IDEAS home Printed from https://ideas.repec.org/p/kob/dpaper/dp2014-35.html
   My bibliography  Save this paper

Stability Analysis for Random Dynamical Systems in Economics

Author

Listed:
  • Takashi Kamihigashi

    (Research Institute for Economics & Business Administration (RIEB), Kobe University, Japan)

  • John Stachurski

    (Research School of Economics, Australian National University, Australia)

Abstract

Random dynamical systems encountered in economics have certain distinctive characteristics that make them particularly well suited to analysis using the tools for studying Markov processes developed by Rabi N. Bhattacharya and his coauthors over the last few decades. In this essay we discuss the significance of these tools for both mathematicians and economists, provide some historical perspective and review some recent related contributions.

Suggested Citation

  • Takashi Kamihigashi & John Stachurski, 2014. "Stability Analysis for Random Dynamical Systems in Economics," Discussion Paper Series DP2014-35, Research Institute for Economics & Business Administration, Kobe University.
  • Handle: RePEc:kob:dpaper:dp2014-35
    as

    Download full text from publisher

    File URL: http://www.rieb.kobe-u.ac.jp/academic/ra/dp/English/DP2014-35.pdf
    File Function: First version, 2014
    Download Restriction: no

    References listed on IDEAS

    as
    1. Kamihigashi, Takashi & Stachurski, John, 2012. "An order-theoretic mixing condition for monotone Markov chains," Statistics & Probability Letters, Elsevier, vol. 82(2), pages 262-267.
    2. Galor, Oded & Ryder, Harl E., 1989. "Existence, uniqueness, and stability of equilibrium in an overlapping-generations model with productive capital," Journal of Economic Theory, Elsevier, vol. 49(2), pages 360-375, December.
    3. Kamihigashi, Takashi & Stachurski, John, 2014. "Stochastic stability in monotone economies," Theoretical Economics, Econometric Society, vol. 9(2), May.
    4. John Stachurski, 2009. "Economic Dynamics: Theory and Computation," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262012774.
    5. Chakraborty, Santanu & Rao, B. V., 1998. "Completeness of Bhattacharya metric on the space of probabilities," Statistics & Probability Letters, Elsevier, vol. 36(4), pages 321-326, January.
    6. Dechert, W. Davis & Nishimura, Kazuo, 1983. "A complete characterization of optimal growth paths in an aggregated model with a non-concave production function," Journal of Economic Theory, Elsevier, vol. 31(2), pages 332-354, December.
    7. 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.
    8. Takashi Kamihigashi & John Stachurski, 2013. "Simple Fixed Point Results for Order-Preserving Self-Maps and Applications to Nonlinear Markov Operators," Discussion Paper Series DP2013-27, Research Institute for Economics & Business Administration, Kobe University.
    9. Cabrales, Antonio & Hopenhayn, Hugo A., 1997. "Labor-market flexibility and aggregate employment volatility," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 46(1), pages 189-228, June.
    10. Zhang, Yuzhe, 2007. "Stochastic optimal growth with a non-compact state space," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 115-129, February.
    11. Rabi Bhattacharya & Mukul Majumdar, 2010. "Random iterates of monotone maps," Review of Economic Design, Springer;Society for Economic Design, vol. 14(1), pages 185-192, March.
    12. Wang Yong, 1993. "Stationary Equilibria in an Overlapping Generations Economy with Stochastic Production," Journal of Economic Theory, Elsevier, vol. 61(2), pages 423-435, December.
    13. Philippe Aghion & Patrick Bolton, 1997. "A Theory of Trickle-Down Growth and Development," Review of Economic Studies, Oxford University Press, vol. 64(2), pages 151-172.
    14. Cai, Yiyong & Kamihigashi, Takashi & Stachurski, John, 2014. "Stochastic optimal growth with risky labor supply," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 167-176.
    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. Thomas F. Cooley & Vincenzo Quadrini, 2001. "Financial Markets and Firm Dynamics," American Economic Review, American Economic Association, vol. 91(5), pages 1286-1310, December.
    17. Thomas Piketty, 1997. "The Dynamics of the Wealth Distribution and the Interest Rate with Credit Rationing," Review of Economic Studies, Oxford University Press, vol. 64(2), pages 173-189.
    18. Takashi Kamihigashi, 2006. "Almost sure convergence to zero in stochastic growth models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(1), pages 231-237, September.
    19. 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.
    20. 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.
    21. Mirman, Leonard J. & Zilcha, Itzhak, 1975. "On optimal growth under uncertainty," Journal of Economic Theory, Elsevier, vol. 11(3), pages 329-339, December.
    22. Stachurski, John, 2002. "Stochastic Optimal Growth with Unbounded Shock," Journal of Economic Theory, Elsevier, vol. 106(1), pages 40-65, September.
    23. Owen, Ann L. & Weil, David N., 1998. "Intergenerational earnings mobility, inequality and growth," Journal of Monetary Economics, Elsevier, vol. 41(1), pages 71-104, February.
    24. Bhattacharya, Rabi N. & Lee, Oesook, 1988. "Ergodicity and central limit theorems for a class of Markov processes," Journal of Multivariate Analysis, Elsevier, vol. 27(1), pages 80-90, October.
    25. Rabi Bhattacharya & Mukul Majumdar, 2003. "Random dynamical systems: a review," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 23(1), pages 13-38, December.
    26. de Hek, Paul A, 1999. "On Endogenous Growth under Uncertainty," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(3), pages 727-744, August.
    27. Kamihigashi, Takashi, 2007. "Stochastic optimal growth with bounded or unbounded utility and with bounded or unbounded shocks," Journal of Mathematical Economics, Elsevier, vol. 43(3-4), pages 477-500, April.
    28. Bhattacharya,Rabi & Majumdar,Mukul, 2007. "Random Dynamical Systems," Cambridge Books, Cambridge University Press, number 9780521825658, January.
    29. Morand, Olivier F. & Reffett, Kevin L., 2007. "Stationary Markovian equilibrium in overlapping generation models with stochastic nonclassical production and Markov shocks," Journal of Mathematical Economics, Elsevier, vol. 43(3-4), pages 501-522, April.
    30. Bhattacharya,Rabi & Majumdar,Mukul, 2007. "Random Dynamical Systems," Cambridge Books, Cambridge University Press, number 9780521532723, January.
    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. 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.
    33. Nishimura, Kazuo & Rudnicki, Ryszard & Stachurski, John, 2006. "Stochastic optimal growth with nonconvexities," Journal of Mathematical Economics, Elsevier, vol. 42(1), pages 74-96, February.
    Full references (including those not matched with items on IDEAS)

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kob:dpaper:dp2014-35. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Office of Promoting Research Collaboration, Research Institute for Economics & Business Administration, Kobe University). General contact details of provider: http://edirc.repec.org/data/rikobjp.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.