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A Note on the Solution of A Two-Point Boundary Value Problem Frequently Encountered in Rational Expectations Models

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  • Willem H. Buiter

Abstract

The paper analyses a class of two-point boundary value problem for systems of linear differential equations with constant coefficients. The boundary conditions are expressed as linear restrictions on the state vector at an initial time and at a finite terminal time. This is applicable even if the terminal conditions involve the asymptotic convergence of the system to steady-state equilibrium. as is frequently the case in eC9nomic applications. It is also a suitable format for numerical applications using existing computer routines. The case in which there are more stable eigenvalues than predetermined state variables is also considered. An example involving a small open economy macroeconomic model is used to illustrate the analysis.

Suggested Citation

  • Willem H. Buiter, 1981. "A Note on the Solution of A Two-Point Boundary Value Problem Frequently Encountered in Rational Expectations Models," NBER Technical Working Papers 0012, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberte:0012
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    References listed on IDEAS

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    1. Buiter, Willem H. & Miller, Marcus, 1980. "Monetary Policy And International Competitiveness," Economic Research Papers 269135, University of Warwick - Department of Economics.
    2. Obstfeld, Maurice, 1981. "Macroeconomic Policy, Exchange-Rate Dynamics, and Optimal Asset Accumulation," Journal of Political Economy, University of Chicago Press, vol. 89(6), pages 1142-1161, December.
    3. Blanchard, Olivier J, 1979. "Backward and Forward Solutions for Economies with Rational Expectations," American Economic Review, American Economic Association, vol. 69(2), pages 114-118, May.
    4. Willem H. Buiter, 1980. "The Role of Economic Policy After the New Classical Macroeconomics," NBER Technical Working Papers 0006, National Bureau of Economic Research, Inc.
    5. Calvo, Guillermo A, 1979. "On Models of Money and Perfect Foresight," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 20(1), pages 83-103, February.
    6. Flood, Robert P & Garber, Peter M, 1980. "Market Fundamentals versus Price-Level Bubbles: The First Tests," Journal of Political Economy, University of Chicago Press, vol. 88(4), pages 745-770, August.
    7. Blanchard, Olivier Jean & Kahn, Charles M, 1980. "The Solution of Linear Difference Models under Rational Expectations," Econometrica, Econometric Society, vol. 48(5), pages 1305-1311, July.
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    Cited by:

    1. Willem H. Buiter, 1984. "Policy evaluation and design for continuous time linear rational expectations models: some recent development," NBER Technical Working Papers 0034, National Bureau of Economic Research, Inc.

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