Computing DSGE models with recursive preferences and stochastic volatility

This paper compares different solution methods for computing the equilibrium of dynamic stochastic general equilibrium (DSGE) models with recursive preferences such as those in Epstein and Zin, 1989 and Epstein and Zin, 1991 and stochastic volatility. Models with these two features have recently become popular, but we know little about the best ways to implement them numerically. To fill this gap, we solve the stochastic neoclassical growth model with recursive preferences and stochastic volatility using four different approaches: second- and third-order perturbation, Chebyshev polynomials, and value function iteration. We document the performance of the methods in terms of computing time, implementation complexity, and accuracy. Our main finding is that perturbations are competitive in terms of accuracy with Chebyshev polynomials and value function iteration while being several orders of magnitude faster to run. Therefore, we conclude that perturbation methods are an attractive approach for computing this class of problems.

► We compare different computational methods for solving DSGE models with Epstein–Zin preferences and stochastic volatility.
► Projection delivers high accuracy but it is slow.
► Perturbation delivers more than acceptable accuracy at great speed.
► Value function iteration requires an inordinate amount of time to deliver an acceptable level of accuracy.
► Hence, we conclude that projection and perturbation methods are the best choices to handle this class of problems.