An Application of Sparse Methods to Solving a Multi-Country Model With Rational Expectations

Anderson and Moore  presents a procedure for solving linear perfect foresight models and Andersonn[Anderson1993] shows how to apply this technique to non linear models. The technique requires eigenvalue computations for a sparse linear system to deal with the long run dynamics and computations with large sparse band diagonal matrices for computing the nonlinear trajectory of the model variables. This paper applies methods for exploiting the special structure of these band diagonal linear systems Bai's SRRIT algorithm [Bai and Stewart1992] for computing vectors spanning the invariant space of a sparse linear system. These techniques dramatically reduce computational requirements while enhancing the accuracy and robustness of the original algorithm. The paper presents solution results for a variant of the multicountry model presented in Edison, Marques and Tyon