Solving SDGE Models: A New Algorithm for Sylvester Equation

This paper presents a new numerical algorithm for solving Sylvester equation involved in higher order perturbation method used for solution of stochastic dynamic general equilibrium models. The new algorithm is better than methods used so far (esp. very popular doubling algorithm) in terms of computational time, memory consumption, and numerical stability. Further, the paper applies the algorithm in a simulation of a large macroeconomy model providing a simple welfare analysis of a few monetary rules. The welfare analysis compares household's lifetime expected utility.