Solution methods for models with rare disasters

Jesús Fernández-Villaverde, Oren Levintal

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18 Scopus citations


This paper compares different solution methods for computing the equilibrium of dynamic stochastic general equilibrium (DSGE) models with rare disasters along the lines 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 nonlinearities triggered by low-probability, high-impact events with 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.

Original languageEnglish
Pages (from-to)903-944
Number of pages42
JournalQuantitative Economics
Issue number2
StatePublished - Jul 2018
Externally publishedYes

Bibliographical note

Publisher Copyright:
Copyright © 2018 The Authors.


  • DSGE models
  • Rare disasters
  • Smolyak
  • Taylor projection
  • perturbation
  • solution methods


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