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Solving Stochastic Saddlepoint Systems: A Qualitative Treatment With Economic Applications

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  • Miller, Marcus
  • Weller, Paul
Abstract
We examine the effect of introducing stochastic shocks into a linear rational expectations model with saddlepoint dynamics generated by a forward-looking asset price. We derive the fundamental differential equation governing the path of the asset price as a function of the "sluggish" variable. The equation does not admit of closed form solutions in general, but we provide a complete qualitative characterization of the solution paths which are symmetric about equilibrium. These are the relevant solutions to consider in the presence of symmetric boundary conditions. We present two applications. The first analyzes how financial markets might react to the implementation of fiscal stabilization policy where public expenditures are only adjusted when GNP moves outside a threshold around a target level. Bond prices are perfectly flexible and move to satisfy an arbitrage condition. The second examines exchange rate behavior in the presence of a currency subject to a known realignment rule requiring an adjustment to monetary policy.

Suggested Citation

  • Miller, Marcus & Weller, Paul, 1988. "Solving Stochastic Saddlepoint Systems: A Qualitative Treatment With Economic Applications," Economic Research Papers 268343, University of Warwick - Department of Economics.
    • Handle: RePEc:ags:uwarer:268343
    DOI: 10.22004/ag.econ.268343
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    1. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
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    4. Blanchard, Olivier J, 1981. "Output, the Stock Market, and Interest Rates," American Economic Review, American Economic Association, vol. 71(1), pages 132-143, March.
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    Cited by:

    1. Robert P. Flood & Peter M. Garber, 1991. "The Linkage Between Speculative Attack and Target Zone Models of Exchange Rates," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 106(4), pages 1367-1372.
    2. Buiter, Willem H. & Pesenti, Paolo A., 1990. "Rational Speculative Bubbles In An Exchange Rate Target Zone," Economic Research Papers 268490, University of Warwick - Department of Economics.
    3. Miller, Marcus & Weller, Paul, 1991. "Exchange Rate Bands with Price Inertia," Economic Journal, Royal Economic Society, vol. 101(409), pages 1380-1399, November.
    4. Barry Eichengreen & Peter M. Garber, 1991. "Before the Accord: U.S. Monetary-Financial Policy, 1945-51," NBER Chapters, in: Financial Markets and Financial Crises, pages 175-206, National Bureau of Economic Research, Inc.
    5. Beetsma, Roel M W J & van der Ploeg, Frederick, 1994. "Intramarginal Interventions, Bands and the Pattern of EMS Exchange Rate Distributions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 583-602, August.
    6. Jean-Pierre Laffargue & Sanvi Avouyi-Dovi, 1992. "Anticipations stabilisatrices dans un système de serpent monétaire. Théorie et application au système monétaire européen," Revue Économique, Programme National Persée, vol. 43(6), pages 1107-1128.
    7. Oppers, Stefan Erik, 2000. "A model of the bimetallic system," Journal of Monetary Economics, Elsevier, vol. 46(2), pages 517-533, October.
    8. Miller, M. & Weller, P. & Williamson, J., 1989. "The Stabilizing Properties Of Target Zones," The Warwick Economics Research Paper Series (TWERPS) 318, University of Warwick, Department of Economics.
    9. Beetsma, Roel M. W. J. & van der Ploeg, Frederick, 1998. "Macroeconomic stabilization and intervention policy under an exchange rate band," Journal of International Money and Finance, Elsevier, vol. 17(2), pages 339-353, April.
    10. Svensson, Lars E. O., 1991. "The term structure of interest rate differentials in a target zone : Theory and Swedish data," Journal of Monetary Economics, Elsevier, vol. 28(1), pages 87-116, August.
    11. Sutherland, Alan, 1990. "Multiple Solutions and Bubbles in Stochastic Models of the Exchange Rate," Economic Research Papers 268383, University of Warwick - Department of Economics.
    12. Svensson, Lars E. O., 1991. "Target zones and interest rate variability," Journal of International Economics, Elsevier, vol. 31(1-2), pages 27-54, August.
    13. Paul Krugman & Julio Rotemberg, 1990. "Target Zones with Limited Reserves," NBER Working Papers 3418, National Bureau of Economic Research, Inc.
    14. Bernd Kempa & Michael Nelles, 1999. "Misalignments of real exchange rates and the credibility of nominal currency bands," Review of World Economics (Weltwirtschaftliches Archiv), Springer;Institut für Weltwirtschaft (Kiel Institute for the World Economy), vol. 135(4), pages 613-628, December.
    15. Kempa, Bernd & Nelles, Michael & Pierdzioch, Christian, 1997. "An analytical approximation of target zone exchange rate functions: the technique of collocation," Economics Letters, Elsevier, vol. 57(3), pages 339-343, December.
    16. Kempa, Bernd & Nelles, Michael & Pierdzioch, Christian, 1999. "The term structure of interest rates in a sticky-price target zone model," Journal of International Money and Finance, Elsevier, vol. 18(5), pages 817-834, October.
    17. Ling Jiang & Lu Han & Daivd Jiang, 2004. "Theories of target zones and realignment of RMB (currency of China) exchange rate," Applied Economics Letters, Taylor & Francis Journals, vol. 11(9), pages 561-568.

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