Working Paper: CEPR ID: DP11115
Authors: Jess Fernández-Villaverde; Oren Levintal
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.
Keywords: DSGE models; perturbation; rare disasters; Smolyak; solution methods; Taylor projection
JEL Codes: C63; C68; E32; E37; E44; G12
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| rare disasters (H84) | significant nonlinearities in models (C32) |
| significant nonlinearities in models (C32) | influence asset pricing and macroeconomic dynamics (G19) |
| low-order perturbation solutions (C69) | high Euler errors (C62) |
| fifth-order perturbations (C69) | computationally expensive (C63) |
| second-order Taylor projections (C69) | favorable balance of accuracy and speed (C52) |
| third-order Taylor projections (C69) | high accuracy but higher computational cost (C51) |
| Smolyak collocation methods (C45) | challenges in implementation and memory constraints (O33) |
| model dimensionality (C52) | accuracy and computational speed (C63) |
| Taylor projection methods (C51) | effectiveness in capturing dynamics of rare disasters (H84) |