Solution of finite-horizon multivariate linear rational expectations models and sparse linear systems

Abstract

This paper presents e$cient methods for the solution of xnite-horizon multivariate linear rational expectations (MLRE) models, linking the solution of such models to the problem of solving sparse linear equation systems with a block-tridiagonal coe$cient matrix structure. Two numerical schemes for the solution of this type of equation systems are discussed, and it is shown how these procedures can be adapted to e$ciently solve nite-horizon MLRE models. As the two numerical schemes are fully recursive and only involve elementary matrix operations, they are also straightforward to implement. The numerical schemes are illustrated by applying them to a nite-horizon adjustment cost problem of expenditure shares under adding-up constraints, and to a nite-horizon linear-quadratic optimal control problem. ( 2000 Elsevier Science B.V. All rights reserved.