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Optimal Monetary Policy with r

Author

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  • Roberto M. Billi
  • Jordi Galí
  • Anton Nakov

Abstract

We study the optimal monetary policy problem in a New Keynesian economy with a zero lower bound (ZLB) on the nominal interest rate, and in which the steady state natural rate (r*) is negative. We show that the optimal policy aims to approach gradually a steady state with positive average inflation. Around that steady state, inflation and output fluctuate optimally in response to shocks to the natural rate. The central bank can implement that optimal outcome by means of an appropriate state-contingent rule, even though in equilibrium the nominal rate remains at zero most (or all) of the time. In order to establish that result, we derive sufficient conditions for local determinacy in a more general model with endogenous regime switches.

Suggested Citation

  • Roberto M. Billi & Jordi Galí & Anton Nakov, 2022. "Optimal Monetary Policy with r," Working Papers 1333, Barcelona School of Economics.
    • Handle: RePEc:bge:wpaper:1333
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    References listed on IDEAS

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    1. Philippe Andrade & Jordi Gali & Hervé Le Bihan & Julien Matheron, 2021. "Should the ECB Adjust Its Strategy in the Face of a Lower r*?," Working Papers 22-1, Federal Reserve Bank of Boston.
    2. Adam, Klaus & Billi, Roberto M., 2006. "Optimal Monetary Policy under Commitment with a Zero Bound on Nominal Interest Rates," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 38(7), pages 1877-1905, October.
    3. Del Negro, Marco & Giannone, Domenico & Giannoni, Marc P. & Tambalotti, Andrea, 2019. "Global trends in interest rates," Journal of International Economics, Elsevier, vol. 118(C), pages 248-262.
    4. Jordi Galí, 2016. "Monetary policy and bubbles in a new Keynesian model with overlapping generations," Economics Working Papers 1561, Department of Economics and Business, Universitat Pompeu Fabra, revised Jan 2020.
    5. Anton Nakov, 2008. "Optimal and Simple Monetary Policy Rules with Zero Floor on the Nominal Interest Rate," International Journal of Central Banking, International Journal of Central Banking, vol. 4(2), pages 73-127, June.
    6. Troy Davig & Eric M. Leeper, 2007. "Generalizing the Taylor Principle," American Economic Review, American Economic Association, vol. 97(3), pages 607-635, June.
    7. Olivier Coibion & Yuriy Gorodnichenko & Johannes Wieland, 2012. "The Optimal Inflation Rate in New Keynesian Models: Should Central Banks Raise Their Inflation Targets in Light of the Zero Lower Bound?," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 79(4), pages 1371-1406.
    8. Barthélemy, Jean & Marx, Magali, 2017. "Solving endogenous regime switching models," Journal of Economic Dynamics and Control, Elsevier, vol. 77(C), pages 1-25.
    9. Holston, Kathryn & Laubach, Thomas & Williams, John C., 2017. "Measuring the natural rate of interest: International trends and determinants," Journal of International Economics, Elsevier, vol. 108(S1), pages 59-75.
    10. Farmer, Roger E.A. & Waggoner, Daniel F. & Zha, Tao, 2009. "Understanding Markov-switching rational expectations models," Journal of Economic Theory, Elsevier, vol. 144(5), pages 1849-1867, September.
    11. Jean Barthélemy & Magali Marx, 2019. "Monetary policy switching and indeterminacy," Quantitative Economics, Econometric Society, vol. 10(1), pages 353-385, January.
    12. Gauti B. Eggertsson & Neil R. Mehrotra & Jacob A. Robbins, 2019. "A Model of Secular Stagnation: Theory and Quantitative Evaluation," American Economic Journal: Macroeconomics, American Economic Association, vol. 11(1), pages 1-48, January.
    13. Brand, Claus & Mazelis, Falk, 2019. "Taylor-rule consistent estimates of the natural rate of interest," Working Paper Series 2257, European Central Bank.
    14. Jung, Taehun & Teranishi, Yuki & Watanabe, Tsutomu, 2005. "Optimal Monetary Policy at the Zero-Interest-Rate Bound," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 37(5), pages 813-835, October.
    15. Andrade, Philippe & Galí, Jordi & Le Bihan, Hervé & Matheron, Julien, 2021. "Should the ECB adjust its strategy in the face of a lower r★?," Journal of Economic Dynamics and Control, Elsevier, vol. 132(C).
    16. Olivier Coibion & Yuriy Gorodnichenko & Johannes Wieland, 2012. "The Optimal Inflation Rate in New Keynesian Models: Should Central Banks Raise Their Inflation Targets in Light of the Zero Lower Bound?," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 79(4), pages 1371-1406.
    17. Gauti B. Eggertsson & Michael Woodford, 2003. "The Zero Bound on Interest Rates and Optimal Monetary Policy," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 34(1), pages 139-235.
    18. Calvo, Guillermo A., 1983. "Staggered prices in a utility-maximizing framework," Journal of Monetary Economics, Elsevier, vol. 12(3), pages 383-398, September.
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    Cited by:

    1. Lucian Briciu & Stefan Hohberger & Luca Onorante & Beatrice Pataracchia & Marco Ratto & Lukas Vogel, 2023. "The ECB Strategy Review - Implications for the Space of Monetary Policy," European Economy - Discussion Papers 193, Directorate General Economic and Financial Affairs (DG ECFIN), European Commission.
    2. Jean-Baptiste Michau, 2022. "The Trilemma for Low Interest Rate Macroeconomics," Working Papers 2022-19, Center for Research in Economics and Statistics.

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    More about this item

    Keywords

    zero lower bound; New Keynesian model; decline in r*; equilibrium determinacy; regime switching models; secular stagnation;
    All these keywords.

    JEL classification:

    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • E52 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Monetary Policy

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