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 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.
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