IDEAS home Printed from https://ideas.repec.org/a/eee/dyncon/v27y2003i3p503-531.html
   My bibliography  Save this article

Dynamics of beliefs and learning under aL-processes -- the heterogeneous case

Author

Listed:
  • Chiarella, Carl
  • He, Xue-Zhong

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.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • 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.
  • Handle: RePEc:eee:dyncon:v:27:y:2003:i:3:p:503-531
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165-1889(01)00059-8
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. Lux, Thomas, 1998. "The socio-economic dynamics of speculative markets: interacting agents, chaos, and the fat tails of return distributions," Journal of Economic Behavior & Organization, Elsevier, vol. 33(2), pages 143-165, January.
    3. Day, Richard H. & Huang, Weihong, 1990. "Bulls, bears and market sheep," Journal of Economic Behavior & Organization, Elsevier, vol. 14(3), pages 299-329, December.
    4. 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.
    5. Bullard James, 1994. "Learning Equilibria," Journal of Economic Theory, Elsevier, vol. 64(2), pages 468-485, December.
    6. Bullard, James & Duffy, John, 1999. "Using Genetic Algorithms to Model the Evolution of Heterogeneous Beliefs," Computational Economics, Springer;Society for Computational Economics, vol. 13(1), pages 41-60, February.
    7. 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.
    8. 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.
    9. 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.
    10. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-1445, November.
    11. 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.
    12. Seppo Honkapohja, 2001. "Learning Dynamics: Complete and Incomplete Learning," International Economic Association Series, in: Jacques Drèze (ed.), Advances in Macroeconomic Theory, chapter 12, pages 239-254, Palgrave Macmillan.
    13. Franke, Reiner & Sethi, Rajiv, 1998. "Cautious trend-seeking and complex asset price dynamics," Research in Economics, Elsevier, vol. 52(1), pages 61-79, March.
    14. Jean-Michel Grandmont, 1998. "Expectations Formation and Stability of Large Socioeconomic Systems," Econometrica, Econometric Society, vol. 66(4), pages 741-782, July.
    15. Evans, George W & Ramey, Garey, 1992. "Expectation Calculation and Macroeconomic Dynamics," American Economic Review, American Economic Association, vol. 82(1), pages 207-224, March.
    16. William A. Brock & Cars H. Hommes, 1997. "A Rational Route to Randomness," Econometrica, Econometric Society, vol. 65(5), pages 1059-1096, September.
    17. Chiarella, Carl & He, Xue-Zhong, 2002. "Heterogeneous Beliefs, Risk and Learning in a Simple Asset Pricing Model," Computational Economics, Springer;Society for Computational Economics, vol. 19(1), pages 95-132, February.
    18. Reiner Franke & Tim Nesemann, 1999. "Two destabilizing strategies may be jointly stabilizing," Journal of Economics, Springer, vol. 69(1), pages 1-18, February.
    19. Lux, Thomas, 1995. "Herd Behaviour, Bubbles and Crashes," Economic Journal, Royal Economic Society, vol. 105(431), pages 881-896, July.
    20. 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.
    21. Brock, W.A. & Hommes, C.H., 1997. "Models of Compelxity in Economics and Finance," Working papers 9706, Wisconsin Madison - Social Systems.
    22. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. 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(4), pages 503-536, September.
    3. Carl Chiarella & Xue-Zhong He, 2000. "Stability of Competitive Equilibria with Heterogeneous Beliefs and Learning," Research Paper Series 37, Quantitative Finance Research Centre, University of Technology, Sydney.
    4. Tai, Chung-Ching & Chen, Shu-Heng & Yang, Lee-Xieng, 2018. "Cognitive ability and earnings performance: Evidence from double auction market experiments," Journal of Economic Dynamics and Control, Elsevier, vol. 91(C), pages 409-440.
    5. Carl Chiarella & Xue-Zhong He & Duo Wang, 2004. "Statistical Properties of a Heterogeneous Asset Price Model with Time-Varying Second Moment," Research Paper Series 142, Quantitative Finance Research Centre, University of Technology, Sydney.
    6. Chiarella, Carl & He, Xue-Zhong & Wang, Duo, 2006. "A behavioral asset pricing model with a time-varying second moment," Chaos, Solitons & Fractals, Elsevier, vol. 29(3), pages 535-555.
    7. Detlef Seese & Christof Weinhardt & Frank Schlottmann (ed.), 2008. "Handbook on Information Technology in Finance," International Handbooks on Information Systems, Springer, number 978-3-540-49487-4, April.
    8. Youwei Li & Xue-Zhong He, 2005. "Long Memory, Heterogeneity, and Trend Chasing," Computing in Economics and Finance 2005 113, Society for Computational Economics.
    9. Hommes, Cars H., 2006. "Heterogeneous Agent Models in Economics and Finance," Handbook of Computational Economics, in: Leigh Tesfatsion & Kenneth L. Judd (ed.), Handbook of Computational Economics, edition 1, volume 2, chapter 23, pages 1109-1186, Elsevier.
    10. Chiarella, Carl & He, Xue-Zhong, 2002. "Heterogeneous Beliefs, Risk and Learning in a Simple Asset Pricing Model," Computational Economics, Springer;Society for Computational Economics, vol. 19(1), pages 95-132, February.
    11. Goldbaum, David, 2017. "Divergent Behavior in Markets with Idiosyncratic Private Information," Review of Behavioral Economics, now publishers, vol. 4(2), pages 181-213, September.
    12. Xue-Zhong He, 2003. "Asset Pricing, Volatility and Market Behaviour: A Market Fraction Approach," Research Paper Series 95, Quantitative Finance Research Centre, University of Technology, Sydney.
    13. He, Xue-Zhong & Li, Youwei, 2007. "Power-law behaviour, heterogeneity, and trend chasing," Journal of Economic Dynamics and Control, Elsevier, vol. 31(10), pages 3396-3426, October.
    14. Youwei Li & Xue-Zhong (Tony) He, 2005. "Heterogeneity, Profitability and Autocorrelations," Computing in Economics and Finance 2005 244, Society for Computational Economics.
    15. Hommes, C.H., 2005. "Heterogeneous Agent Models in Economics and Finance, In: Handbook of Computational Economics II: Agent-Based Computational Economics, edited by Leigh Tesfatsion and Ken Judd , Elsevier, Amsterdam 2006," CeNDEF Working Papers 05-03, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    16. Troy Tassier, 2013. "Handbook of Research on Complexity, by J. Barkley Rosser, Jr. and Edward Elgar," Eastern Economic Journal, Palgrave Macmillan;Eastern Economic Association, vol. 39(1), pages 132-133.
    17. Maciej K. Dudek, 2004. "Expectation Formation and Endogenous Fluctuations in Aggregate Demand," Econometric Society 2004 Latin American Meetings 103, Econometric Society.
    18. Antonio Doria, Francisco, 2011. "J.B. Rosser Jr. , Handbook of Research on Complexity, Edward Elgar, Cheltenham, UK--Northampton, MA, USA (2009) 436 + viii pp., index, ISBN 978 1 84542 089 5 (cased)," Journal of Economic Behavior & Organization, Elsevier, vol. 78(1-2), pages 196-204, April.
    19. Daniele Giachini, 2018. "Rationality and Asset Prices under Belief Heterogeneity," LEM Papers Series 2018/07, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    20. Hommes, C.H., 2005. "Heterogeneous Agents Models: two simple examples, forthcoming In: Lines, M. (ed.) Nonlinear Dynamical Systems in Economics, CISM Courses and Lectures, Springer, 2005, pp.131-164," CeNDEF Working Papers 05-01, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.

    More about this item

    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:eee:dyncon:v:27:y:2003:i:3:p:503-531. 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: . General contact details of provider: http://www.elsevier.com/locate/jedc .

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jedc .

    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.