IDEAS home Printed from https://ideas.repec.org/p/sce/scecfa/446.html
   My bibliography  Save this paper

Stochastic Gradient versus Recursive Least Squares Learning

Author

Listed:
  • 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. RLS is characterized by a very small region of attraction of the Self—Confirming Equilibrium (SCE) under the mean, or averaged, dynamics, and “escapes†, or large distance movements of perceived model parameters from their SCE values. 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 the SG learning. As a result of our paper, we express a warning regarding the behavior of constant gain learning algorithm in real time. If many eigenvalues of the mean dynamics map are close to the unit circle, Stochastic Recursive Algorithm which describes the actual dynamics under learning might exhibit divergent behavior despite convergent mean dynamics.

Suggested Citation

  • Sergey Slobodyan & Anna Bogomolova & Dmitri Kolyuzhnov, 2006. "Stochastic Gradient versus Recursive Least Squares Learning," Computing in Economics and Finance 2006 446, Society for Computational Economics.
  • Handle: RePEc:sce:scecfa:446
    as

    Download full text from publisher

    File URL: http://repec.org/sce2006/up.28420.1141162925.pdf
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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, April.
    2. 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.
    3. George W. Evans & Seppo Honkapohja & Noah Williams, 2010. "Generalized Stochastic Gradient Learning," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 51(1), pages 237-262, February.
    4. Kolyuzhnov, Dmitri & Bogomolova, Anna & Slobodyan, Sergey, 2014. "Escape dynamics: A continuous-time approximation," Journal of Economic Dynamics and Control, Elsevier, vol. 38(C), pages 161-183.
    5. Seppo Honkapohja & Kaushik Mitra, 2006. "Learning Stability in Economies with Heterogeneous Agents," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 9(2), pages 284-309, April.
    6. Chryssi Giannitsarou, 2003. "Heterogeneous Learning," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 6(4), pages 885-906, October.
    7. In-Koo Cho & Noah Williams & Thomas J. Sargent, 2002. "Escaping Nash Inflation," Review of Economic Studies, Oxford University Press, vol. 69(1), pages 1-40.
    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


    Cited by:

    1. George W. Evans & Seppo Honkapohja, 2009. "Robust Learning Stability with Operational Monetary Policy Rules," Central Banking, Analysis, and Economic Policies Book Series,in: Klaus Schmidt-Hebbel & Carl E. Walsh & Norman Loayza (Series Editor) & Klaus Schmidt-Hebbel (Series (ed.), Monetary Policy under Uncertainty and Learning, edition 1, volume 13, chapter 5, pages 145-170 Central Bank of Chile.

    More about this item

    Keywords

    constant gain adaptive learning; E—stability; recursive least squares; stochastic gradient learning;

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • E10 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - General
    • E17 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Forecasting and Simulation: Models and Applications

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:sce:scecfa:446. 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: (Christopher F. Baum). General contact details of provider: http://edirc.repec.org/data/sceeeea.html .

    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 CitEc recognized a reference but did not link an item in RePEc 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 RePEc Author Service 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.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.