Skip to main content


  • William A. Barnett (a1) and Evgeniya A. Duzhak (a2)

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.

Corresponding author
Address correspondence to: Evgeniya A. Duzhak, Federal Reserve Bank of San Francisco, 101 Market Street, San Francisco, CA 94105, USA; e-mail:
Hide All

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.

Hide All
Andrews Donald W. K. (1993) Tests for parameter instability and structural change with unknown change point. Econometrica 61 (4), 821856.
Barnett William A. and Evgeniya A. Duzhak (2008) Non-robust dynamic inferences from macroeconometric models: Bifurcation stratification of confidence regions. Physica A 387 (15), 38173825.
Barnett William A. and Duzhak Evgeniya A. (2010) Empirical assessment of bifurcation regions within New Keynesian models. Economic Theory 45 (1–2), 99128.
Barnett William A. and He Yijun (1999) Stability analysis of continuous-time macroeconometric systems. Studies in Nonlinear Dynamics and Econometrics 3 (4), 169188.
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. 167187. Dordrecht: Kluwer Academic Publishers.
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), 713747.
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. 95112. Cambridge, UK: Cambridge University Press.
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.
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), 421444.
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.
Clarida Richard, Gali Jordi, and Gertler Mark (1999) The science of monetary policy: A New Keynesian perspective. Journal of Economic Literature 37 (Dec.), 16611707.
Davig Troy and Leeper Eric M. (2006) Generalizing the Taylor principle. American Economic Review 97 (3), 607635.
Evans George (1985) Expectational stability and the multiple equilibria problem in linear rational expectations models. Quarterly Journal of Economics 100 (4), 12171233.
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.
Gali Jordi and Gertler Mark (1999) Inflation dynamics: A structural econometric analysis. Journal of Monetary Economics 44 (2), 195222.
Groen Jan J. J. and Mumtaz Haroon (2008) Investigating the Structural Stability of the Phillips Curve Relationship. Bank of England working paper no. 350.
Hamilton James D. (1989) A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica, 57, 357384.
Hansen Bruce E. (1992) Testing for parameter instability in linear models. Journal of Policy Modeling 14 (4), 517533.
Hopf Eberhard (1942) Abzweigung Einer Periodischen Lösung von Einer Stationaren Lösung Eines Differentialsystems. Sáchsische Akademie der Wissenschaften Mathematische-Physikalische, Leipzig 94, 122.
Kuznetsov Yuri A. (1998) Elements of Applied Bifurcation Theory. New York: Springer-Verlag.
Leeper Edward and Sims Christopher A. (1994) Toward a modern macro model usable for policy analysis. NBER Macroeconomics Annual, 9, 81117.
Nyblom Jukka (1989) Testing for the constancy of parameters over time. Journal of the American Statistical Association 84 (405), 223230.
Seydel Rüdiger (1994) Practical Bifurcation and Stability Analysis. New York: Springer-Verlag.
Sims Christopher A. and Zha Tao (2006) Were there regime switches in U.S. monetary policy? American Economic Review 96 (1), 5481.
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.
Walsh Carl E. (2003) Monetary Theory and Policy, 2nd ed. Cambridge, MA: MIT Press.
Warne Anders (2000) Causality and Regime Inference in a Markov Switching VAR. Sveriges Riksbank working paper no. 118, 2000.
Woodford Michael (2003) Interest and Prices: Foundations of a Theory of Monetary Policy. Princeton, NJ: Princeton University Press.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Macroeconomic Dynamics
  • ISSN: 1365-1005
  • EISSN: 1469-8056
  • URL: /core/journals/macroeconomic-dynamics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Full text views

Total number of HTML views: 2
Total number of PDF views: 30 *
Loading metrics...

Abstract views

Total abstract views: 102 *
Loading metrics...

* Views captured on Cambridge Core between 4th September 2017 - 23rd February 2018. This data will be updated every 24 hours.