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Heterogeneous beliefs and the non-linear cobweb model

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  • Goeree, Jacob K.
  • Hommes, Cars H.

Abstract

This paper investigates price fluctuations in an evolutionary cobweb model with heterogeneous beliefs. Agents choose between free naive expectations and costly rational expectations, and update their beliefs according to a "fitness" measure such as past realized net profits. For non-linear, monotonic demand and supply curves, it is shown that the evolutionary dynamics exhibits bifurcation routes to strange attractors when the intensity of choice to switch prediction strategies increases.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Dynamics and Control.

Volume (Year): 24 (2000)
Issue (Month): 5-7 (June)
Pages: 761-798

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Handle: RePEc:eee:dyncon:v:24:y:2000:i:5-7:p:761-798

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References

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  1. William A. Brock & Cars H. Hommes, 1997. "A Rational Route to Randomness," Econometrica, Econometric Society, vol. 65(5), pages 1059-1096, September.
  2. Cabrales, Antonio & Hoshi, Takeo, . "Heterogeneous Beliefs, Wealth Accumulation, and Asset Price Dynamics," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/3513, Universidad Carlos III de Madrid.
  3. Cars Hommes & Gerhard Sorger, 1997. "Consistent Expectations Equilibria," Tinbergen Institute Discussion Papers 97-051/1, Tinbergen Institute.
  4. Jean-Michel Grandmont, 1998. "Expectations Formation and Stability of Large Socioeconomic Systems," Econometrica, Econometric Society, vol. 66(4), pages 741-782, July.
  5. James Bullard, 1991. "Learning equilibria," Working Papers 1991-004, Federal Reserve Bank of St. Louis.
  6. Arifovic, Jasmina, 1996. "The Behavior of the Exchange Rate in the Genetic Algorithm and Experimental Economies," Journal of Political Economy, University of Chicago Press, vol. 104(3), pages 510-41, June.
  7. Marimon, R. & Spear, S. & Sunder, S., 1991. "Expectationally-Driven Market Volatility: An Experimental Study," GSIA Working Papers 1991-3, Carnegie Mellon University, Tepper School of Business.
  8. 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.
  9. 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.
  10. Arifovic, Jasmina & Gencay, Ramazan, 2000. "Statistical properties of genetic learning in a model of exchange rate," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 981-1005, June.
  11. Arifovic, Jasmina, 1994. "Genetic algorithm learning and the cobweb model," Journal of Economic Dynamics and Control, Elsevier, vol. 18(1), pages 3-28, January.
  12. Lux, Thomas, 1995. "Herd Behaviour, Bubbles and Crashes," Economic Journal, Royal Economic Society, vol. 105(431), pages 881-96, July.
  13. Grandmont Jean-michel & Laroque Guy, 1985. "Stability of cycles and expectations," CEPREMAP Working Papers (Couverture Orange) 8519, CEPREMAP.
  14. William A. Brock, 1993. "Pathways to randomness in the economy: Emergent nonlinearity and chaos in economics and finance," Estudios Económicos, El Colegio de México, Centro de Estudios Económicos, vol. 8(1), pages 3-55.
  15. Brock, W.A. & Hommes, C.H., 1995. "Rational Routes to Randomness," Working papers 9506, Wisconsin Madison - Social Systems.
  16. Carl Chiarella, 1992. "The Dynamics of Speculative Behaviour," Working Paper Series 13, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
  17. Sethi, Rajiv, 1996. "Endogenous regime switching in speculative markets," Structural Change and Economic Dynamics, Elsevier, vol. 7(1), pages 99-118, March.
  18. Bullard, James & Duffy, John, 1998. "Learning And The Stability Of Cycles," Macroeconomic Dynamics, Cambridge University Press, vol. 2(01), pages 22-48, March.
  19. Grandmont, Jean-Michel, 1985. "On Endogenous Competitive Business Cycles," Econometrica, Econometric Society, vol. 53(5), pages 995-1045, September.
  20. Bray, Margaret, 1982. "Learning, estimation, and the stability of rational expectations," Journal of Economic Theory, Elsevier, vol. 26(2), pages 318-339, April.
  21. Blume, Lawrence & Easley, David, 1992. "Evolution and market behavior," Journal of Economic Theory, Elsevier, vol. 58(1), pages 9-40, October.
  22. Bray, Margaret M & Savin, Nathan E, 1986. "Rational Expectations Equilibria, Learning, and Model Specification," Econometrica, Econometric Society, vol. 54(5), pages 1129-60, September.
  23. 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.
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Citations

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Cited by:
  1. Colucci, Domenico & Valori, Vincenzo, 2011. "Adaptive expectations and cobweb phenomena: Does heterogeneity matter?," Journal of Economic Dynamics and Control, Elsevier, vol. 35(8), pages 1307-1321, August.
  2. Laurence Lasselle & Serge Svizzero & Clem Tisdell, 2007. " Stability and Cycles in a Cobweb Model with Heterogeneous Expectations," CDMA Working Paper Series 0706, Centre for Dynamic Macroeconomic Analysis.
  3. Femenia, Fabienne & Alexandre, Gohin, 2009. "Dynamic modelling of agricultural policies: the role of expectation schemes," 2009 Conference, August 16-22, 2009, Beijing, China 51665, International Association of Agricultural Economists.
  4. He, Xue-Zhong & Westerhoff, Frank H., 2005. "Commodity markets, price limiters and speculative price dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 29(9), pages 1577-1596, September.
  5. Onozaki, Tamotsu & Sieg, Gernot & Yokoo, Masanori, 2003. "Stability, chaos and multiple attractors: a single agent makes a difference," Journal of Economic Dynamics and Control, Elsevier, vol. 27(10), pages 1917-1938, August.
  6. Domenico Colucci & Vincenzo Valori, 2011. "Can Endogenous Participation Explain Price Volatility? Evidence from an Agent-Based Cobweb Model," Computational Economics, Society for Computational Economics, vol. 38(3), pages 425-437, October.
  7. Waters, George A., 2010. "Instability in the cobweb model under the BNN dynamic," Journal of Mathematical Economics, Elsevier, vol. 46(2), pages 230-237, March.
  8. Brock, W.A. & Dindo, P.D.E. & Hommes, C.H., 2005. "Adaptive Rational Equilibrium with Forward Looking Agents, fortcoming in International Journal of Economic Theory (IJET) 2006, special issue in honor of Jean-Michel Grandmont," CeNDEF Working Papers 05-15, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
  9. Hommes, C.H., 2007. "Bounded Rationality and Learning in Complex Markets," CeNDEF Working Papers 07-01, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
  10. 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.
  11. Dieci, Roberto & Westerhoff, Frank, 2010. "Interacting cobweb markets," Journal of Economic Behavior & Organization, Elsevier, vol. 75(3), pages 461-481, September.
  12. Negroni, Giorgio, 2003. "Adaptive expectations coordination in an economy with heterogeneous agents," Journal of Economic Dynamics and Control, Elsevier, vol. 28(1), pages 117-140, October.
  13. 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.
  14. Negroni, Giorgio, 2005. "Eductive expectations coordination on deterministic cycles in an economy with heterogeneous agents," Journal of Economic Dynamics and Control, Elsevier, vol. 29(5), pages 931-952, May.
  15. Gomes, Orlando, 2009. "A two-dimensional non-equilibrium dynamic model," Structural Change and Economic Dynamics, Elsevier, vol. 20(3), pages 221-238, September.
  16. Caulkins, Jonathan P. & Baker, David, 2010. "Cobweb dynamics and price dispersion in illicit drug markets," Socio-Economic Planning Sciences, Elsevier, vol. 44(4), pages 220-230, December.
  17. Orlando Gomes, 2010. "Consumer confidence, endogenous growth and endogenous cycles," Journal of Economic Studies, Emerald Group Publishing, vol. 37(4), pages 377-404, September.

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