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Solving the new Keynesian model in continuous time

Author

Listed:
  • Olaf Posch

    (Aarhus University and CREATES)

  • Juan F. Rubio-Ramírez

    (Duke University, FRB Atlanta, and FEDEA)

  • Jesús Fernández-Villaverde

    (University of Pennsylvania, NBER, CEPR, and FEDEA)

Abstract

We show how to formulate and solve the new Keynesian model in continuous time. In our economy, monopolistic firms engage in infrequent price setting á la Calvo. We introduce shocks for preferences, total factor productivity and government expenditure, and then show how the equilibrium system can be written in terms of 8 state variables. Our nonlinear and global numerical solution technique uses the collocation method based on Chebychev polynomials directly computing the continuous-time Bellman equation.

Suggested Citation

  • Olaf Posch & Juan F. Rubio-Ramírez & Jesús Fernández-Villaverde, 2011. "Solving the new Keynesian model in continuous time," 2011 Meeting Papers 829, Society for Economic Dynamics.
    • Handle: RePEc:red:sed011:829
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    References listed on IDEAS

    as
    1. Lars Peter Hansen & José A. Scheinkman, 2009. "Long-Term Risk: An Operator Approach," Econometrica, Econometric Society, vol. 77(1), pages 177-234, January.
    2. 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. Offick Sven & Wohltmann Hans-Werner, 2016. "Partially Anticipated Monetary Policy Shocks – Are They Stabilizing or Destabilizing?," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 236(1), pages 95-127, February.
    2. Cochrane, John H., 2017. "The new-Keynesian liquidity trap," Journal of Monetary Economics, Elsevier, vol. 92(C), pages 47-63.
    3. Fernández-Villaverde, Jesús & Guerrón-Quintana, Pablo & Rubio-Ramírez, Juan F., 2015. "Estimating dynamic equilibrium models with stochastic volatility," Journal of Econometrics, Elsevier, vol. 185(1), pages 216-229.
    4. Sacht, Stephen, 2014. "Analysis of various shocks within the high-frequency versions of the baseline New-Keynesian model," Economics Working Papers 2014-02, Christian-Albrechts-University of Kiel, Department of Economics.
    5. Posch, Olaf & Trimborn, Timo, 2013. "Numerical solution of dynamic equilibrium models under Poisson uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2602-2622.
    6. John H. Cochrane, 2013. "The New-Keynesian Liquidity Trap," NBER Working Papers 19476, National Bureau of Economic Research, Inc.

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