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Monetary Policy as an Optimal Control Problem

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  • Jan Kodera
  • Van Quang TRAN

Abstract

This paper analyses the monetary policy of a central bank in a simple deterministic and continuous dynamic non-linear New-Keynesian model with an active central bank conducting monetary policy within inflation targeting framework. To meet this purpose, first we derive two differential equations capturing the dynamics in the economy: the dynamic IS curve representing the commodity market and the Phillips curve capturing the connection between the real and nominal sectors of the economy in a continuous form. By introducing a quadratic loss function commonly used in New Keynesian Economics we get optimal control problem which solution will be analysed with the use of fuzzy control. Then we introduce a modified form of the Taylor rule and analyse the solution of the same differential equations capturing the dynamics of the economy using Taylor rule instead of loss function. The comparison of the solutions of both models will be demonstrated in examples in which the main characteristic of dynamics of production and inflation are displayed.

Suggested Citation

  • Jan Kodera & Van Quang TRAN, 2013. "Monetary Policy as an Optimal Control Problem," European Financial and Accounting Journal, Prague University of Economics and Business, vol. 2013(1), pages 18-38.
    • Handle: RePEc:prg:jnlefa:v:2013:y:2013:i:1:id:94:p:18-38
    DOI: 10.18267/j.efaj.94
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    References listed on IDEAS

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    1. Levin, Andrew T. & Williams, John C., 2003. "Robust monetary policy with competing reference models," Journal of Monetary Economics, Elsevier, vol. 50(5), pages 945-975, July.
    2. Barro, Robert J. & Gordon, David B., 1983. "Rules, discretion and reputation in a model of monetary policy," Journal of Monetary Economics, Elsevier, vol. 12(1), pages 101-121.
    3. Dieter Grass & Jonathan P. Caulkins & Gustav Feichtinger & Gernot Tragler & Doris A. Behrens, 2008. "Optimal Control of Nonlinear Processes," Springer Books, Springer, number 978-3-540-77647-5, April.
    4. Chow, Gregory C, 1976. "Control Methods for Macroeconomic Policy Analysis," American Economic Review, American Economic Association, vol. 66(2), pages 340-345, May.
    5. Michal Andrle & Tibor Hledik & Ondra Kamenik & Jan Vlcek, 2009. "Implementing the New Structural Model of the Czech National Bank," Working Papers 2009/2, Czech National Bank.
    6. Taylor, John B., 1993. "Discretion versus policy rules in practice," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 39(1), pages 195-214, December.
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    More about this item

    Keywords

    Deterministic continuous model; Dynamic IS curve; Loss function; Modified Taylor rule; New- Keynesian Phillips curve; Optimal control problem;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • 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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