Chatelain, JeanBernard and Ralf, Kirsten (2020): Hopf Bifurcation from newKeynesian Taylor rule to Ramsey Optimal Policy. Published in: Macroeconomic Dyanmics (18 January 2020): pp. 133.
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Abstract
This paper compares different implementations of monetary policy in a newKeynesian setting. We can show that a shift from Ramsey optimal policy under shortterm 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 forwardlooking variable when policy targets (inflation and output gap) are forwardlooking variables in the newKeynesian theory.
Item Type:  MPRA Paper 

Original Title:  Hopf Bifurcation from newKeynesian Taylor rule to Ramsey Optimal Policy 
Language:  English 
Keywords:  Bifurcations, Taylor rule, Taylor principle, newKeynesian model, Ramsey optimal policy. 
Subjects:  C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61  Optimization Techniques ; Programming Models ; Dynamic Analysis C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C62  Existence and Stability Conditions of Equilibrium C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C73  Stochastic and Dynamic Games ; Evolutionary Games ; Repeated Games E  Macroeconomics and Monetary Economics > E4  Money and Interest Rates > E43  Interest Rates: Determination, Term Structure, and Effects E  Macroeconomics and Monetary Economics > E4  Money and Interest Rates > E47  Forecasting and Simulation: Models and Applications E  Macroeconomics and Monetary Economics > E5  Monetary Policy, Central Banking, and the Supply of Money and Credit > E52  Monetary Policy E  Macroeconomics and Monetary Economics > E5  Monetary Policy, Central Banking, and the Supply of Money and Credit > E58  Central Banks and Their Policies 
Item ID:  98653 
Depositing User:  JeanBernard Chatelain 
Date Deposited:  17 Feb 2020 04:59 
Last Modified:  17 Feb 2020 04:59 
References:  Ackermann, J. (1972). Der Entwurf linearer Regelungssysteme im Zustandsraum. Regelungstechnik, 7, 297300. 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. (editors) Handbook of Computational Economics, Elsevier, Amsterdam, 171252. Aström K.J. & Kumar, P. R. (2014). Control: A perspective. Automatica, 50, pp. 343. Azariadis, C. (1993). Intertemporal macroeconomics, Blackwell Publishers, Oxford. Ball, L. (1994). Credible disinflation with staggered pricesetting. The American Economic Review, 84, pp. 282289. Barnett W.A. and Duzhak E.A. (2008). NonRobust Dynamic Inferences from Macroeconometric Models: Bifurcation stratification of Confidence Region. Physica A, 387, pp. 38173825. Barnett W.A. and Duzhak E.A. (2010). Empirical Assessment of Bifurcations Regions within NewKeynesian models. Economic Theory, 45, pp. 99128. Barnett W.A. and Chen G. (2015). Bifurcation of Macroeconometric Models and Robustness of Dynamical Inferences. Foundations and Trends®in Econometrics, 8, pp. 1144. Benati L. and Goodhart C. (2010). Monetary Policy Regimes and Economic Performance: The historical record 19792008. In Handbook of Monetary Economics, vol 3, Friedman B.M. and Woodford M. editors, Elsevier B.V., pp. 11591236. Blanchard O.J. and Kahn C. (1980). The solution of linear difference models under rational expectations. Econometrica, 48, pp. 13051311. Bilbiie F.O. (2008). Limited asset market participation, monetary policy and (inverted) aggregate demand logic. Journal of Economic Theory, 140, pp. 162196. Bilbiie F.O. and Straub R. (2013). Asset Market Participation, Monetary Policy Rules, and the Great Inflation. Review of Economics and Statistics, 95, pp. 377392. Bratsiotis, G. J. and Robinson, W. A. (2016). Unit Total Costs: An Alternative Marginal Cost Proxy for Inflation Dynamics. Macroeconomic Dynamics, 20, pp. 124. Cardani, R., L. Menna, L. and P. Tirelli (2018). The optimal policy mix to achieve public debt consolidation. Macroeconomic Dynamics, 117. Chari, V. V., & Kehoe, P. J. (1990). Sustainable plans. Journal of political economy, 98, pp. 783802. Chatelain, J. B. and K. Ralf (2014) Peuton identifier les politiques économiques stabilisant une économie instable? Revue française d'économie, 29, pp. 143178. Chatelain J.B. and Ralf K. (2016) Countercyclical versus Procyclical Taylor Principles. SSRN working paper. Chatelain J.B. and Ralf K. (2017) Can we Identify the Fed's Preferences? PSE working paper. Chatelain J.B. and K. Ralf (2018a) Publish and Perish: Creative Destruction and Macroeconomic Theory. History of Economic Ideas, 27, pp. 65101. Chatelain, J. B. and K. Ralf (2020) Imperfect Credibility versus No Credibility of Optimal Monetary Policy. Revue Economique. Chatelain, J. B. and K. Ralf (2018c) Superinertial interest rate rules are not solutions of Ramsey optimal monetary policy. PSE working paper. Chatelain J.B. and K. Ralf (2019a) A Simple Algorithm for Solving Ramsey Optimal Policy with Exogenous Forcing Variables. Economics Bulletin 39(4), 24292440. Chatelain, J. B. and K. Ralf (2020b) How Macroeconomists Lost Control: Towards Dark Ages. Research Gate working paper. Chatelain, J. B. and K. Ralf (2019c) Policy Maker's Credibility with Predetermined Instruments for ForwardLooking Targets. PSE working paper. Chatelain, J. B. and K. Ralf (2020) Ramsey Optimal Policy versus Multiple Equilibria with Fiscal and Monetary Interactions. Economics Bulletin. 40(1), pp. 140147. Chatelain, J. B. and K. Ralf (2019e) Ramsey Optimal Policy in the NewKeynesian Model with Public Debt. PSE working paper. Christiano, L. J., Trabandt, M., & Walentin, K. (2010). DSGE models for monetary policy analysis. In Handbook of Monetary Economics, vol 3, Friedman B.M. and Woodford M. editors, Elsevier B.V., pp. 285368. Cochrane J.H. (2011). Determinacy and identification with Taylor Rules. Journal of Political Economy, 119, pp. 565615. Currie, D., & Levine, P. (1985). Macroeconomic policy design in an interdependent world. In International Economic Policy Coordination, pp. 228273. NBER. Cambridge University Press. Doyle J.C. (1978). Guaranteed Margins for LQG Regulators. IIIE Transactions on Automatic Control. AC23, pp. 756757. Freiling, G. (2002). A survey of nonsymmetric Riccati equations. Linear algebra and its applications, 351, pp. 243270. Fujiwara, I., Kam, T., & Sunakawa, T. (2019). On two notions of imperfect credibility in optimal monetary policies. Economics Letters, 174, pp. 2225. Gali J. (2015). Monetary Policy, Inflation and the Business Cycle. 2nd. edition, Princeton University Press, Princeton. Giannoni, M. P. & Woodford M. (2003). How forwardlooking is optimal monetary policy? Journal of Money, Credit, and Banking, 35, pp. 14251469. Giordani P. and Söderlind P. (2004). Solutions of macromodels with HansenSargent robust policies: some extensions. Journal of Economics Dynamics and Control, 28, pp. 23672397. GomisPorqueras, P., & Zhang, C. (2019). Optimal monetary and fiscal policy in a currency union with frictional goods markets. Macroeconomic Dynamics, 129 Hall, R. E. (1988). Intertemporal substitution in consumption. Journal of political economy, 96, pp. 339357. Hansen L.P. and Sargent T. (2008). Robustness, Princeton University Press, Princeton. Hansen L.P. and Sargent T. (2011). Wanting Robustness in Macroeconomics. In Handbook of Monetary Economics, vol 3(B), Friedman B.M. and Woodford M. editors, Elsevier B.V., pp. 10971155. Havranek T., Horvath R., Irsova Z. and Ruznak M. (2015). Crosscountry heterogeneity in intertemporal substitution. Journal of International Economics, 96, pp. 100118. Havránek, T. (2015). Measuring intertemporal substitution: The importance of method choices and selective reporting. Journal of the European Economic Association, 13, pp. 11801204. Kalman R.E. (1960). Contributions to the Theory of Optimal Control. Boletin de la Sociedad Matematica Mexicana, 5, pp. 102109. Kara, H. (2007). Monetary policy under imperfect commitment: Reconciling theory with evidence. International Journal of Central Banking, 3, pp. 149177. Leeper, E. M. (1991). Equilibria under `active'and `passive'monetary and fiscal policies. Journal of monetary Economics, 27, pp. 129147. Ljungqvist L. and Sargent T.J. (2012). Recursive Macroeconomic Theory. 3rd edition. The MIT Press. Cambridge, Massaschussets. Mavroeidis S., PlagbordMoller M. and Stock J. (2014). Empirical Evidence of Inflation Expectations in the NewKeynesian Phillips Curve. Journal of Economic Literature, 52, pp. 124188. Roberds, W. (1987). Models of policy under stochastic replanning. International Economic Review, 28, pp. 731755. Romer D. (2012). Advanced Macroeconomics. 4th edition. McGrawHill. Schaumburg, E., and Tambalotti, A. (2007). An investigation of the gains from commitment in monetary policy. Journal of Monetary Economics, 54, pp. 302324. Söderlind P. (1999). Solution and Estimation of RE Macromodels with Optimal Policy. European Economic Review, 43, pp. 81323. Simaan, M., & Cruz, J. B. (1973). Additional aspects of the Stackelberg strategy in nonzerosum games. Journal of Optimization Theory and Applications, 11, pp. 613626. Simon H.A. (1956). Dynamic Programming under Uncertainty with a Quadratic Criterion Function. Econometrica, 24, pp. 7481. Sims, C. A. (2010). Rational inattention and monetary economics. In Handbook of Monetary Economics, vol 3, Friedman B.M. and Woodford M. editors, Elsevier B.V., pp. 155181. 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, pp. 655679. Tinbergen J. (1952). On the theory of economic policy. North Holland. Wonham W.N. (1967). On pole assignment in multiinput controllable linear system. IEEE transactions on automatic control. 12, pp. 660665. Zhou K, Doyle D.C. and Glover K. (1995). Robust and Optimal Control. Prentice Hall, New Jersey. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/98653 
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