Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-22T21:31:28.707Z Has data issue: false hasContentIssue false
  • English
  • Français

HOPF BIFURCATION FROM NEW-KEYNESIAN TAYLOR RULE TO RAMSEY OPTIMAL POLICY

Published online by Cambridge University Press:  17 January 2020

Jean-Bernard Chatelain  and
Kirsten Ralf
Jean-Bernard Chatelain*
Affiliation:
Paris School of Economics
Kirsten Ralf
Affiliation:
Inseec U. Research Center ESCE
*
Address correspondence to: Jean-Bernard Chatelain, Paris School of Economics, Université Paris 1 Pantheon Sorbonne, 48 Boulevard Jourdan, 75014Paris, France. e-mail: [email protected].
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper compares different implementations of monetary policy in a new-Keynesian setting. We can show that a shift from Ramsey optimal policy under short-term commitment (based on a negative feedback mechanism) to a Taylor rule (based on a positive feedback mechanism) corresponds to a Hopf bifurcation with opposite policy advice and a change of the dynamic properties. This bifurcation occurs because of the ad hoc assumption that interest rate is a forward-looking variable when policy targets (inflation and output gap) are forward-looking variables in the new-Keynesian theory.

Keywords

BifurcationsTaylor RuleTaylor PrincipleNew-Keynesian ModelRamsey Optimal Policy
Type
Articles
Information
Macroeconomic Dynamics , Volume 25 , Issue 8 , December 2021 , pp. 2204 - 2236
Copyright
© Cambridge University Press 2020

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.)

References

REFERENCES

Ackermann, J. (1972) Der Entwurf linearer Regelungssysteme im Zustandsraum. Regelungstechnik 7, 297–300.Google Scholar
Anderson, E. W., Hansen, L. P., McGrattan, E. R. and Sargent, T. J. (1996) Mechanics of forming and estimating dynamic linear economies. In: Amman, H. M., Kendrick, D. A. and Rust, J. (eds.), Handbook of Computational Economics, pp. 171–252. Amsterdam: Elsevier.Google Scholar
Aström, K. J. and Kumar, P. R. (2014) Control: A perspective. Automatica 50, 3–43.CrossRefGoogle Scholar
Azariadis, C. (1993) Intertemporal Macroeconomics. Oxford: Blackwell Publishers.Google Scholar
Ball, L. (1994) Credible disinflation with staggered price-setting. The American Economic Review 84, 282–289.Google Scholar
Barnett, W. A. and Chen, G. (2015) Bifurcation of macroeconometric models and robustness of dynamical inferences. Foundations and Trends in Econometrics 8, 1–144.CrossRefGoogle Scholar
Barnett, W. A. and Duzhak, E. A. (2008) Non-robust dynamic inferences from macroeconometric models: Bifurcation stratification of confidence region. Physica A 387, 3817–3825.CrossRefGoogle Scholar
Barnett, W. A. and Duzhak, E. A. (2010) Empirical assessment of bifurcations regions within New-Keynesian models. Economic Theory 45, 99–128.CrossRefGoogle Scholar
Benati, L. and Goodhart, C. (2010) Monetary policy regimes and economic performance: The historical record 1979–2008. In: Friedman, B. M. and Woodford, M. (eds.), Handbook of Monetary Economics, vol. 3, pp. 1159–1236. Amsterdam: Elsevier B.V. Google Scholar
Blanchard, O. J. and Kahn, C. (1980) The solution of linear difference models under rational expectations. Econometrica 48, 1305–1311.CrossRefGoogle Scholar
Bilbiie, F. O. (2008) Limited asset market participation, monetary policy and (inverted) aggregate demand logic. Journal of Economic Theory 140, 162–196.CrossRefGoogle Scholar
Bilbiie, F. O. and Straub, R. (2013) Asset market participation, monetary policy rules, and the great inflation. Review of Economics and Statistics 95, 377–392.CrossRefGoogle Scholar
Bratsiotis, G. J. and Robinson, W. A. (2016) Unit total costs: An alternative marginal cost proxy for inflation dynamics. Macroeconomic Dynamics 20, 1–24.CrossRefGoogle Scholar
Cardani, R., Menna, L., and Tirelli, P. (2018) The optimal policy mix to achieve public debt consolidation. Macroeconomic Dynamics, 1–17. https://doi.org/10.1017/S1365100518000433 Google Scholar
Chari, V. V. and Kehoe, P. J. (1990) Sustainable plans. Journal of Political Economy 98, 783–802.CrossRefGoogle Scholar
Chatelain, J. B. and Ralf, K. (2014) Peut-on identifier les politiques économiques stabilisant une économie instable? Revue française d’économie 29, 143–178.CrossRefGoogle Scholar
Chatelain, J. B. and Ralf, K. (2016) Countercyclical versus Procyclical Taylor Principles. SSRN Working Paper.CrossRefGoogle Scholar
Chatelain, J. B. and Ralf, K. (2017) Can We Identify the Fed’s Preferences? PSE Working Paper.CrossRefGoogle Scholar
Chatelain, J. B. and Ralf, K. (2018a) Publish and Perish: Creative destruction and macroeconomic theory. History of Economic Ideas 27, 65–101.Google Scholar
Chatelain, J. B. and Ralf, K. (2018b) Imperfect Credibility versus No Credibility of Optimal Monetary Policy. PSE Working paper.CrossRefGoogle Scholar
Chatelain, J. B. and Ralf, K. (2018c) Super-Inertial Interest Rate Rules are not Solutions of Ramsey Optimal Monetary Policy. PSE Working Paper.CrossRefGoogle Scholar
Chatelain, J. B. and Ralf, K. (2019a) A Simple Algorithm for Solving Ramsey Optimal Policy with Exogenous Forcing Variables. Economics Bulletin 39(4), 2429–2440.Google Scholar
Chatelain, J. B. and Ralf, K. (2019b) How Macroeconomists Lost Control: Towards Dark Ages. Research Gate Working Paper.Google Scholar
Chatelain, J. B. and Ralf, K. (2019c) Policy Maker’s Credibility with Predetermined Instruments for Forward-Looking Targets. PSE Working Paper.CrossRefGoogle Scholar
Chatelain, J. B. and Ralf, K. (2019d) Ramsey Optimal Policy versus Multiple Equilibria with Fiscal and Monetary Interactions. PSE Working Paper.CrossRefGoogle Scholar
Chatelain, J. B. and Ralf, K. (2019e) Ramsey Optimal Policy in the New-Keynesian Model with Public Debt. PSE Working Paper.CrossRefGoogle Scholar
Christiano, L. J., Trabandt, M. and Walentin, K. (2010) DSGE models for monetary policy analysis. In: Friedman, B. M. and Woodford, M. (eds.), Handbook of Monetary Economics, vol. 3, pp. 285–368. Amsterdam: Elsevier B.V.CrossRefGoogle Scholar
Cochrane, J. H. (2011) Determinacy and identification with Taylor Rules. Journal of Political Economy 119, 565–615.CrossRefGoogle Scholar
Currie, D. and Levine, P. (1985) Macroeconomic policy design in an interdependent world. In: International Economic Policy Coordination, pp. 228–273. Cambridge, UK: NBER. Cambridge University Press.Google Scholar
Doyle, J. C. (1978). Guaranteed margins for LQG regulators. IIIE Transactions on Automatic Control AC-23, 756–757.CrossRefGoogle Scholar
Freiling, G. (2002) A survey of nonsymmetric Riccati equations. Linear Algebra and its Applications 351, 243–270.CrossRefGoogle Scholar
Fujiwara, I., Kam, T. and Sunakawa, T. (2019) On two notions of imperfect credibility in optimal monetary policies. Economics Letters 174, 22–25.CrossRefGoogle Scholar
Gali, J. (2015) Monetary Policy, Inflation and the Business Cycle, 2nd ed. Princeton: Princeton University Press.Google Scholar
Giannoni, M. P. and Woodford, M. (2003) How forward-looking is optimal monetary policy? Journal of Money, Credit, and Banking 35, 1425–1469.CrossRefGoogle Scholar
Giordani, P. and Söderlind, P. (2004) Solutions of macromodels with Hansen-Sargent robust policies: Some extensions. Journal of Economics Dynamics and Control 28, 2367–2397.CrossRefGoogle Scholar
Gomis-Porqueras, P. and Zhang, C. (2019) Optimal monetary and fiscal policy in a currency union with frictional goods markets. Macroeconomic Dynamics, 1–29. https://doi.org/10.1017/S1365100519000841Google Scholar
Hall, R. E. (1988) Intertemporal substitution in consumption. Journal of Political Economy 96, 339–357.CrossRefGoogle Scholar
Hansen, L. P. and Sargent, T. (2008) Robustness. Princeton: Princeton University Press.Google Scholar
Hansen, L. P. and Sargent, T. (2011) Wanting robustness in macroeconomics. In: Friedman, B. M. and Woodford, M. (eds.), Handbook of Monetary Economics, vol. 3(B), pp. 1097–1155. Amsterdam: Elsevier B.V.CrossRefGoogle Scholar
Havranek, T., Horvath, R., Irsova, Z. and Ruznak, M. (2015) Cross-country heterogeneity in intertemporal substitution. Journal of International Economics 96, 100–118.CrossRefGoogle Scholar
Havrnek, T. (2015) Measuring intertemporal substitution: The importance of method choices and selective reporting. Journal of the European Economic Association 13, 1180–1204.CrossRefGoogle Scholar
Kalman, R. E. (1960) Contributions to the theory of optimal control. Boletin de la Sociedad Matematica Mexicana 5, 102–109.Google Scholar
Kara, H. (2007) Monetary policy under imperfect commitment: Reconciling theory with evidence. International Journal of Central Banking 3, 149–177.Google Scholar
Leeper, E. M. (1991) Equilibria under ‘active’ and ‘passive’ monetary and fiscal policies. Journal of monetary Economics 27, 129–147.CrossRefGoogle Scholar
Ljungqvist, L. and Sargent, T. J. (2012) Recursive Macroeconomic Theory, 3rd ed. Cambridge, Massaschussets: The MIT Press.Google Scholar
Mavroeidis, S., Plagbord-Moller, M. and Stock, J. (2014) Empirical evidence of inflation expectations in the New-Keynesian Phillips Curve. Journal of Economic Literature 52, 124–188.CrossRefGoogle Scholar
Roberds, W. (1987) Models of policy under stochastic replanning. International Economic Review 28, 731–755.CrossRefGoogle Scholar
Romer, D. (2012) Advanced Macroeconomics, 4th ed. New York: McGraw-Hill.Google Scholar
Schaumburg, E. and Tambalotti, A. (2007) An investigation of the gains from commitment in monetary policy. Journal of Monetary Economics 54, 302–324.CrossRefGoogle Scholar
Söderlind, P. (1999) Solution and estimation of RE macromodels with optimal policy. European Economic Review 43, 813–823.CrossRefGoogle Scholar
Simaan, M. and Cruz, J. B. (1973) Additional aspects of the Stackelberg strategy in nonzero-sum games. Journal of Optimization Theory and Applications 11, 613–626.CrossRefGoogle Scholar
Simon, H. A. (1956) Dynamic programming under uncertainty with a quadratic criterion function. Econometrica 24, 74–81.CrossRefGoogle Scholar
Sims, C. A. (2010) Rational inattention and monetary economics. In: Friedman, B. M. and Woodford, M. (eds.), Handbook of Monetary Economics, vol. 3, pp. 155–181. Amsterdam: Elsevier B.V.CrossRefGoogle Scholar
Taylor, J. B. (1999) The robustness and efficiency of monetary policy rules as guidelines for interest rate setting by the European central bank. Journal of Monetary Economics 43, 655–679.CrossRefGoogle Scholar
Tinbergen, J. (1952) On the Theory of Economic Policy. Amsterdam: North Holland.Google Scholar
Wonham, W. N. (1967) On pole assignment in multi-input controllable linear system. IEEE Transactions on Automatic Control 12, 660–665.CrossRefGoogle Scholar
Zhou, K., Doyle, D. C. and Glover, K. (1995) Robust and Optimal Control. New Jersey: Prentice Hall.Google Scholar