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Numerical Solution of Dynamic Equilibrium Models under Poisson Uncertainty

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  • Olaf Posch
  • Timo Trimborn

Abstract

We propose a simple and powerful numerical algorithm to compute the transition process in continuous-time dynamic equilibrium models with rare events. In this paper we transform the dynamic system of stochastic differential equations into a system of functional differential equations of the retarded type. We apply the Waveform Relaxation algorithm, i.e., we provide a guess of the policy function and solve the resulting system of (deterministic) ordinary differential equations by standard techniques. For parametric restrictions, analytical solutions to the stochastic growth model and a novel solution to Lucas' endogenous growth model under Poisson uncertainty are used to compute the exact numerical error. We show how (potential) catastrophic events such as rare natural disasters substantially affect the economic decisions of households.

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  • Olaf Posch & Timo Trimborn, 2011. "Numerical Solution of Dynamic Equilibrium Models under Poisson Uncertainty," DEGIT Conference Papers c016_044, DEGIT, Dynamics, Economic Growth, and International Trade.
  • Handle: RePEc:deg:conpap:c016_044
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    Cited by:

    1. Posch, Olaf, 2011. "Risk premia in general equilibrium," Journal of Economic Dynamics and Control, Elsevier, vol. 35(9), pages 1557-1576, September.
    2. Yoji Kunimitsu, 2018. "Effects of restoration measures from the east Japan earthquake in the Iwate coastal area: application of a DSGE model," Asia-Pacific Journal of Regional Science, Springer, vol. 2(2), pages 317-335, August.
    3. Posch, Olaf, 2018. "Resurrecting the New-Keynesian Model: (Un)conventional Policy and the Taylor rule," VfS Annual Conference 2018 (Freiburg, Breisgau): Digital Economy 181616, Verein für Socialpolitik / German Economic Association.
    4. Parra-Alvarez, Juan Carlos, 2018. "A Comparison Of Numerical Methods For The Solution Of Continuous-Time Dsge Models," Macroeconomic Dynamics, Cambridge University Press, vol. 22(6), pages 1555-1583, September.
    5. Holger Strulik & Timo Trimborn, 2019. "Natural Disasters and Macroeconomic Performance," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 72(4), pages 1069-1098, April.
    6. Santanu Chatterjee & Olaf Posch & Dennis Wesselbaum, 2017. "Delays in Public Goods," CESifo Working Paper Series 6341, CESifo.

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    More about this item

    Keywords

    Continuous-time DSGE; Poisson uncertainty; Waveform Relaxation;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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