A new algorithm for solving dynamic stochastic macroeconomic models

This paper introduces a new algorithm, the recursive upwind Gauss-Seidel method, and applies it to solve a standard stochastic growth model in which the technology shocks exhibit heteroskedasticity. This method exploits the fact that the equations defining equilibrium can be viewed as a set of algebraic equations in the neighborhood of the steady-state. In a non-stochastic setting, the algorithm, in essence, continually extends a local solution to a globally accurate solution. When stochastic elements are introduced, it then uses a recursive scheme in order to determine the global solution. This method is compared to projection, perturbation, and linearization approaches and is shown to be fast and globally accurate. We also demonstrate that linearization methods perform poorly in an environment of heteroskedasticity even though the unconditional variance of technology shocks is relatively small and similar to that typically used in RBC analysis.