Computing Models with Recursive Preferences

This paper compares different solution methods for the computation of the equilibrium of dynamic stochastic general equilibrium (DSGE) models with recursive preferences. Over the last decade, a growing number of researchers have investigated models with recursive preferences of the type first proposed by Kreps and Porteus (1978) and later generalized by Epstein and Zin, (1989 and 1991) and Weil (1990). These economist have been attracted by the extra flexibility of separating risk aversion and intertemporal elasticity of substitution and some for the intuitive appealing of having preferences for early or later resolution of uncertainty. Despite a large manifold of papers using recursive preferences, little is known about the numerical properties of the different solution methods that solve models with these type of preferences. This paper attempts at filling this gap in the literature. We solve the model using three different approaches: value function iteration, Chebyshev polynomials, and perturbation. This paper complements a previous paper by Aruoba, Fernández-Villaverde, and Rubio-Ramírez (2006), where a similar exercise is performed with the neoclassical growth model with CRRA utility function.