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

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Buiter, W

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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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Publisher Info
Paper provided by University of Warwick, Department of Economics in its series The Warwick Economics Research Paper Series (TWERPS) with number 200.

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Length: 31 pages
Date of creation: 1982
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Handle: RePEc:wrk:warwec:200

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Wilson, Charles A, 1979. "Anticipated Shocks and Exchange Rate Dynamics," Journal of Political Economy, University of Chicago Press, vol. 87(3), pages 639-47, June. [Downloadable!] (restricted)
  2. Dornbusch, Rudiger, 1976. "Expectations and Exchange Rate Dynamics," Journal of Political Economy, University of Chicago Press, vol. 84(6), pages 1161-76, December. [Downloadable!] (restricted)
  3. Brock, William A., 1975. "A simple perfect foresight monetary model," Journal of Monetary Economics, Elsevier, vol. 1(2), pages 133-150, April. [Downloadable!] (restricted)
  4. Krugman, Paul, 1979. "A Model of Balance-of-Payments Crises," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 11(3), pages 311-25, August. [Downloadable!] (restricted)
  5. Blanchard, Olivier Jean & Kahn, Charles M, 1980. "The Solution of Linear Difference Models under Rational Expectations," Econometrica, Econometric Society, vol. 48(5), pages 1305-11, July. [Downloadable!] (restricted)
  6. Dornbusch, Rudiger & Fischer, Stanley, 1980. "Exchange Rates and the Current Account," American Economic Review, American Economic Association, vol. 70(5), pages 960-71, December. [Downloadable!] (restricted)
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  1. Pierre-Olivier Weill, 2004. "Liquidity Premia in Dynamic Bargaining Markets," Econometric Society 2004 North American Winter Meetings 648, Econometric Society. [Downloadable!]
  2. Domenico Scalera, 1996. "Optimal consumption and the environment Choosing between ‘clean’ and ‘dirty’ goods," Environmental & Resource Economics, European Association of Environmental and Resource Economists, vol. 7(4), pages 375-389, June. [Downloadable!] (restricted)
  3. Manuel Gómez, 2005. "Transitional Dynamics in an Endogenous Growth Model with Physical Capital, Human Capital and R&D," Studies in Nonlinear Dynamics & Econometrics, Berkeley Electronic Press, vol. 9(1), pages 1240-1240. [Downloadable!] (restricted)
  4. Kenneth L. Judd, 1984. "The Macroeconomic Effects of Uncertain Fiscal Policy," Discussion Papers 682, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
  5. Serven, Luis, 1990. "Anticipated real exchange-rate changes and the dynamics of investment," Policy Research Working Paper Series 562, The World Bank. [Downloadable!]
  6. Ana Lamo & Julian Messina & Etienne Wasmer, 2007. "Are Specific Skills an Obstacle to Labor Market Adjustment? Theory and an Application to the EU Enlargement," CSEF Working Papers 172, Centre for Studies in Economics and Finance (CSEF), University of Salerno, Italy. [Downloadable!]
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  7. Jhy-hwa Chen & Ching-chong Lai & Jhy-yuan Shieh, 2003. "Anticipated Environmental Policy and Transitional Dynamics in an Endogenous Growth Model," Environmental & Resource Economics, European Association of Environmental and Resource Economists, vol. 25(2), pages 233-254, June. [Downloadable!] (restricted)
  8. Olivier, CARDI, 2005. "Another View of the J-Curve," Université catholique de Louvain, Département des Sciences Economiques Working Paper 2005029, Université catholique de Louvain, Département des Sciences Economiques. [Downloadable!]
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  9. Schmidt-Hebbel, Klaus & Serven, Luis, 1995. "Fiscal and monetary contraction in Chile : a rational-expectations approach," Policy Research Working Paper Series 1472, The World Bank. [Downloadable!]
  10. Willem H. Buiter, 1989. "A "Gold Standard" Isn't Viable Unless Supported by Sufficiently FlexibleMonetary and Fiscal Policy," NBER Working Papers 1903, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  11. Wohltmann, Hans-Werner & Clausen, Volker, 2003. "Oil Price Shocks and Monetary Policy in an Asymmetric Monetary Union§," Economics working papers 2003,11, Christian-Albrechts-University of Kiel, Department of Economics. [Downloadable!]
  12. Francisco A. Gallego & Klaus Schmidt-Hebbel & Luis Servén, 2004. "General Equilibrium Dynamics of External Shocks and Policy Changes in Chile," Working Papers Central Bank of Chile 271, Central Bank of Chile. [Downloadable!]
  13. Olivier, CARDI, 2005. "The Zero-Root Property : Permanent vs Temporary Terms of Trade Shocks," Université catholique de Louvain, Département des Sciences Economiques Working Paper 2005030, Université catholique de Louvain, Département des Sciences Economiques. [Downloadable!]
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  14. Chris Tsoukis & Naveed Naqvi, 2007. "Price rigidities, inventories, and growth fluctuations," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 28(6), pages 619-631. [Downloadable!]
  15. Willem H. Buiter, 1989. "Structural and Stabilization Aspects of Fiscal and Financial Policy in the Dependent Economy," NBER Working Papers 2023, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  16. Wohltmann, Hans-Werner & Winkler, Roland, 2005. "Oil Price Shocks and Currency Denomination (A revised version of EWP 2005-01)," Economics working papers 2005,10, Christian-Albrechts-University of Kiel, Department of Economics. [Downloadable!]
  17. Wohltmann, Hans-Werner & Winkler, Roland, 2005. "Dynamic Effects of Raw Materials Price Shocks for Large Oil-Dependent Economies," Economics working papers 2005,01, Christian-Albrechts-University of Kiel, Department of Economics. [Downloadable!]
  18. Volker Clausen & Hans-Werner Wohltmann, 2002. "Monetary and Fiscal Policy Dynamics in an Asymmetric Monetary Union," Macroeconomics 0201001, EconWPA. [Downloadable!]
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