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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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File URL: http://www.business.uts.edu.au/qfrc/research/research_papers/rp53.pdf
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Bibliographic Info

Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 53.

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Date of creation: 01 Jun 2001
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Handle: RePEc:uts:rpaper:53

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Keywords: homogeneous beliefs; least-squares l-process; genera; al-process; stability; instability; bifurcation; cobweb model;

References

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  1. 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.
  2. 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.
  3. 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.
  4. Grandmont, Jean-Michel, 1985. "On Endogenous Competitive Business Cycles," Econometrica, Econometric Society, vol. 53(5), pages 995-1045, September.
  5. Grandmont, Jean-Michel, 1994. "Expectations formation and stability of large socioeconomic systems," CEPREMAP Working Papers (Couverture Orange) 9424, CEPREMAP.
  6. 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.
  7. 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.
  8. 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.
  9. Grandmont Jean-michel & Laroque Guy, 1985. "Stability of cycles and expectations," CEPREMAP Working Papers (Couverture Orange) 8519, CEPREMAP.
  10. Xue-Zhong (Tony) He & Carl Chiarella, 2001. "Asset Price and Wealth Dynamics under Heterogeneous Expectations," CeNDEF Workshop Papers, January 2001 5A.2, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
  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. 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.
  13. Grandmont Jean-michel & Laroque Guy, 1987. "Stability, expectations, and predetermined variables," CEPREMAP Working Papers (Couverture Orange) 8714, CEPREMAP.
  14. 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.
  15. repec:att:wimass:9530 is not listed on IDEAS
  16. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November.
  17. Brock, W.A. & Hommes, C.H., 1996. "A Rational Route to Randomness," Working papers 9530r, Wisconsin Madison - Social Systems.
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Citations

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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, 2005. "Expectation Formation and Endogenous Fluctuations in Aggregate Demand," Computing in Economics and Finance 2005 263, Society for Computational Economics.
  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. 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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