Hostname: page-component-89b8bd64d-nlwjb Total loading time: 0 Render date: 2026-05-08T23:18:39.639Z Has data issue: false hasContentIssue false
  • English
  • Français

STOCHASTIC GRADIENT LEARNING AND INSTABILITY: AN EXAMPLE

Published online by Cambridge University Press:  28 January 2016

Sergey Slobodyan ,
Anna Bogomolova  and
Dmitri Kolyuzhnov
Sergey Slobodyan*
Affiliation:
CERGE-EI
Anna Bogomolova
Affiliation:
CERGE-EI and Novosibirsk State University
Dmitri Kolyuzhnov
Affiliation:
CERGE-EI and Institute of Economics and Industrial Engineering of the Siberian Branch of the Russian Academy of Sciences
*
Address correspondence to: Sergey Slobodyan, CERGE-EI, a joint workplace of Charles University in Prague and the Economics Institute of the Academy of Sciences of the Czech Republic, Politickych veznu 7, 111 21 Prague, Czech Republic; e-mail: Sergey.Slobodyan@cerge-ei.cz.
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper, we investigate real-time behavior of constant-gain stochastic gradient (SG) learning, using the Phelps model of monetary policy as a testing ground. We find that whereas the self-confirming equilibrium is stable under the mean dynamics in a very large region, real-time learning diverges for all but the very smallest gain values. We employ a stochastic Lyapunov function approach to demonstrate that the SG mean dynamics is easily destabilized by the noise associated with real-time learning, because its Jacobian contains stable but very small eigenvalues. We also express caution on usage of perpetual learning algorithms with such small eigenvalues, as the real-time dynamics might diverge from the equilibrium that is stable under the mean dynamics.

Keywords

Constant GainAdaptive LearningE-stabilityStochastic Gradient Learning

Information

Type
Articles
Information
Macroeconomic Dynamics , Volume 20 , Issue 3 , April 2016 , pp. 777 - 790
Copyright
Copyright © Cambridge University Press 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

Berardi, M. (2013) Escape dynamics and policy specification. Macroeconomic Dynamics 17, 123–142.Google Scholar
Branch, W.A., Davig, T., and McGough, B. (2013) Adaptive learning in regime-switching models. Macroeconomic Dynamics 17, 998–1022.Google Scholar
Branch, W. and Evans, G. (2006) A simple recursive forecasting model. Economics Letters 91, 158–166.Google Scholar
Bullard, J., Evans, G.W. and Honkapohja, S. (2010) A model of near-rational exuberance. Macroeconomic Dynamics 14, 166–188.Google Scholar
Bullard, J. and Mitra, K. (2002) Learning about monetary policy rules. Journal of Monetary Economics 49 (6), 1105–1129.CrossRefGoogle Scholar
Cho, I.-K., Williams, N., and Sargent, T.J. (2002) Escaping Nash inflation. Review of Economic Studies 69 (1), 1–40.Google Scholar
Evans, G.W. and Honkapohja, S. (2001) Learning and Expectations in Macroeconomics. Princeton, NJ: Princeton University Press.CrossRefGoogle Scholar
Evans, G.W. and Honkapohja, S. (2009) Robust learning stability with operational monetary policy rules. In Schmidt-Hebbel, K. and Walsh, C. E. (eds.), Monetary Policy under Uncertainty and Learning, pp. 145–170. Santiago: Central Bank of Chile.Google Scholar
Evans, G.W., Honkapohja, S., and Williams, N. (2010) Generalized stochastic gradient learning.' International Economic Review 51, 237–262.Google Scholar
Hommes, C. and Lux, T. (2013) Individual expectations and aggregate behavior in learning-to-forecast experiments. Macroeconomic Dynamics 17, 373–401.Google Scholar
Loparo, K.A. and Feng, X. (1999) Stability of stochastic systems. In Levine, W.S. (ed.), The Control Handbook, pp. 1105–1126. CRC Press with IEEE Press.Google Scholar
Mao, X. (1994) Stochastic stabilization and destabilization. Systems and Control Letters 23, 279–290.Google Scholar
Milani, F. (2008) Learning, monetary policy rules, and macroeconomic stability. Journal of Economic Dynamics and Control 32, 3148–3165.Google Scholar
Orphanides, A. and Williams, J.C. (2007) Inflation targeting under imperfect knowledge. FRBSF Economic Review 2007, 1–23.Google Scholar
Orphanides, A. and Williams, J.C. (2009) Imperfect knowledge and the pitfalls of optimal control monetary policy In Schmidt-Hebbel, K. and Walsh, C.E. (ed.), Monetary Policy under Uncertainty and Learning, pp. 115–144. Santiago: Central Bank of Chile.Google Scholar
Sargent, T.J. (1999) The Conquest of American Inflation. Princeton, NJ: Princeton University Press.CrossRefGoogle Scholar
Slobodyan, S. and Wouters, R. (2012) Learning in an estimated medium-scale DSGE model. Journal of Economic Dynamics and Control 36, 26–46.Google Scholar
Williams, N. (2009) Escape Dynamics in Learning Models. Mimeo, University of Wisconsin–Madison.Google Scholar