Advanced Search
MyIDEAS: Login to save this paper or follow this series

Stochastic Gradient versus Recursive Least Squares Learning

Contents:

Author Info

  • Sergey Slobodyan
  • Anna Bogomolova,
  • Dmitri Kolyuzhnov

Abstract

In this paper, we perform an in—depth investigation of relative merits of two adaptive learning algorithms with constant gain, Recursive Least Squares (RLS) and Stochastic Gradient (SG), using the Phelps model of monetary policy as a testing ground. The behavior of the two learning algorithms is very different. Under the mean (averaged) RLS dynamics, the Self—Confirming Equilibrium (SCE) is stable for initial conditions in a very small region around the SCE. Large distance movements of perceived model parameters from their SCE values, or “escapes”, are observed. On the other hand, the SCE is stable under the SG mean dynamics in a large region. However, actual behavior of the SG learning algorithm is divergent for a wide range of constant gain parameters, including those that could be justified as economically meaningful. We explain the discrepancy by looking into the structure of eigenvalues and eigenvectors of the mean dynamics map under SG learning. Results of our paper hint that caution is needed when constant gain learning algorithms are used. If the mean dynamics map is stable but not contracting in every direction, and most eigenvalues of the map are close to the unit circle, the constant gain learning algorithm might diverge.

Download Info

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.cerge-ei.cz/pdf/wp/Wp309.pdf
Download Restriction: no

Bibliographic Info

Paper provided by The Center for Economic Research and Graduate Education - Economic Institute, Prague in its series CERGE-EI Working Papers with number wp309.

as in new window
Length:
Date of creation: Oct 2006
Date of revision:
Handle: RePEc:cer:papers:wp309

Contact details of provider:
Postal: P.O. Box 882, Politickych veznu 7, 111 21 Praha 1
Phone: (+420) 224 005 123
Fax: (+420) 224 005 333
Email:
Web page: http://www.cerge-ei.cz
More information through EDIRC

Related research

Keywords: Constant gain adaptive learning; E—stability; recursive least squares; stochastic gradient learning.;

Other versions of this item:

Find related papers by JEL classification:

This paper has been announced in the following NEP Reports:

References

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. William Poole, 2002. "Flation," Speech 49, Federal Reserve Bank of St. Louis.
  2. Cho, In-Koo & Williams, Noah & Sargent, Thomas J, 2002. "Escaping Nash Inflation," Review of Economic Studies, Wiley Blackwell, vol. 69(1), pages 1-40, January.
  3. Chryssi Giannitsarou, 2003. "Heterogeneous Learning," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 6(4), pages 885-906, October.
  4. Thomas Sargent & Noah Williams & Tao Zha, 2009. "The Conquest of South American Inflation," Journal of Political Economy, University of Chicago Press, vol. 117(2), pages 211-256, 04.
  5. Kaushik Mitra & Seppo Honkapohja, 2004. "Learning Stability in Economies with Heterogenous Agents," Royal Holloway, University of London: Discussion Papers in Economics 04/17, Department of Economics, Royal Holloway University of London, revised Jul 2004.
  6. George W. Evans & Seppo Honkapohja & Noah Williams, 2005. "Generalized Stochastic Gradient Learning," University of Oregon Economics Department Working Papers 2005-17, University of Oregon Economics Department, revised 18 May 2008.
  7. Dmitri Kolyuzhnov & Anna Bogomolova & Sergey Slobodyan, 2006. "Escape Dynamics: A Continuous—Time Approximation," CERGE-EI Working Papers wp285, The Center for Economic Research and Graduate Education - Economic Institute, Prague.
Full references (including those not matched with items on IDEAS)

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. Evans , George W & Honkapohja, Seppo, 2007. "Robust learning stability with operational monetary policy rules," Research Discussion Papers 31/2007, Bank of Finland.

Lists

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

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:cer:papers:wp309. 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: (Jana Koudelkova).

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.