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The Zero Root Problem: A Note on the Dynamic Determination of the Stationary Equilibrium in Linear Models

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  • Francesco Giavazzi
  • Charles Wyplosz

Abstract

Singularity of the transition matrix in differential equation systems implies indeterminacy of the stationary equilibrium: we show that this indeterminacy is only apparent, and we provide the unique solution. There are many examples of, and good theoretical reasons for, singular transition matrices. The main result is that, when stability conditions arc satisfied, the resulting stationary equilibrium will depend upon the intial conditions and the parameters describing the speed of adjustment.

Suggested Citation

  • Francesco Giavazzi & Charles Wyplosz, 1985. "The Zero Root Problem: A Note on the Dynamic Determination of the Stationary Equilibrium in Linear Models," Review of Economic Studies, Oxford University Press, vol. 52(2), pages 353-357.
    • Handle: RePEc:oup:restud:v:52:y:1985:i:2:p:353-357.
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    File URL: http://hdl.handle.net/10.2307/2297627
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    1. Antoine d'Autume, 1992. "Coïntégration et modèles dynamiques," Économie et Prévision, Programme National Persée, vol. 106(5), pages 71-83.
    2. van de Klundert, Theo C. M. J. & van Schaik, Anton B. T. M., 1990. "Unemployment persistence and loss of productive capacity: A Keynesian approach," Journal of Macroeconomics, Elsevier, vol. 12(3), pages 363-380.
    3. Cepii & Cepremap, 2001. "MARMOTTE : a Multinational Model," Working Papers 2001-15, CEPII research center.
    4. van de Klundert, T.C.M.J. & van Schaik, A.B.T.M., 1990. "Liquidity constraints and the Keynesian corridor," Research Memorandum FEW 429, Tilburg University, School of Economics and Management.
    5. Michael Reutter, 2000. "Hysteresis in West German Unemployment Reconsidered," CESifo Working Paper Series 240, CESifo Group Munich.
    6. Jenny Ligthart & Gerard C. van der Meijdenz, 2011. "The Dynamics of Revenue-Neutral Trade Liberalization," International Center for Public Policy Working Paper Series, at AYSPS, GSU paper1124, International Center for Public Policy, Andrew Young School of Policy Studies, Georgia State University.
    7. Alessandra Pelloni, 1993. "Long-run consequences of finite exchange rate bubbles," Open Economies Review, Springer, vol. 4(1), pages 5-26, March.
    8. Alejandro Cunat & Marco Maffezzoli, 2004. "Hecksher-Ohlin Business Cycles," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 7(3), pages 555-585, July.
    9. Möller, Joachim, 1988. "Identifying the causes of unemployment: Estimation and control of a small macroeconomic model," Discussion Papers, Series I 236, University of Konstanz, Department of Economics.
    10. Sasaki, Hiroaki, 2012. "Is the long-run equilibrium wage-led or profit-led? A Kaleckian approach," Structural Change and Economic Dynamics, Elsevier, vol. 23(3), pages 231-244.
    11. Rod Cross & Julia Darby & Jonathan Ireland & Laura Piscitelli, 1999. "Hysteresis and Unemployment: a Preliminary Investigation," Computing in Economics and Finance 1999 721, Society for Computational Economics.
    12. Koichi Futagami & Akihiko Kaneko & Yoshiyasu Ono & Akihisa Shibata, 2008. "International Asset Trade, Capital Income Taxation, and Specialization Patterns," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 10(5), pages 743-763, October.
    13. Olivier Cardi, 2007. "The Zero-root Property: Permanent vs Temporary Terms-of-trade Shocks," Review of International Economics, Wiley Blackwell, vol. 15(4), pages 782-802, September.
    14. bruno amable & jerome henry & frederic lordon & richard topol, 2005. "Complex Remanence vs. Simple Persistence: Are Hysteresis and Unit-Root Processes observationally equivalent?," Computational Economics 0501001, EconWPA.
    15. Marc-Andre Letendre, 2000. "Linear Approximation Methods and International Real Business Cycles with Incomplete Asset Markets," Econometric Society World Congress 2000 Contributed Papers 1539, Econometric Society.
    16. Alberto Petrucci, 2004. "Asset Accumulation, Fertility Choice and Nondegenerate Dynamics in a Small Open Economy," Working Papers 2004.121, Fondazione Eni Enrico Mattei.
    17. Alfonso Palacio Vera, 2008. "Money wage rigidity, monopoly power and hysteresis," Documentos de trabajo de la Facultad de Ciencias Económicas y Empresariales 08-02, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales.
    18. Heijdra, Ben J. & Ligthart, Jenny E., 2010. "The Transitional Dynamics Of Fiscal Policy In Small Open Economies," Macroeconomic Dynamics, Cambridge University Press, vol. 14(01), pages 1-28, February.
    19. Laffargue, J.-P.Jean-Pierre, 2004. "A sufficient condition for the existence and the uniqueness of a solution in macroeconomic models with perfect foresight," Journal of Economic Dynamics and Control, Elsevier, vol. 28(10), pages 1955-1975, September.
    20. Luis-Felipe Zanna, 2003. "Interest rate rules and multiple equilibria in the small open economy," International Finance Discussion Papers 785, Board of Governors of the Federal Reserve System (U.S.).
    21. Loïc Cadiou & Stéphane Dées & Jean-Pierre Laffargue, 2000. "A computable General Equilibrium Model with Vintage Capital," Working Papers 2000-20, CEPII research center.
    22. Schmidt-Hebbel, Klaus & Serven, Luis, 1992. "Dynamic response to foreign transfers and terms-of-trade shocks in open economies," Policy Research Working Paper Series 1061, The World Bank.

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