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Dynamics of Beliefs and Learning Under aL Processes - The Heterogeneous 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 recursive processes with bounded memory. Under the assumptions of heterogeneous expectations (or beliefs) and that the agents update their expectations by recursive L- and general aL-processes, the dynamics of the resulting expectations and learning schemes are analyzed. It is shown that the dynamics of the system, including stability, instability and bifurcation, are affected differently by the recursive processes. The cobweb model with a simple heterogeneous expectation scheme is employed as an example to illustrate the stability results, the various types of bifurcations and the routes to complicated price dynamics. In particular, the double edged effect of heterogeneity on the dynamics of the model is demonstrated.

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File URL: http://www.business.uts.edu.au/qfrc/research/research_papers/rp55.pdf
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Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 55.

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Date of creation: 01 Jun 2001
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Handle: RePEc:uts:rpaper:55

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Keywords: heterogeneous beliefs; recursive L-process; general aL-process; stability; instability; bifucation; cobweb model;

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  1. Xue-Zhong He & Carl Chiarella, 1999. "Heterogeneous Beliefs, Risk and Learning in a Simple Asset-Pricing Model," Computing in Economics and Finance 1999 223, Society for Computational Economics.
  2. Lux, Thomas, 1995. "Herd Behaviour, Bubbles and Crashes," Economic Journal, Royal Economic Society, Royal Economic Society, vol. 105(431), pages 881-96, July.
  3. James Bullard & John Duffy, 1994. "Using genetic algorithms to model the evolution of heterogeneous beliefs," Working Papers 1994-028, Federal Reserve Bank of St. Louis.
  4. Carl Chiarella & Xue-Zhong He, 1999. "The Dynamics of the Cobweb when Producers are Risk Averse Learners," Working Paper Series, Finance Discipline Group, UTS Business School, University of Technology, Sydney 90, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
  5. repec:att:wimass:9530 is not listed on IDEAS
  6. Day, Richard H. & Huang, Weihong, 1990. "Bulls, bears and market sheep," Journal of Economic Behavior & Organization, Elsevier, vol. 14(3), pages 299-329, December.
  7. Carl Chiarella & Xue-Zhong He, 2001. "Dynamics of Beliefs and Learning Under aL Processes - The Homogeneous Case," Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney 53, Quantitative Finance Research Centre, University of Technology, Sydney.
  8. Jean-Michel Grandmont, 1998. "Expectations Formation and Stability of Large Socioeconomic Systems," Econometrica, Econometric Society, Econometric Society, vol. 66(4), pages 741-782, July.
  9. Brock, William A. & Hommes, Cars H., 1998. "Heterogeneous beliefs and routes to chaos in a simple asset pricing model," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1235-1274, August.
  10. Brock, W.A. & Hommes, C.H., 1996. "A Rational Route to Randomness," Working papers 9530r, Wisconsin Madison - Social Systems.
  11. Balasko, Yves & Royer, Daniel, 1996. "Stability of Competitive Equilibrium with Respect to Recursive and Learning Processes," Journal of Economic Theory, Elsevier, vol. 68(2), pages 319-348, February.
  12. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, Econometric Society, vol. 46(6), pages 1429-45, November.
  13. Lux, Thomas, 1997. "Time variation of second moments from a noise trader/infection model," Journal of Economic Dynamics and Control, Elsevier, vol. 22(1), pages 1-38, November.
  14. James Bullard, 1991. "Learning equilibria," Working Papers 1991-004, Federal Reserve Bank of St. Louis.
  15. Evans, George W. & Honkapohja, Seppo, 1999. "Learning dynamics," Handbook of Macroeconomics, Elsevier, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 7, pages 449-542 Elsevier.
  16. 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.
  17. Reiner Franke & Tim Nesemann, 1999. "Two destabilizing strategies may be jointly stabilizing," Journal of Economics, Springer, vol. 69(1), pages 1-18, February.
  18. Franke, Reiner & Sethi, Rajiv, 1998. "Cautious trend-seeking and complex asset price dynamics," Research in Economics, Elsevier, vol. 52(1), pages 61-79, March.
  19. 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.
  20. repec:att:wimass:9706 is not listed on IDEAS
  21. Evans, George W & Ramey, Garey, 1992. "Expectation Calculation and Macroeconomic Dynamics," American Economic Review, American Economic Association, vol. 82(1), pages 207-24, March.
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