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Solutions of multivariate Rational Expectations Models

Published online by Cambridge University Press:  11 February 2009

Laurence Broze ,
Christian Gouriéroux  and
Ariane Szafarz
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Abstract

The aim of this paper is the study of the path solutions of a multivariate rational expectations model. We describe several procedures for solving such dynamic systems based on either the adjoint operator method or the Smith form. As a by-product, we derive the dimension of the set of solutions in terms of martingale differences and the dimension of the set of linear stationary solutions when we restrict ourselves to the linear case. These dimensions are functions of the number of equations in the system, of the maximum lead, and of the orders of some eigenvalues of the characteristic equation associated with the system.

Type
Research Article
Information
Econometric Theory , Volume 11 , Issue 2 , February 1995 , pp. 229 - 257
Copyright
Copyright © Cambridge University Press 1995

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References

REFERENCES

Aoki, M. & Canzoneri, M. (1979) Reduced forms of rational expectations models. Quarterly Journal of Economics 93, 59–71.10.2307/1882598CrossRefGoogle Scholar
Blanchard, O.J. (1979) Backward and forward solutions for economies with rational expectations. American Economic Review, Papers and Proceedings 69, 114–118.Google Scholar
Blanchard, O.J. & Kahn, C.M. (1980) The solution of linear difference models under rational expectations. Econometrica 48, 1305–1311.10.2307/1912186CrossRefGoogle Scholar
Broze, L., Gouriéroux, C. & Szafarz, A. (1985) Solutions of dynamic linear rational expectations models. Econometric Theory 1, 341–368.10.1017/S0266466600011257CrossRefGoogle Scholar
Broze, L., Gouriéroux, C. & Szafarz, A. (1990) Reduced Forms of Rational Expectations Models, Fundamentals of Pure and Applied Economics, vol. 42. Chur, Switzerland: Harwood Academic Publishers.Google Scholar
Broze, L. & Szafarz, A. (1984) On linear models which admit a unique solution. European Economic Review 24, 103–111.10.1016/0014-2921(84)90015-1CrossRefGoogle Scholar
Broze, L. & Szafarz, A. (1991) The Econometric Analysis of Non-Uniqueness in Rational Expectation Models, Contributions to Economic Analysis, vol. 201. Amsterdam: Elsevier Science.Google Scholar
d'Autume, A. (1990) On the solution of linear difference equations with rational expectations. Review of Economic Studies 57, 677–688.10.2307/2298092CrossRefGoogle Scholar
Evans, G. (1985) Expectational stability and the multiple equilibria problem in linear rational expectations models. Quarterly Journal of Economics 100, 1217–1233.10.2307/1885681CrossRefGoogle Scholar
Evans, G. (1987) The structure of ARMA solutions to a general linear model with rational expectations. Journal of Economic Dynamics and Control 11, 79–91.10.1016/0165-1889(87)90025-XCrossRefGoogle Scholar
Evans, G. & Honkapohja, S. (1986) A complete characterization of ARMA solutions to linear rational expectations models. Review of Economic Studies 53, 227–239.10.2307/2297648CrossRefGoogle Scholar
Gantmacher, F.R. (1959) The Theory of Matrices, vols. I and II. New York: Chelsea.Google Scholar
Gohberg, P., Lancaster, P. & Rodman, L. (1982) Matrix Polynomials. New York: Academic Press.Google Scholar
Gouriéroux, C., Laffont, J.J. & Monfort, A. (1982) Rational expectations in linear models: Analysis of solutions. Econometrica 50, 409–425.10.2307/1912635CrossRefGoogle Scholar
Gouriéroux, C., Monfort, A. & Renault, E. (1991) A general framework for factor models. Discussion Paper, INSEE.Google Scholar
Lancaster, P. & Tismenetsky, M. (1985) The Theory of Matrices, Second Edition with Applications. New York: Academic Press.Google Scholar
MacCallum, B.T. (1983). On non–uniqueness in rational expectations models: An attempt at perspective. Journal of Monetary Economics 11, 134–168.Google Scholar
Muth, J.F. (1961) Rational expectations and the theory of price movements. Econometrica 29, 315–335.10.2307/1909635CrossRefGoogle Scholar
Pesaran, M.H. (1981) Identification of rational expectations models. Journal of Econometrics 16, 375–398.10.1016/0304-4076(81)90036-1CrossRefGoogle Scholar
Salemi, M.K. & Song, J. (1992) Saddlepath solutions for multivariate linear rational expectations models. Journal of Econometrics 53, 245–270.10.1016/0304-4076(92)90087-8CrossRefGoogle Scholar
Shiller, R. (1978) Rational expectations and the dynamic structure of macroeconomic models. Journal of Monetary Economics 4, 1–44.10.1016/0304-3932(78)90032-6CrossRefGoogle Scholar
Taylor, J.B. (1977) Conditions for a unique solution in stochastic macroeconomic models rational expectations. Econometrica 45, 1377–1387.10.2307/1912306CrossRefGoogle Scholar
Visco, I. (1981) On the derivation of reduced forms of rational expectations models. European Economic Review 16, 355–365.10.1016/0014-2921(81)90008-8CrossRefGoogle Scholar
Visco, I. (1984) On linear models with rational expectations: An addendum. European Economic Review 24, 113–115.10.1016/0014-2921(84)90016-3CrossRefGoogle Scholar
Wallis, K.F. (1980) Econometric implications of the rational expectations hypothesis. Econometrica 48, 49–73.10.2307/1912018CrossRefGoogle Scholar
Wegge, L.L. (1984) The Canonical Form of the Dynamic Muth-Rational Future Expectations Model. Discussion paper, University of California, Davis.Google Scholar
Whiteman, C. (1983) Linear Rational Expectations Models: A User's Guide. Minneapolis: University of Minnesota Press.10.5749/j.ctttsf26CrossRefGoogle Scholar