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Some Stability Results for Markovian Economic Semigroups

Author

Listed:
  • Leonard J. Mirman
  • Kevin Reffett
  • John Stachurski

Abstract

The paper studies existence, uniqueness and stability of stationary equilibrium distributions in a class of stochastic dynamic models common to economic analysis. The stability conditions provided are suitable for treating multi-sector models and nonlinear time series models with unbounded state.

Suggested Citation

  • Leonard J. Mirman & Kevin Reffett & John Stachurski, 2004. "Some Stability Results for Markovian Economic Semigroups," Department of Economics - Working Papers Series 902, The University of Melbourne.
  • Handle: RePEc:mlb:wpaper:902
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    File URL: http://www.economics.unimelb.edu.au/downloads/wpapers-04/902.pdf
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    References listed on IDEAS

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    1. Donaldson, John B. & Mehra, Rajnish, 1983. "Stochastic growth with correlated production shocks," Journal of Economic Theory, Elsevier, vol. 29(2), pages 282-312, April.
    2. Hopenhayn, Hugo A & Prescott, Edward C, 1992. "Stochastic Monotonicity and Stationary Distributions for Dynamic Economies," Econometrica, Econometric Society, vol. 60(6), pages 1387-1406, November.
    3. Stachurski, John, 2002. "Stochastic Optimal Growth with Unbounded Shock," Journal of Economic Theory, Elsevier, vol. 106(1), pages 40-65, September.
    4. Lisa Morhaim & Charles-Henri Dimaria & Cuong Le Van, 2002. "The discrete time version of the Romer model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(1), pages 133-158.
    5. Razin, Assaf & Yahav, Joseph A, 1979. "On Stochastic Models of Economic Growth," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 20(3), pages 599-604, October.
    6. Mirman, Leonard J. & Morand, Olivier F. & Reffett, Kevin L., 2008. "A qualitative approach to Markovian equilibrium in infinite horizon economies with capital," Journal of Economic Theory, Elsevier, vol. 139(1), pages 75-98, March.
    7. repec:cup:macdyn:v:1:y:1997:i:4:p:740-69 is not listed on IDEAS
    8. Bray, Margaret, 1982. "Learning, estimation, and the stability of rational expectations," Journal of Economic Theory, Elsevier, vol. 26(2), pages 318-339, April.
    9. Futia, Carl A, 1982. "Invariant Distributions and the Limiting Behavior of Markovian Economic Models," Econometrica, Econometric Society, vol. 50(2), pages 377-408, March.
    10. Stachurski, John, 2003. "Economic dynamical systems with multiplicative noise," Journal of Mathematical Economics, Elsevier, vol. 39(1-2), pages 135-152, February.
    11. Tapan Mitra & Santanu Roy, 2006. "Optimal exploitation of renewable resources under uncertainty and the extinction of species," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 28(1), pages 1-23, May.
    12. Farmer, Roger E.A. & Woodford, Michael, 1997. "Self-Fulfilling Prophecies And The Business Cycle," Macroeconomic Dynamics, Cambridge University Press, vol. 1(04), pages 740-769, December.
    13. Mehmet Caner & Bruce E. Hansen, 2001. "Threshold Autoregression with a Unit Root," Econometrica, Econometric Society, vol. 69(6), pages 1555-1596, November.
    14. Brock, William A. & Mirman, Leonard J., 1972. "Optimal economic growth and uncertainty: The discounted case," Journal of Economic Theory, Elsevier, vol. 4(3), pages 479-513, June.
    15. Long, John B, Jr & Plosser, Charles I, 1983. "Real Business Cycles," Journal of Political Economy, University of Chicago Press, vol. 91(1), pages 39-69, February.
    16. Rabi Bhattacharya & Mukul Majumdar, 2003. "Dynamical systems subject to random shocks: An introduction," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 23(1), pages 1-12, December.
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    Citations

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    Cited by:

    1. Azariadis, Costas & Stachurski, John, 2005. "Poverty Traps," Handbook of Economic Growth,in: Philippe Aghion & Steven Durlauf (ed.), Handbook of Economic Growth, edition 1, volume 1, chapter 5 Elsevier.
    2. John Stachurski, 2009. "Economic Dynamics: Theory and Computation," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262012774, January.

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