System reduction of dynamic stochastic general equilibrium models solved by gensys

Abstract

We propose a simple system reduction method to efficiently evaluate the likelihood of a linear dynamic stochastic general equilibrium (DSGE) model solved by the solution method of Sims (2002) or gensys. Since Sims (2002) decouples the stable and unstable block of a DSGE model and solves the unstable block forward as a constant, we do not need to track the dynamics of the unstable block, which effectively reduces the dimension of the model. The present method reduces time to evaluate the likelihood of popular DSGE models by 8.9% to 28.8% compared to the standard method without system reduction. The implementation cost of the present method is almost nil.