 146(3), pages 1224-1252, May.
  25. Xavier Gabaix, 2008. "Power Laws in Economics and Finance," NBER Working Papers 14299, National Bureau of Economic Research, Inc.
  26. Chang-Jin Kim & Charles R. Nelson, 1999. "State-Space Models with Regime Switching: Classical and Gibbs-Sampling Approaches with Applications," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262112388.
  27. Eva Carceles-Poveda & Chryssi Giannitsarou, 2007. "Online Appendix to Asset Pricing with Adaptive Learning," Technical Appendices carceles08, Review of Economic Dynamics.
  28. Brennan, Michael J. & Xia, Yihong, 2001. "Stock price volatility and equity premium," Journal of Monetary Economics, Elsevier, vol. 47(2), pages 249-283, April.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:nbr:nberwo:16816. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ()

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.