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Interest Rate Policy in Continuous Time with Discrete Delays

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  • Benhabib, Jess

Abstract

We study the design of monetary policy in a continuous-time framework with delays. More explicitly, we consider a linear, flexible-price model where inflation and nominal interest rates change continuously, but where nominal rates are set by the Central Bank in response to a lagged inflation measure, and where the measure of inflation can be constructed as a flexible distributed delay. Therefore, the Central Bank has, in addition to the choice of an "active" or "passive" response to inflation, two additional parameters to select: the lag of the inflation measure, and the coefficient for the distributed delay to construct the inflation measure. The pure continuous-time and discrete-time frameworks emerge as special cases of our differential-delay system. This richer framework also allows us to reconcile results on the local uniqueness and multiplicity of equilibria that are obtained in the two pure cases, to uncover special assumptions embedded in the pure cases, and to prescribe effective policy options to avoid the problem of local indeterminacy and its unintended consequences.

Suggested Citation

  • Benhabib, Jess, 2004. "Interest Rate Policy in Continuous Time with Discrete Delays," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 36(1), pages 1-15, February.
    • Handle: RePEc:mcb:jmoncb:v:36:y:2004:i:1:p:1-15
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    Cited by:

    1. Loisel, Olivier, 2021. "The implementation of stabilization policy," Theoretical Economics, Econometric Society, vol. 16(2), May.
    2. d'Albis, Hippolyte & Augeraud-Véron, Emmanuelle & Hupkes, Hermen Jan, 2014. "Bounded interest rate feedback rules in continuous-time," Journal of Economic Dynamics and Control, Elsevier, vol. 39(C), pages 227-236.
    3. d’Albis, Hippolyte & Augeraud-Véron, Emmanuelle & Hupkes, Hermen Jan, 2014. "Multiple solutions in systems of functional differential equations," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 50-56.
    4. Joanne S. Ercolani, 2014. "Cyclical Activity and Gestation Lags in Investment," Manchester School, University of Manchester, vol. 82(5), pages 620-630, September.
    5. Chryssi Giannitsarou & Alexia Anagnostopoulos, 2005. "Modeling Time and Macroeconomic Dynamics," Money Macro and Finance (MMF) Research Group Conference 2005 60, Money Macro and Finance Research Group.
    6. Hippolyte d'Albis & Emmanuelle Augeraud-Véron & Hermen Jan Hupkes, 2012. "Discontinuous Initial Value Problems for Funtional Differential-Algebraic Equations of Mixed Type," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00717412, HAL.
    7. Hippolyte d'Albis & Emmanuelle Augeraud-Véron & Hermen Jan Hupkes, 2012. "Backward- versus Forward-Looking Feedback Interest Rate Rules," Documents de travail du Centre d'Economie de la Sorbonne 12051, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    8. Bao, Jianhai & Yuan, Chenggui, 2013. "Long-term behavior of stochastic interest rate models with jumps and memory," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 266-272.
    9. Alet Roux & 'Alvaro Guinea Juli'a, 2024. "Closed form solution to zero coupon bond using a linear stochastic delay differential equation," Papers 2402.16428, arXiv.org.
    10. Walter M. Rusin, 2006. "On some inflation model based on the past price dynamics," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 16(2), pages 73-80.
    11. Omar Licandro & Luis A. Puch & Jesús Ruiz, 2018. "Continuous vs Discrete Time Modelling in Growth and Business Cycle Theory," Documentos de Trabajo del ICAE 2018-28, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    12. Loisel, Olivier, 2024. "Stabilization policy and lags," Journal of Mathematical Economics, Elsevier, vol. 111(C).

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