A new algorithm for solving dynamic stochasticmacroeconomic models

This paper introduces a new algorithm, the recursive upwind Gauss–Seidel method, andapplies it to solve a standard stochastic growth model in which the technology shocksexhibit heteroskedasticity. This method exploits the fact that the equations definingequilibrium can be viewed as a set of algebraic equations in the neighborhood of thesteady-state. In a non-stochastic setting, the algorithm, in essence, continually extends alocal 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 iscompared to projection, perturbation, and linearization approaches and is shown to befast and globally accurate. We also demonstrate that linearization methods performpoorly in an environment of heteroskedasticity even though the unconditional varianceof technology shocks is relatively small and similar to that typically used in RBCanalysis....