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Continuous Time Versus Discrete Time in the New Keynesian Model: Closed-Form Solutions and Implications for Liquidity Trap

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  • Maliar, Lilia

Abstract

Economists often use interchangeably the discrete- and continuous-time versions of the Keynesian model. In the paper, I ask whether or not the two versions effectively lead to the same implications. I analyze several alternative monetary policies, including a Taylor rule, discretionary interest rate choice and forward guidance. I show that the answer depends on a specific scenario and parameterization considered. In particular, in the presence of liquidity trap, the discrete-time analysis helps overcome some negative implications of the continuous-time model, such as excessively strong impact of price stickiness on inflation and output, unrealistically large government multipliers, as well as implausibly large effects of forward guidance.

Suggested Citation

  • Maliar, Lilia, 2018. "Continuous Time Versus Discrete Time in the New Keynesian Model: Closed-Form Solutions and Implications for Liquidity Trap," CEPR Discussion Papers 13384, C.E.P.R. Discussion Papers.
    • Handle: RePEc:cpr:ceprdp:13384
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    References listed on IDEAS

    as
    1. Carlstrom, Charles T. & Fuerst, Timothy S. & Paustian, Matthias, 2015. "Inflation and output in New Keynesian models with a transient interest rate peg," Journal of Monetary Economics, Elsevier, vol. 76(C), pages 230-243.
    2. Taylor, John, 2018. "Taylor Rules and Forward Guidance: A Rule is not a Path," CEPR Discussion Papers 13383, C.E.P.R. Discussion Papers.
    3. John H. Cochrane, 2011. "Determinacy and Identification with Taylor Rules," Journal of Political Economy, University of Chicago Press, vol. 119(3), pages 565-615.
    4. Marco Del Negro & Marc P. Giannoni & Christina Patterson, 2023. "The Forward Guidance Puzzle," Journal of Political Economy Macroeconomics, University of Chicago Press, vol. 1(1), pages 43-79.
    5. Alisdair McKay & Emi Nakamura & Jón Steinsson, 2016. "The Power of Forward Guidance Revisited," American Economic Review, American Economic Association, vol. 106(10), pages 3133-3158, October.
    6. Taylor, John B., 1986. "New econometric approaches to stabilization policy in stochastic models of macroeconomic fluctuations," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 3, chapter 34, pages 1997-2055, Elsevier.
    7. Cochrane, John H., 2017. "The new-Keynesian liquidity trap," Journal of Monetary Economics, Elsevier, vol. 92(C), pages 47-63.
    8. 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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    Citations

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    Cited by:

    1. Taylor, John, 2018. "Taylor Rules and Forward Guidance: A Rule is not a Path," CEPR Discussion Papers 13383, C.E.P.R. Discussion Papers.
    2. Alexeeva, Tatyana A. & Kuznetsov, Nikolay V. & Mokaev, Timur N., 2021. "Study of irregular dynamics in an economic model: attractor localization and Lyapunov exponents," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    3. Lilia Maliar & John B. Taylor, 2019. "Forward Guidance: Is It Useful Away from the Lower Bound?," NBER Working Papers 26053, National Bureau of Economic Research, Inc.
    4. Maliar, Lilia & Taylor, John B., 2024. "Odyssean forward guidance in normal times," Journal of Economic Dynamics and Control, Elsevier, vol. 165(C).

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    More about this item

    Keywords

    Forward guidance; Continuous time; New keynesian model; Zlb. liquidity trap; Closed-form solution;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models
    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation
    • E52 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Monetary Policy

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