Solving Reduced-form Linear Rational Expectations

This paper proposes an improvement on popular solution methods for linear rational expectations models (for example, Sims 2002) in terms of computational performance: When a model can be transformed into a reduced form, the QZ decomposition to decouple the dynamics of the stable and unstable block of the model can be replaced with the Schur decomposition. The latter runs faster. The new method is applicable to a wide class of models in the literature. It is especially useful for a large-scale model such as a multisector model and a heterogeneous agent model that are increasingly popular recently. Compared to the method that uses the QZ decomposition, the new method that uses the Schur decomposition reduces computing time by 33.0% for a medium-scale model with 39 equations and 91.3% for a large-scale model with 1,908 equations.