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Hopf Bifurcation from new-Keynesian Taylor rule to Ramsey Optimal Policy

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  • Jean-Bernard Chatelain

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  • Kirsten Ralf

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.

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  • Jean-Bernard Chatelain & Kirsten Ralf, 2020. "Hopf Bifurcation from new-Keynesian Taylor rule to Ramsey Optimal Policy," Papers 2002.07479, arXiv.org.
    • Handle: RePEc:arx:papers:2002.07479
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    1. Jean-Bernard Chatelain & Kirsten Ralf, 2017. "Can We Identify the Fed's Preferences?," Working Papers halshs-01549908, HAL.
    2. Giordani, Paolo & Soderlind, Paul, 2004. "Solution of macromodels with Hansen-Sargent robust policies: some extensions," Journal of Economic Dynamics and Control, Elsevier, vol. 28(12), pages 2367-2397, December.
    3. Soderlind, Paul, 1999. "Solution and estimation of RE macromodels with optimal policy," European Economic Review, Elsevier, vol. 43(4-6), pages 813-823, April.
    4. Taylor, John 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, Elsevier, vol. 43(3), pages 655-679, June.
    5. Davide Debortoli & Ricardo Nunes, 2014. "Monetary Regime Switches and Central Bank Preferences," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 46(8), pages 1591-1626, December.
    6. Florin O. Bilbiie & Roland Straub, 2013. "Asset Market Participation, Monetary Policy Rules, and the Great Inflation," The Review of Economics and Statistics, MIT Press, vol. 95(2), pages 377-392, May.
    7. Jean-Bernard Chatelain & Kirsten Ralf, 2021. "Imperfect Credibility versus No Credibility of Optimal Monetary Policy," Revue économique, Presses de Sciences-Po, vol. 72(1), pages 43-63.
    8. Jean-Bernard Chatelain & Kirsten Ralf, 2020. "Policy Maker’s Credibility with Predetermined Instruments for Forward-Looking Targets," Revue d'économie politique, Dalloz, vol. 130(5), pages 823-846.
    9. Jean-Bernard Chatelain & Kirsten Ralf, 2019. "A Simple Algorithm for Solving Ramsey Optimal Policy with Exogenous Forcing Variables," Economics Bulletin, AccessEcon, vol. 39(4), pages 2429-2440.
    10. William Barnett & Evgeniya Duzhak, 2010. "Empirical assessment of bifurcation regions within New Keynesian models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 45(1), pages 99-128, October.
    11. Jean-Bernard Chatelain & Kirsten Ralf, 2020. "How macroeconomists lost control of stabilization policy: towards dark ages," The European Journal of the History of Economic Thought, Taylor & Francis Journals, vol. 27(6), pages 938-982, November.
    12. Barnett, William A. & Chen, Guo, 2015. "Bifurcation of Macroeconometric Models and Robustness of Dynamical Inferences," Foundations and Trends(R) in Econometrics, now publishers, vol. 8(1-2), pages 1-144, September.
    13. David Currie & Paul Levine, 1985. "Macroeconomic Policy Design in an Interdependent World," NBER Chapters, in: International Economic Policy Coordination, pages 228-273, National Bureau of Economic Research, Inc.
    14. John H. Cochrane, 2011. "Determinacy and Identification with Taylor Rules," Journal of Political Economy, University of Chicago Press, vol. 119(3), pages 565-615.
    15. Barnett, William A. & Duzhak, Evgeniya Aleksandrovna, 2008. "Non-robust dynamic inferences from macroeconometric models: Bifurcation stratification of confidence regions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3817-3825.
    16. Chari, V V & Kehoe, Patrick J, 1990. "Sustainable Plans," Journal of Political Economy, University of Chicago Press, vol. 98(4), pages 783-802, August.
    17. Bilbiie, Florin O., 2008. "Limited asset markets participation, monetary policy and (inverted) aggregate demand logic," Journal of Economic Theory, Elsevier, vol. 140(1), pages 162-196, May.
    18. Bratsiotis, George J. & Robinson, Wayne A., 2016. "Unit Total Costs: An Alternative Marginal Cost Proxy For Inflation Dynamics," Macroeconomic Dynamics, Cambridge University Press, vol. 20(7), pages 1826-1849, October.
    19. Schaumburg, Ernst & Tambalotti, Andrea, 2007. "An investigation of the gains from commitment in monetary policy," Journal of Monetary Economics, Elsevier, vol. 54(2), pages 302-324, March.
    20. Marc Giannoni & Michael Woodford, 2003. "How forward-looking is optimal monetary policy?," Proceedings, Federal Reserve Bank of Cleveland, pages 1425-1483.
    21. Anderson, Evan W. & McGrattan, Ellen R. & Hansen, Lars Peter & Sargent, Thomas J., 1996. "Mechanics of forming and estimating dynamic linear economies," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 4, pages 171-252, Elsevier.
    22. Chatelain, Jean-Bernard & Ralf, Kirsten, 2020. "Ramsey Optimal Policy versus Multiple Equilibria with Fiscal and Monetary Interactions," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 40(1), pages 140-147.
    23. Roberds, William, 1987. "Models of Policy under Stochastic Replanning," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 28(3), pages 731-755, October.
    24. Benati, Luca & Goodhart, Charles, 2010. "Monetary Policy Regimes and Economic Performance: The Historical Record, 1979-2008," Handbook of Monetary Economics, in: Benjamin M. Friedman & Michael Woodford (ed.), Handbook of Monetary Economics, edition 1, volume 3, chapter 21, pages 1159-1236, Elsevier.
    25. V. V. Chari & Patrick J. Kehoe, 1993. "Sustainable Plans and Mutual Default," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(1), pages 175-195.
    26. Jean-Bernard Chatelain & Kirsten Ralf, 2014. "A finite set of equilibria for the indeterminacy of linear rational expectations models," Post-Print halshs-01053484, HAL.
    27. Havranek, Tomas & Horvath, Roman & Irsova, Zuzana & Rusnak, Marek, 2015. "Cross-country heterogeneity in intertemporal substitution," Journal of International Economics, Elsevier, vol. 96(1), pages 100-118.
    28. Jean-Bernard Chatelain & Kirsten Ralf, 2018. "Super-inertial interest rate rules are not solutions of Ramsey optimal monetary policy," Working Papers halshs-01863367, HAL.
    29. Chatelain, Jean-Bernard & Ralf, Kirsten, 2018. "Publish and Perish: Creative Destruction and Macroeconomic Theory," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 46(2), pages 65-101.
    30. Chatelain, Jean-Bernard & Ralf, Kirsten, 2014. "Stability and Identification with Optimal Macroprudential Policy Rules," EconStor Preprints 95979, ZBW - Leibniz Information Centre for Economics.
    31. Leeper, Eric M., 1991. "Equilibria under 'active' and 'passive' monetary and fiscal policies," Journal of Monetary Economics, Elsevier, vol. 27(1), pages 129-147, February.
    32. Jean-Bernard Chatelain & Kirsten Ralf, 2019. "A Simple Algorithm for Solving Ramsey Optimal Policy with Exogenous Forcing Variables," Economics Bulletin, AccessEcon, vol. 39(4), pages 2429-2440.
    33. A. Hakan Kara, 2007. "Monetary Policy under Imperfect Commitment: Reconciling Theory with Evidence," International Journal of Central Banking, International Journal of Central Banking, vol. 3(1), pages 149-178, March.
    34. Sophocles Mavroeidis & Mikkel Plagborg-Møller & James H. Stock, 2014. "Empirical Evidence on Inflation Expectations in the New Keynesian Phillips Curve," Journal of Economic Literature, American Economic Association, vol. 52(1), pages 124-188, March.
    35. Tomáš Havránek, 2015. "Measuring Intertemporal Substitution: The Importance Of Method Choices And Selective Reporting," Journal of the European Economic Association, European Economic Association, vol. 13(6), pages 1180-1204, December.
    36. John B. Taylor, 1999. "Monetary Policy Rules," NBER Books, National Bureau of Economic Research, Inc, number tayl99-1, March.
    37. Jean-Bernard Chatelain & Kirsten Ralf, 2018. "Publish and Perish: Creative Destruction and Macroeconomic Theory," Post-Print halshs-01884160, HAL.
    38. Chatelain, Jean-Bernard & Ralf, Kirsten, 2022. "Ramsey Optimal Policy In The New-Keynesian Model With Public Debt," Macroeconomic Dynamics, Cambridge University Press, vol. 26(6), pages 1588-1614, September.
    39. Jean-Bernard Chatelain & Kirsten Ralf, 2014. "A finite set of equilibria for the indeterminacy of linear rational expectations models," Papers 1407.6222, arXiv.org.
    40. Christiano, Lawrence J. & Trabandt, Mathias & Walentin, Karl, 2010. "DSGE Models for Monetary Policy Analysis," Handbook of Monetary Economics, in: Benjamin M. Friedman & Michael Woodford (ed.), Handbook of Monetary Economics, edition 1, volume 3, chapter 7, pages 285-367, Elsevier.
    41. Pedro, Gomis-Porqueras & Cathy, Zhang, 2018. "Optimal Monetary and Fiscal Policy with Migration in a Currency Union," MPRA Paper 83754, University Library of Munich, Germany.
    42. Cardani, Roberta & Menna, Lorenzo & Tirelli, Patrizio, 2020. "The Optimal Policy Mix To Achieve Public Debt Consolidation," Macroeconomic Dynamics, Cambridge University Press, vol. 24(1), pages 113-129, January.
    43. Hall, Robert E, 1988. "Intertemporal Substitution in Consumption," Journal of Political Economy, University of Chicago Press, vol. 96(2), pages 339-357, April.
    44. Ball, Laurence, 1994. "Credible Disinflation with Staggered Price-Setting," American Economic Review, American Economic Association, vol. 84(1), pages 282-289, March.
    45. Sims, Christopher A., 2010. "Rational Inattention and Monetary Economics," Handbook of Monetary Economics, in: Benjamin M. Friedman & Michael Woodford (ed.), Handbook of Monetary Economics, edition 1, volume 3, chapter 4, pages 155-181, Elsevier.
    46. Blanchard, Olivier Jean & Kahn, Charles M, 1980. "The Solution of Linear Difference Models under Rational Expectations," Econometrica, Econometric Society, vol. 48(5), pages 1305-1311, July.
    47. Chatelain, Jean-Bernard & Ralf Kirsten, 2016. "Countercyclical versus Procyclical Taylor Principles," EconStor Preprints 129796, ZBW - Leibniz Information Centre for Economics.
    48. Tomas Havranek, 2013. "Publication Bias in Measuring Intertemporal Substitution," Working Papers IES 2013/15, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, revised Oct 2013.
    49. Jean-Bernard Chatelain & Kirsten Ralf, 2018. "Publish and Perish: Creative Destruction and Macroeconomic Theory," PSE-Ecole d'économie de Paris (Postprint) halshs-01884160, HAL.
    50. Fujiwara, Ippei & Kam, Timothy & Sunakawa, Takeki, 2019. "On two notions of imperfect credibility in optimal monetary policies," Economics Letters, Elsevier, vol. 174(C), pages 22-25.
    51. Jean-Bernard Chatelain & Kirsten Ralf, 2014. "Peut-on identifier les politiques économiques stabilisant une économie instable ?," Revue française d'économie, Presses de Sciences-Po, vol. 0(3), pages 143-178.
    52. Ippei Fujiwara & Timothy Kam & Takeki Sunakawa, 2016. "A note on imperfect credibility," CAMA Working Papers 2016-37, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    53. Ljungqvist, Lars & Sargent, Thomas J., 2012. "Recursive Macroeconomic Theory, Third Edition," MIT Press Books, The MIT Press, edition 3, volume 1, number 0262018748, December.
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    Cited by:

    1. Jean-Bernard Chatelain & Kirsten Ralf, 2019. "A Simple Algorithm for Solving Ramsey Optimal Policy with Exogenous Forcing Variables," Economics Bulletin, AccessEcon, vol. 39(4), pages 2429-2440.
    2. Jean-Bernard Chatelain & Kirsten Ralf, 2020. "Policy Maker’s Credibility with Predetermined Instruments for Forward-Looking Targets," Revue d'économie politique, Dalloz, vol. 130(5), pages 823-846.
    3. Jean-Bernard Chatelain & Kirsten Ralf, 2018. "Super-inertial interest rate rules are not solutions of Ramsey optimal monetary policy," Working Papers halshs-01863367, HAL.
    4. Jean-Bernard Chatelain & Kirsten Ralf, 2019. "A Simple Algorithm for Solving Ramsey Optimal Policy with Exogenous Forcing Variables," Economics Bulletin, AccessEcon, vol. 39(4), pages 2429-2440.
    5. Chatelain, Jean-Bernard & Ralf, Kirsten, 2022. "Ramsey Optimal Policy In The New-Keynesian Model With Public Debt," Macroeconomic Dynamics, Cambridge University Press, vol. 26(6), pages 1588-1614, September.
    6. Jean-Bernard Chatelain & Kirsten Ralf, 2021. "Imperfect Credibility versus No Credibility of Optimal Monetary Policy," Revue économique, Presses de Sciences-Po, vol. 72(1), pages 43-63.
    7. Jean-Bernard Chatelain & Kirsten Ralf, 2017. "Can We Identify the Fed's Preferences?," Working Papers halshs-01549908, HAL.
    8. Jean-bernard Chatelain & Kirsten Ralf, 2020. "The Welfare of Ramsey Optimal Policy Facing Auto-Regressive Shocks," Economics Bulletin, AccessEcon, vol. 40(2), pages 1797-1803.

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    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • E47 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Forecasting and Simulation: Models and Applications
    • E52 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Monetary Policy
    • E58 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Central Banks and Their Policies

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