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ADAPTIVE LEARNING IN REGIME-SWITCHING MODELS

Published online by Cambridge University Press:  06 March 2012

William A. Branch ,
Troy Davig  and
Bruce McGough
William A. Branch*
Affiliation:
University of California, Irvine
Troy Davig
Affiliation:
Barclays Capital
Bruce McGough
Affiliation:
Oregon State University
*
Address correspondence to: William A. Branch, Department of Economics, 3151 Social Science Plaza, Irvine, CA 92697-5100, USA; e-mail: wbranch@uci.edu.
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Abstract

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We study adaptive learning in economic environments subject to recurring structural change. Stochastically evolving institutional and policymaking features can be described by regime-switching models with parameters that evolve according to finite state Markov processes. We demonstrate that in nonlinear models of this form, the presence of sunspot equilibria implies two natural schemes for learning the conditional means of endogenous variables: under mean value learning, agents condition on a sunspot variable that captures the self-fulfilling serial correlation in the equilibrium, whereas under vector autoregression learning (VAR learning), the self-fulfilling serial correlation must be learned. We show that an intuitive condition ensures convergence to a regime-switching rational expectations equilibrium. However, the stability of sunspot equilibria, when they exist, depends on whether agents adopt mean value or VAR learning: coordinating on sunspot equilibria via a VAR learning rule is not possible. To illustrate these phenomena, we develop results for an overlapping-generations model and a New Keynesian model.

Keywords

E-StabilityAdaptive LearningRegime SwitchingSunspots

Information

Type
Articles
Information
Macroeconomic Dynamics , Volume 17 , Issue 5 , July 2013 , pp. 998 - 1022
Copyright
Copyright © Cambridge University Press 2012 

References

REFERENCES

Andolfatto, D. and Gomme, P. (2003) Monetary policy regimes and beliefs. International Economic Review 44 (1), 1–30.CrossRefGoogle Scholar
Benhabib, J. (2009) A Note on Regime Switching, Monetary Policy and Multiple Equilibria. Working paper, New York University.CrossRefGoogle Scholar
Bernanke, B. S. (2004) The Great Moderation. Remarks by Governor Ben S. Bernanke at the Meetings of the Eastern Economic Association, Washington, DC, February 20.Google Scholar
Blanchard, O. and Kahn, C. M. (1980) The solution of linear difference models under rational expectations. Econometrica 48 (5), 1305–1312.CrossRefGoogle Scholar
Brainard, W. C. (1967) Uncertainty and the effectiveness of policy. American Economic Review 57 (2), 411–425.Google Scholar
Branch, W. A., Davig, T., and McGough, B. (2011) Adaptive Learning in Regime-Switching Models. Working paper. Available at www.socsci.uci.edu/wbranch.Google Scholar
Bray, M. M. and Savin, N. E. (1986) Rational expectations equilibria, learning and model specification. Econometrica 54 (5), 1129–1160.CrossRefGoogle Scholar
Chung, H., Davig, T., and Leeper, E. M. (2007) Monetary and fiscal policy switching. Journal of Money, Credit and Banking 39 (4), 809–842.CrossRefGoogle Scholar
Clarida, R., Gali, J., and Gertler, M. (2000) Monetary policy rules and macroeconomic stability: Evidence and some theory. Quarterly Journal of Economics 115 (1), 147–180.CrossRefGoogle Scholar
Davig, T. (2004) Regime-switching debt and taxation. Journal of Monetary Economics 51 (4), 837–859.CrossRefGoogle Scholar
Davig, T. and Leeper, E. M. (2007) Generalizing the Taylor principle. American Economic Review 97 (3), 607–635.CrossRefGoogle Scholar
Dennis, R. (2006) The policy preferences of the U.S. Federal Reserve. Journal of Applied Econometrics 21 (1), 55–77.CrossRefGoogle Scholar
Evans, G. W. (1985) Expectational stability and the multiple equilibria problem in linear rational expectations models. Quarterly Journal of Economics 100, 1217–1233.CrossRefGoogle 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. (2003) Expectational stability of stationary sunspot equilibria in a forward-looking linear model. Journal of Economic Dynamics and Control 28, 171–181.CrossRefGoogle Scholar
Evans, G. W. and McGough, B. (2005a) Monetary policy, indeterminacy, and learning. Journal of Economic Dynamics and Control 29, 1809–1840.CrossRefGoogle Scholar
Evans, G. W. and McGough, B. (2005b) Stable sunspot solutions in models with predetermined variables. Journal of Economic Dynamics and Control 29, 601–625.CrossRefGoogle Scholar
Farmer, R. A., Waggoner, D. F., and Zha, T. (2009) Indeterminacy in a forward looking regime switching model. International Journal of Economic Theory 5, 69–84.CrossRefGoogle Scholar
Farmer, R. A., Waggoner, D. F., and Zha, T. (2010) Generalizing the Taylor principle: A comment. American Economic Review 100 (1), 608–617.CrossRefGoogle Scholar
Hamilton, J. D. (1989) A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica 57, 357–384.CrossRefGoogle Scholar
Kim, C.-J. and Nelson, C. R. (1999) State-Space Models with Regime Switching. Cambridge, MA: MIT Press.Google Scholar
Leeper, E. M. and Zha, T. (2003) Modest policy interventions. Journal of Monetary Economics 50, 1673–1700.CrossRefGoogle Scholar
Lucas, R. E. (1986) Adaptive behavior and economic theory. Journal of Business 59 (4), S401–S426.Google Scholar
Marcet, A. and Sargent, T. J. (1989) Convergence of least-squares learning mechanisms in self-referential models. Journal of Economic Theory 48, 337–368.CrossRefGoogle Scholar
McCallum, B. T. (1983) On non-uniqueness in rational expectations models: An attempt at perspective. Journal of Monetary Economics 11, 139–168.CrossRefGoogle Scholar
Sims, C. A. and Zha, T. (2006) Were there regime switches in U.S. monetary policy. American Economic Review 96 (1), 54–81.CrossRefGoogle Scholar
Svensson, L. E. and Williams, N. (2007) Monetary Policy with Model Uncertainty : Distributional Forecast Targeting. Mimeo, Princeton University.Google Scholar
Taylor, J. B. (1993) Discretion versus policy rules in practice. Carnegie–Rochester Conference Series on Public Policy 39, 195–214.CrossRefGoogle Scholar
Zampolli, F. (2006) Optimal monetary policy in a regime-switching economy: The response to abrupt shifts in exchange rate dynamics. Journal of Economic Dynamics and Control 30, 1527–1567.CrossRefGoogle Scholar