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Dynamics of Beliefs and Learning Under aL Processes - The Homogeneous Case

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Abstract

This paper studies a class of models in which agents' expectations influence the actual dynamics while the expectations themselves are the outcome of some learning process. Under the assumptions that agents have homogeneous expectations (or beliefs) and that they update their expectations by least-squares L- and general aL - processes, the dynamic of the resulting expectations and learning schemes are analyzed. It is shown how the dynamics of the system, including stability, instability and bifurcation, are affected by the learning processes. The cobweb model with a simple homogeneous expectation scheme is employed as an example to illustrate the stability results, the various types of bifurcations and the routes to complicated price dynamics.

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  • Carl Chiarella & Xue-Zhong He, 2001. "Dynamics of Beliefs and Learning Under aL Processes - The Homogeneous Case," Research Paper Series 53, Quantitative Finance Research Centre, University of Technology, Sydney.
  • Handle: RePEc:uts:rpaper:53
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    File URL: http://www.qfrc.uts.edu.au/research/research_papers/rp53.pdf
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    1. Hommes, Cars H., 1991. "Adaptive learning and roads to chaos : The case of the cobweb," Economics Letters, Elsevier, vol. 36(2), pages 127-132, June.
    2. Marcet, Albert & Sargent, Thomas J., 1989. "Convergence of least squares learning mechanisms in self-referential linear stochastic models," Journal of Economic Theory, Elsevier, vol. 48(2), pages 337-368, August.
    3. C. Chiarella & X-Z. He, 2001. "Asset price and wealth dynamics under heterogeneous expectations," Quantitative Finance, Taylor & Francis Journals, vol. 1(5), pages 509-526.
    4. Grandmont, Jean-Michel, 1985. "On Endogenous Competitive Business Cycles," Econometrica, Econometric Society, vol. 53(5), pages 995-1045, September.
    5. Chiarella, Carl & He, Xue-Zhong, 2003. "Dynamics of beliefs and learning under aL-processes -- the heterogeneous case," Journal of Economic Dynamics and Control, Elsevier, vol. 27(3), pages 503-531, January.
    6. William A. Brock & Cars H. Hommes, 1997. "A Rational Route to Randomness," Econometrica, Econometric Society, vol. 65(5), pages 1059-1096, September.
    7. Jean-Michel Grandmont, 1998. "Expectations Formation and Stability of Large Socioeconomic Systems," Econometrica, Econometric Society, vol. 66(4), pages 741-782, July.
    8. Grandmont, Jean-Michel & Laroque, Guy, 1986. "Stability of cycles and expectations," Journal of Economic Theory, Elsevier, vol. 40(1), pages 138-151, October.
    9. Hommes, Cars H., 1994. "Dynamics of the cobweb model with adaptive expectations and nonlinear supply and demand," Journal of Economic Behavior & Organization, Elsevier, vol. 24(3), pages 315-335, August.
    10. Hommes, Cars H., 1998. "On the consistency of backward-looking expectations: The case of the cobweb," Journal of Economic Behavior & Organization, Elsevier, vol. 33(3-4), pages 333-362, January.
    11. Chiarella, Carl, 1988. "The cobweb model: Its instability and the onset of chaos," Economic Modelling, Elsevier, vol. 5(4), pages 377-384, October.
    12. Evans, George W. & Honkapohja, Seppo, 1999. "Learning dynamics," Handbook of Macroeconomics,in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 7, pages 449-542 Elsevier.
    13. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-1445, November.
    14. Carl Chiarella & Xue-Zhong He, 1999. "The Dynamics of the Cobweb when Producers are Risk Averse Learners," Working Paper Series 90, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    15. Barucci, Emilio & Bischi, Gian Italo & Gardini, Laura, 1999. "Endogenous Fluctuations in a Bounded Rationality Economy: Learning Non-perfect Foresight Equilibria," Journal of Economic Theory, Elsevier, vol. 87(1), pages 243-253, July.
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    Cited by:

    1. C. Chiarella & X-Z. He, 2001. "Asset price and wealth dynamics under heterogeneous expectations," Quantitative Finance, Taylor & Francis Journals, vol. 1(5), pages 509-526.
    2. Maciej K. Dudek, 2004. "Expectation Formation and Endogenous Fluctuations in Aggregate Demand," Econometric Society 2004 Latin American Meetings 103, Econometric Society.
    3. Chiarella, Carl & He, Xue-Zhong & Hung, Hing & Zhu, Peiyuan, 2006. "An analysis of the cobweb model with boundedly rational heterogeneous producers," Journal of Economic Behavior & Organization, Elsevier, vol. 61(4), pages 750-768, December.
    4. Volker Böhm & Carl Chiarella, 2005. "Mean Variance Preferences, Expectations Formation, And The Dynamics Of Random Asset Prices," Mathematical Finance, Wiley Blackwell, vol. 15(1), pages 61-97.
    5. Xue-Zhong He & Youwei Li, 2008. "Heterogeneity, convergence, and autocorrelations," Quantitative Finance, Taylor & Francis Journals, vol. 8(1), pages 59-79.
    6. Chiarella, Carl & He, Xue-Zhong, 2003. "Heterogeneous Beliefs, Risk, And Learning In A Simple Asset-Pricing Model With A Market Maker," Macroeconomic Dynamics, Cambridge University Press, vol. 7(04), pages 503-536, September.
    7. Chiarella, Carl & He, Xue-Zhong, 2003. "Dynamics of beliefs and learning under aL-processes -- the heterogeneous case," Journal of Economic Dynamics and Control, Elsevier, vol. 27(3), pages 503-531, January.

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