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�
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- Ray C. Fair & John B. Taylor, 1980.
"Solution and Maximum Likelihood Estimation of Dynamic Nonlinear RationalExpectations Models,"
NBER Technical Working Papers
0005, National Bureau of Economic Research, Inc.
- Fair, Ray C & Taylor, John B, 1983. "Solution and Maximum Likelihood Estimation of Dynamic Nonlinear Rational Expectations Models," Econometrica, Econometric Society, vol. 51(4), pages 1169-85, July.
- Ray C. Fair & John B. Taylor, 1980. "Solution and Maximum Likelihood Estimation of Dynamic Nonlinear Rational Expectations Models," Cowles Foundation Discussion Papers 564, Cowles Foundation for Research in Economics, Yale University.
- Anderson, Gary & Moore, George, 1985. "A linear algebraic procedure for solving linear perfect foresight models," Economics Letters, Elsevier, vol. 17(3), pages 247-252.
- Boucekkine, Raouf, 1995. "An alternative methodology for solving nonlinear forward-looking models," Journal of Economic Dynamics and Control, Elsevier, vol. 19(4), pages 711-734, May.
- Jean-Pierre LAFFARGUE, 1990. "Résolution d'un modèle macroéconomique avec anticipations rationnelles," Annales d'Economie et de Statistique, ENSAE, issue 17, pages 97-119.
- Gilli, Manfred & Pauletto, Giorgio, 1997. "Sparse direct methods for model simulation," Journal of Economic Dynamics and Control, Elsevier, vol. 21(6), pages 1093-1111, June.
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