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Existence, Uniqueness and Stability of Invariant Distributions in Continuous-Time Stochastic Models

Author

Listed:
  • Christian Bayer

    () (Department of Mathematics, University of Vienna, Austria)

  • Klaus Waelde

    () (Department of Economics, Johannes Gutenberg-Universitaet Mainz, Germany)

Abstract

We study a dynamic stochastic general equilibrium model in continuous time. Related work has proven that optimal consumption in this model is a smooth function of state variables. This allows us to describe the evolution of optimal state variables (wealth and labour market status) by stochastic differential equations. We derive conditions under which an invariant distribution for state variables exists and is unique. We also provide conditions such that initial distributions converge to the long-run distribution.

Suggested Citation

  • Christian Bayer & Klaus Waelde, 2011. "Existence, Uniqueness and Stability of Invariant Distributions in Continuous-Time Stochastic Models," Working Papers 1111, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz, revised 21 Jul 2011.
  • Handle: RePEc:jgu:wpaper:1111
    as

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    File URL: http://www.macro.economics.uni-mainz.de/RePEc/pdf/Discussion_Paper_1111.pdf
    File Function: First version, 2011
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    References listed on IDEAS

    as
    1. Matsuyama, Kiminori, 2001. "Growing through Cycles in an Infinitely Lived Agent Economy," Journal of Economic Theory, Elsevier, vol. 100(2), pages 220-234, October.
    2. Robert Shimer & Lones Smith, 2000. "Assortative Matching and Search," Econometrica, Econometric Society, vol. 68(2), pages 343-370, March.
    3. Fwu-Ranq Chang & A. G. Malliaris, 2005. "Asymptotic Growth under Uncertainty: Existence and Uniqueness," World Scientific Book Chapters,in: Economic Uncertainty, Instabilities And Asset Bubbles Selected Essays, chapter 1, pages 3-8 World Scientific Publishing Co. Pte. Ltd..
    4. Pierre Cahuc & Fabien Postel-Vinay & Jean-Marc Robin, 2006. "Wage Bargaining with On-the-Job Search: Theory and Evidence," Econometrica, Econometric Society, vol. 74(2), pages 323-364, March.
    5. Lo, Andrew W., 1988. "Maximum Likelihood Estimation of Generalized Itô Processes with Discretely Sampled Data," Econometric Theory, Cambridge University Press, vol. 4(02), pages 231-247, August.
    6. Gong, Liutang & Zou, Heng-fu, 2002. "Direct preferences for wealth, the risk premium puzzle, growth, and policy effectiveness," Journal of Economic Dynamics and Control, Elsevier, vol. 26(2), pages 247-270, February.
    7. Leo Kaas & Philipp Kircher, 2015. "Efficient Firm Dynamics in a Frictional Labor Market," American Economic Review, American Economic Association, vol. 105(10), pages 3030-3060, October.
    8. Futia, Carl A, 1982. "Invariant Distributions and the Limiting Behavior of Markovian Economic Models," Econometrica, Econometric Society, vol. 50(2), pages 377-408, March.
    9. Patrick Francois & Huw Lloyd-Ellis, 2003. "Animal Spirits Through Creative Destruction," American Economic Review, American Economic Association, vol. 93(3), pages 530-550, June.
    10. Jessica A. Wachter, 2013. "Can Time-Varying Risk of Rare Disasters Explain Aggregate Stock Market Volatility?," Journal of Finance, American Finance Association, vol. 68(3), pages 987-1035, June.
    11. Lentz, Rasmus, 2010. "Sorting by search intensity," Journal of Economic Theory, Elsevier, vol. 145(4), pages 1436-1452, July.
    12. Bental, Benjamin & Peled, Dan, 1996. "The Accumulation of Wealth and the Cyclical Generation of New Technologies: A Search Theoretic Approach," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 37(3), pages 687-718, August.
    13. Kenneth Burdett & Carlos Carrillo‐Tudela & Melvyn G. Coles, 2011. "Human Capital Accumulation And Labor Market Equilibrium," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 52(3), pages 657-677, August.
    14. Olaf POSCH & Klaus WALDE, 2009. "On the non-causal link between volatility and growth," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2009025, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    15. 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.
    16. Magill, Michael J. P., 1977. "A local analysis of N-sector capital accumulation under uncertainty," Journal of Economic Theory, Elsevier, vol. 15(1), pages 211-219, June.
    17. Julien Prat, 2007. "The Impact of Disembodied Technological Progress on Unemployment," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 10(1), pages 106-125, January.
    18. Xavier Gabaix, 1999. "Zipf's Law for Cities: An Explanation," The Quarterly Journal of Economics, Oxford University Press, vol. 114(3), pages 739-767.
    19. Evans, Lynne & Kenc, Turalay, 2003. "Welfare Cost Of Monetary And Fiscal Policy Shocks," Macroeconomic Dynamics, Cambridge University Press, vol. 7(02), pages 212-238, April.
    20. Robert C. Merton, 1975. "An Asymptotic Theory of Growth Under Uncertainty," Review of Economic Studies, Oxford University Press, vol. 42(3), pages 375-393.
    21. Posch, Olaf, 2009. "Structural estimation of jump-diffusion processes in macroeconomics," Journal of Econometrics, Elsevier, vol. 153(2), pages 196-210, December.
    22. Grinols, Earl L & Turnovsky, Stephen J, 1998. "Consequences of Debt Policy in a Stochastically Growing Monetary Economy," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(2), pages 495-521, May.
    23. Olson, Lars J. & Roy, Santanu, 2005. "Theory of Stochastic Optimal Economic Growth," Working Papers 28601, University of Maryland, Department of Agricultural and Resource Economics.
    24. Kiminori Matsuyama, 1999. "Growing Through Cycles," Econometrica, Econometric Society, vol. 67(2), pages 335-348, March.
    25. Gokan, Yoichi, 2002. "Alternative government financing and stochastic endogenous growth," Journal of Economic Dynamics and Control, Elsevier, vol. 26(4), pages 681-706, April.
    26. Bismut, Jean-Michel, 1975. "Growth and optimal intertemporal allocation of risks," Journal of Economic Theory, Elsevier, vol. 10(2), pages 239-257, April.
    27. Scott, Louis O., 1987. "Option Pricing when the Variance Changes Randomly: Theory, Estimation, and an Application," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(04), pages 419-438, December.
    28. Giuseppe Moscarini & Fabien Postel-Vinay, 2009. "The Timing of Labor Market Expansions: New Facts and a New Hypothesis," NBER Chapters,in: NBER Macroeconomics Annual 2008, Volume 23, pages 1-51 National Bureau of Economic Research, Inc.
    29. Bandi, Federico M. & Nguyen, Thong H., 2003. "On the functional estimation of jump-diffusion models," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 293-328.
    30. Brock, William A & Magill, Michael J P, 1979. "Dynamics under Uncertainty," Econometrica, Econometric Society, vol. 47(4), pages 843-868, July.
    31. Nishimura, Kazuo & Stachurski, John, 2005. "Stability of stochastic optimal growth models: a new approach," Journal of Economic Theory, Elsevier, vol. 122(1), pages 100-118, May.
    32. Steger, Thomas M., 2005. "Stochastic growth under Wiener and Poisson uncertainty," Economics Letters, Elsevier, vol. 86(3), pages 311-316, March.
    33. Giuseppe Moscarini, 2005. "Job Matching and the Wage Distribution," Econometrica, Econometric Society, vol. 73(2), pages 481-516, March.
    34. Huggett, Mark, 1993. "The risk-free rate in heterogeneous-agent incomplete-insurance economies," Journal of Economic Dynamics and Control, Elsevier, vol. 17(5-6), pages 953-969.
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    More about this item

    Keywords

    uncertainty in continuous time; Poisson process; existence; uniqueness; stability;

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making
    • E24 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Employment; Unemployment; Wages; Intergenerational Income Distribution; Aggregate Human Capital; Aggregate Labor Productivity
    • J63 - Labor and Demographic Economics - - Mobility, Unemployment, Vacancies, and Immigrant Workers - - - Turnover; Vacancies; Layoffs

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