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Solution Methods for Models with Rare Disasters

Jesús Fernández-Villaverde, Oren Levintal

NBER Working Paper No. 21997
Issued in February 2016
NBER Program(s):Economic Fluctuations and Growth

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.

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Document Object Identifier (DOI): 10.3386/w21997

Published: Jesús Fernández-Villaverde & Oren Levintal, 2018. "Solution methods for models with rare disasters," Quantitative Economics, vol 9(2), pages 903-944. citation courtesy of

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