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The Forward Solution for Linear Rational Expectations Models

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  • Seonghoon Cho

    () (Yonsei University)

  • Antonio Moreno

    () (University of Navarra)

Abstract

This paper derives a recursive method and the corresponding forward solution for linear Rational Expectations (RE) models in the class of fundamental solutions. Our recursive method is a generalization of the traditional forward method of recursive substitution when predetermined variables are present. This recursive method detects the existence of the real-valued solution to a given model by simply examining whether the model can be solved forward and its solution does not depend on the expectations of the future endogenous variables. The resulting forward solution is unique by construction, whenever it exists. Consequently, as long as one seeks for the stationary forward solution, the issue of multiple stationary solutions is irrelevant. We show that seemingly legitimate model solutions obtained by other methods may not be admissible as valid RE solutions.

Suggested Citation

  • Seonghoon Cho & Antonio Moreno, 2007. "The Forward Solution for Linear Rational Expectations Models," Faculty Working Papers 07/07, School of Economics and Business Administration, University of Navarra.
  • Handle: RePEc:una:unccee:wp0707
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    References listed on IDEAS

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    1. McCallum, Bennett T., 2004. "On the relationship between determinate and MSV solutions in linear RE models," Economics Letters, Elsevier, vol. 84(1), pages 55-60, July.
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    3. Paul A. Samuelson, 1958. "An Exact Consumption-Loan Model of Interest with or without the Social Contrivance of Money," Journal of Political Economy, University of Chicago Press, vol. 66, pages 467-467.
    4. Carl E. Walsh, 2003. "Monetary Theory and Policy, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262232316.
    5. Farmer Roger E. A. & Guo Jang-Ting, 1994. "Real Business Cycles and the Animal Spirits Hypothesis," Journal of Economic Theory, Elsevier, vol. 63(1), pages 42-72, June.
    6. 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.
    7. McCallum, Bennett T., 1983. "On non-uniqueness in rational expectations models : An attempt at perspective," Journal of Monetary Economics, Elsevier, vol. 11(2), pages 139-168.
    8. Binder, M. & Pesaran, H., 1996. "Multivariate Linear Rational Expectations Models: Characterisation of the Nature of the Solutions and Their Fully Recursive Computation," Cambridge Working Papers in Economics 9619, Faculty of Economics, University of Cambridge.
    9. Driskill, Robert, 2006. "Multiple equilibria in dynamic rational expectations models: A critical review," European Economic Review, Elsevier, vol. 50(1), pages 171-210, January.
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