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STRUCTURAL STABILITY OF THE GENERALIZED TAYLOR RULE

Published online by Cambridge University Press:  04 September 2017

William A. Barnett  and
Evgeniya A. Duzhak
William A. Barnett
Affiliation:
University of Kansas
Evgeniya A. Duzhak*
Affiliation:
Federal Reserve Bank of San Francisco
*
Address correspondence to: Evgeniya A. Duzhak, Federal Reserve Bank of San Francisco, 101 Market Street, San Francisco, CA 94105, USA; e-mail: [email protected].
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Abstract

This paper analyzes the dynamical properties of monetary models with regime switching. We start with the analysis of the evolution of inflation when policy is guided by a simple monetary rule where coefficients switch with the policy regime. We rule out the possibility of a Hopf bifurcation and demonstrate the possibility of a period-doubling bifurcation. As a result, a small change in the parameters (e.g., a more active policy response) can lead to a drastic change in the path of inflation. We show that the New Keynesian model with a current-looking Taylor rule is not prone to bifurcations. A New Keynesian model with a hybrid rule, however, exhibits the same pattern of period-doubling bifurcations as the analysis with a simple monetary rule.

Keywords

New KeynesianTaylor RuleRegime SwitchingBifurcation AnalysisStructural Stability
Type
Articles
Information
Macroeconomic Dynamics , Volume 23 , Issue 4 , June 2019 , pp. 1664 - 1678
Copyright
Copyright © Cambridge University Press 2017 

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Footnotes

The views in this paper are solely the responsibility of the authors and should not be interpreted as reflecting the views of the Federal Reserve Bank of San Francisco or the Board of Governors of the Federal Reserve System.

References

REFERENCES

Andrews, Donald W. K. (1993) Tests for parameter instability and structural change with unknown change point. Econometrica 61 (4), 821–856.Google Scholar
Barnett, William A. and Evgeniya, A. Duzhak (2008) Non-robust dynamic inferences from macroeconometric models: Bifurcation stratification of confidence regions. Physica A 387 (15), 3817–3825.Google Scholar
Barnett, William A. and Duzhak, Evgeniya A. (2010) Empirical assessment of bifurcation regions within New Keynesian models. Economic Theory 45 (1–2), 99–128.Google Scholar
Barnett, William A. and He, Yijun (1999) Stability analysis of continuous-time macroeconometric systems. Studies in Nonlinear Dynamics and Econometrics 3 (4), 169–188.Google Scholar
Barnett, William A. and He, Yijun (2001) Nonlinearity, chaos, and bifurcation: A competition and an experiment. In Negishi, Takashi, Ramachandran, Rama V., and Mino, Kazuo (eds.), Economic Theory, Dynamics and Markets: Essays in Honor of Ryuzo Sato, pp. 167–187. Dordrecht: Kluwer Academic Publishers.Google Scholar
Barnett, William A. and He, Yijun (2002) Stabilization policy as bifurcation selection: Would stabilization policy work if the economy really were unstable? Macroeconomic Dynamics 6 (5), 713–747.Google Scholar
Barnett, William A. and He, Yijun (2004) Bifurcations in macroeconomic models. In Dowrick, Steve, Pitchford, Rohan, and Turnovsky, Steven (eds.), Economic Growth and Macroeconomic Dynamics: Recent Developments in Economic Theory, pp. 95–112. Cambridge, UK: Cambridge University Press.Google Scholar
Barnett, William A. and He, Yijun (2006) Robustness of inferences to singularity bifurcation. In Proceedings of the Joint Statistical Meetings of the 2005 American Statistical Society, vol. 100. Alexandria, VA: American Statistical Association.Google Scholar
Benhabib, Jess and Nishimura, Kazuo (1979) The Hopf bifurcation and the existence and stability of closed orbits in multisector models of optimal economic growth. Journal of Economic Theory 21 (3), 421–444.Google Scholar
Bernanke, Ben S., Laubach, Thomas, Mishkin, Frederic S., and Posen, Adam S. (1999) Inflation Targeting: Lessons from the International Experience. Princeton, NJ: Princeton University Press.Google Scholar
Clarida, Richard, Gali, Jordi, and Gertler, Mark (1999) The science of monetary policy: A New Keynesian perspective. Journal of Economic Literature 37 (Dec.), 1661–1707.Google Scholar
Davig, Troy and Leeper, Eric M. (2006) Generalizing the Taylor principle. American Economic Review 97 (3), 607–635.Google Scholar
Evans, George (1985) Expectational stability and the multiple equilibria problem in linear rational expectations models. Quarterly Journal of Economics 100 (4), 1217–1233.Google Scholar
Farmer, Roger E. A., Waggoner, Daniel F., and Zha, Tao (2007) Understanding the New Keynesian Model When Monetary Policy Switches Regimes. Working paper 2007-12, NBER working paper no. 12965.Google Scholar
Gali, Jordi and Gertler, Mark (1999) Inflation dynamics: A structural econometric analysis. Journal of Monetary Economics 44 (2), 195–222.Google Scholar
Groen, Jan J. J. and Mumtaz, Haroon (2008) Investigating the Structural Stability of the Phillips Curve Relationship. Bank of England working paper no. 350.Google Scholar
Hamilton, James D. (1989) A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica, 57, 357–384.Google Scholar
Hansen, Bruce E. (1992) Testing for parameter instability in linear models. Journal of Policy Modeling 14 (4), 517–533.Google Scholar
Hopf, Eberhard (1942) Abzweigung Einer Periodischen Lösung von Einer Stationaren Lösung Eines Differentialsystems. Sáchsische Akademie der Wissenschaften Mathematische-Physikalische, Leipzig 94, 1–22.Google Scholar
Kuznetsov, Yuri A. (1998) Elements of Applied Bifurcation Theory. New York: Springer-Verlag.Google Scholar
Leeper, Edward and Sims, Christopher A. (1994) Toward a modern macro model usable for policy analysis. NBER Macroeconomics Annual, 9, 81–117.Google Scholar
Nyblom, Jukka (1989) Testing for the constancy of parameters over time. Journal of the American Statistical Association 84 (405), 223–230.Google Scholar
Seydel, Rüdiger (1994) Practical Bifurcation and Stability Analysis. New York: Springer-Verlag.Google Scholar
Sims, Christopher A. and Zha, Tao (2006) Were there regime switches in U.S. monetary policy? American Economic Review 96 (1), 54–81.Google Scholar
Taylor, John B. (1999) A historical analysis of monetary policy rules. In Taylor, John B. (ed.), Monetary Policy Rules, pp. 319–40. Chicago: University of Chicago Press for NBER.Google Scholar
Walsh, Carl E. (2003) Monetary Theory and Policy, 2nd ed. Cambridge, MA: MIT Press.Google Scholar
Warne, Anders (2000) Causality and Regime Inference in a Markov Switching VAR. Sveriges Riksbank working paper no. 118, 2000.Google Scholar
Woodford, Michael (2003) Interest and Prices: Foundations of a Theory of Monetary Policy. Princeton, NJ: Princeton University Press.Google Scholar