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

This paper presents efficient methods for the solution of finite-horizon mu ltivariate linear rational expectations (MLRE) models, linking the solution of such models to the problem of solving sparse linear equation systems wi th a block-tridiagonal coefficient 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 efficiently solve finite-horiz on MLRE models. As the two numerical schemes are fully recursive and only i nvolve elementary matrix operations, they are also straightforward to imple ment. The numerical schemes are illustrated by applying them to a finite-ho rizon adjustment cost problem of expenditure shares under adding-up constra ints, and to a finite-horizon linear-quadratic optimal control problem. (C) 2000 Elsevier Science B.V. All rights reserved.