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Saddlepoint Problems in Continuous Time Rational Expectations Models : A General Method and Some Macroeconomic Examples

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Abstract

This paper presents a general solution method for rational expectations models that can be represented by systems of deterministic first order linear differential equations with constant coefficients. It is the continuous time adaptation of the method of Blanchard and Khan. To obtain a unique solution there must be as many linearly independent boundary conditions as there are linearly independent state variables. Three slightly different versions of a well-known small open economy macroeconomic model were used to illustrate three fairly general ways of specifying the required boundary conditions. The first represents the standard case in which the number of stable characteristic roots equals the number of predetermined variables. The second represents the case where the number of stable roots exceeds the number of predetermined variables but equals the number of predetermined variables plus the number of "backward-looking" but non-predetermined variables whose discontinuities are linear functions of the discontinuities in the forward-looking variables. The third represents the case where the number of unstable roots is less than the number of forward-looking state variables. For the last case, boundary conditions are suggested that involve linear restrictions on the values of the state variables at a future date.

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  • Buiter, W, 1982. "Saddlepoint Problems in Continuous Time Rational Expectations Models : A General Method and Some Macroeconomic Examples," The Warwick Economics Research Paper Series (TWERPS) 200, University of Warwick, Department of Economics.
  • Handle: RePEc:wrk:warwec:200
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    1. Wilson, Charles A, 1979. "Anticipated Shocks and Exchange Rate Dynamics," Journal of Political Economy, University of Chicago Press, vol. 87(3), pages 639-647, June.
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    3. Krugman, Paul, 1979. "A Model of Balance-of-Payments Crises," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 11(3), pages 311-325, August.
    4. 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.
    5. Dornbusch, Rudiger & Fischer, Stanley, 1980. "Exchange Rates and the Current Account," American Economic Review, American Economic Association, vol. 70(5), pages 960-971, December.
    6. Dornbusch, Rudiger, 1976. "Expectations and Exchange Rate Dynamics," Journal of Political Economy, University of Chicago Press, vol. 84(6), pages 1161-1176, December.
    7. 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.
    8. Olivier Jean Blanchard, 1980. "The Monetary Mechanism in the Light of Rational Expectations," NBER Chapters,in: Rational Expectations and Economic Policy, pages 75-116 National Bureau of Economic Research, Inc.
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