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Solution of Multivariate Linear Rational Expectations Models and Large Sparse Linear Systems

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Abstract

This paper establishes a link between the problem of solving multivariate linear rational expectations models and the problem of solving large sparse linear systems with a block-tridiagonal matrix coefficient structure. Such large linear systems arise in a wide variety of scientific problems, including the numerical solution of certain classes of partial differential equations, linear-quadratic optimal control problems, and Gaussian optimal filtering problems. Two numerical schemes that allow efficient solution of large sparse linear systems with a block-tridiagonal matrix coefficient structure are presented, and it is shown how these procedures can be readily adapted to solve multivariate linear rational expectations models. Furthermore, the solution of multivariate linear rational expectations models by means of solving large sparse linear systems is linked to the fully recursive method for the solution of multivariate linear rational expectations models recently advanced in Binder and Pesaran (1996). Finally, the numerical schemes are illustrated by applying them to obtain the solution of a simple stochastic growth model.

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  • Pesaran, M. H. & Binder, M., 1997. "Solution of Multivariate Linear Rational Expectations Models and Large Sparse Linear Systems," Cambridge Working Papers in Economics 9708, Faculty of Economics, University of Cambridge.
    • Handle: RePEc:cam:camdae:9708
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    Cited by:

    1. Binder, Michael & Hsiao, Cheng & Pesaran, M. Hashem, 2005. "Estimation And Inference In Short Panel Vector Autoregressions With Unit Roots And Cointegration," Econometric Theory, Cambridge University Press, vol. 21(4), pages 795-837, August.
    2. Bernd Funovits, 2014. "Implications of Stochastic Singularity in Linear Multivariate Rational Expectations Models," Vienna Economics Papers 1405, University of Vienna, Department of Economics.
    3. Bernd Funovits, 2020. "The Dimension of the Set of Causal Solutions of Linear Multivariate Rational Expectations Models," Papers 2002.04369, arXiv.org.
    4. Al-Sadoon, Majid M., 2018. "The Linear Systems Approach To Linear Rational Expectations Models," Econometric Theory, Cambridge University Press, vol. 34(3), pages 628-658, June.
    5. Alessandro Cologni & Matteo Manera, 2011. "Exogenous Oil Shocks, Fiscal Policy and Sector Reallocations in Oil Producing Countries," Working Papers 2011.55, Fondazione Eni Enrico Mattei.
    6. Bernd Funovits, 2014. "Implications of Stochastic Singularity in Linear Multivariate Rational Expectations Models," Vienna Economics Papers vie1405, University of Vienna, Department of Economics.
    7. Klein, Paul, 2000. "Using the generalized Schur form to solve a multivariate linear rational expectations model," Journal of Economic Dynamics and Control, Elsevier, vol. 24(10), pages 1405-1423, September.

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