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Solution Methods for Models with Rare Disasters

Author

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  • Fernández-Villaverde, Jesús
  • Levintal, Oren

Abstract

This paper compares different solution methods for computing the equilibrium of dynamic stochastic general equilibrium (DSGE) models with rare disasters along the line of those proposed by Rietz (1988), Barro (2006}, Gabaix (2012), and Gourio (2012). DSGE models with rare disasters require solution methods that can handle the large non-linearities triggered by low-probability, high-impact events with sufficient accuracy and speed. We solve a standard New Keynesian model with Epstein-Zin preferences and time-varying disaster risk with perturbation, Taylor projection, and Smolyak collocation. Our main finding is that Taylor projection delivers the best accuracy/speed tradeoff among the tested solutions. We also document that even third-order perturbations may generate solutions that suffer from accuracy problems and that Smolyak collocation can be costly in terms of run time and memory requirements.

Suggested Citation

  • Fernández-Villaverde, Jesús & Levintal, Oren, 2016. "Solution Methods for Models with Rare Disasters," CEPR Discussion Papers 11115, C.E.P.R. Discussion Papers.
  • Handle: RePEc:cpr:ceprdp:11115
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    References listed on IDEAS

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    1. Fernández-Villaverde, Jesús & Gordon, Grey & Guerrón-Quintana, Pablo & Rubio-Ramírez, Juan F., 2015. "Nonlinear adventures at the zero lower bound," Journal of Economic Dynamics and Control, Elsevier, vol. 57(C), pages 182-204.
    2. Isoré, Marlène & Szczerbowicz, Urszula, 2017. "Disaster risk and preference shifts in a New Keynesian model," Journal of Economic Dynamics and Control, Elsevier, vol. 79(C), pages 97-125.
    3. Gourio, François & Siemer, Michael & Verdelhan, Adrien, 2013. "International risk cycles," Journal of International Economics, Elsevier, vol. 89(2), pages 471-484.
    4. Martin M Andreasen & Jesús Fernández-Villaverde & Juan F Rubio-Ramírez, 2018. "The Pruned State-Space System for Non-Linear DSGE Models: Theory and Empirical Applications," Review of Economic Studies, Oxford University Press, vol. 85(1), pages 1-49.
    5. Jerry Tsai & Jessica A. Wachter, 2015. "Disaster Risk and its Implications for Asset Pricing," NBER Working Papers 20926, National Bureau of Economic Research, Inc.
    6. Jessica A. Wachter, 2013. "Can Time-Varying Risk of Rare Disasters Explain Aggregate Stock Market Volatility?," Journal of Finance, American Finance Association, vol. 68(3), pages 987-1035, June.
    7. Judd, Kenneth L. & Maliar, Lilia & Maliar, Serguei & Valero, Rafael, 2014. "Smolyak method for solving dynamic economic models: Lagrange interpolation, anisotropic grid and adaptive domain," Journal of Economic Dynamics and Control, Elsevier, vol. 44(C), pages 92-123.
    8. Martin Andreasen, 2012. "On the Effects of Rare Disasters and Uncertainty Shocks for Risk Premia in Non-Linear DSGE Models," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 15(3), pages 295-316, July.
    9. Xavier Gabaix, 2012. "Variable Rare Disasters: An Exactly Solved Framework for Ten Puzzles in Macro-Finance," The Quarterly Journal of Economics, Oxford University Press, vol. 127(2), pages 645-700.
    10. repec:eee:macchp:v2-527 is not listed on IDEAS
    11. Epstein, Larry G & Zin, Stanley E, 1989. "Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: A Theoretical Framework," Econometrica, Econometric Society, vol. 57(4), pages 937-969, July.
    12. Malin, Benjamin A. & Krueger, Dirk & Kubler, Felix, 2011. "Solving the multi-country real business cycle model using a Smolyak-collocation method," Journal of Economic Dynamics and Control, Elsevier, vol. 35(2), pages 229-239, February.
    13. Marlène Isoré & Urszula Szczerbowicz, 2013. "Disaster Risk in a New Keynesian Model," Working Papers 2013-12, CEPII research center.
    14. Fernández-Villaverde, J. & Rubio-Ramírez, J.F. & Schorfheide, F., 2016. "Solution and Estimation Methods for DSGE Models," Handbook of Macroeconomics, Elsevier.
    15. repec:eee:dyncon:v:80:y:2017:i:c:p:1-16 is not listed on IDEAS
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    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
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    Cited by:

    1. Robert J. Barro & Jesús Fernández-Villaverde & Oren Levintal & Andrew Mollerus, 2014. "Safe Assets," NBER Working Papers 20652, National Bureau of Economic Research, Inc.
      • Barro, Robert J. & Fern�ndez-Villaverde, Jes�s & Levintal, Oren & Mollerus, Andrew, 2017. "Safe Assets," CEPR Discussion Papers 12043, C.E.P.R. Discussion Papers.
    2. Giorgio Fagiolo & Andrea Roventini, 2017. "Macroeconomic Policy in DSGE and Agent-Based Models Redux: New Developments and Challenges Ahead," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 20(1), pages 1-1.
    3. repec:eee:macchp:v2-527 is not listed on IDEAS
    4. Isoré, Marlène & Szczerbowicz, Urszula, 2017. "Disaster risk and preference shifts in a New Keynesian model," Journal of Economic Dynamics and Control, Elsevier, vol. 79(C), pages 97-125.
    5. Fernández-Villaverde, J. & Rubio-Ramírez, J.F. & Schorfheide, F., 2016. "Solution and Estimation Methods for DSGE Models," Handbook of Macroeconomics, Elsevier.
    6. repec:eee:dyncon:v:80:y:2017:i:c:p:1-16 is not listed on IDEAS

    More about this item

    Keywords

    DSGE models; perturbation; rare disasters; Smolyak; solution methods; Taylor projection;

    JEL classification:

    • 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
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications
    • E44 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Financial Markets and the Macroeconomy
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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