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Heterogeneity as a Natural Source of Randomness

Author

Listed:
  • Cees Diks

    (Faculty of Economics and Econometrics, University of Amsterdam)

  • Roy van der Weide

    (Faculty of Economics and Econometrics, University of Amsterdam)

Abstract

We propose a new framework for studying the evolution of heterogeneous beliefs in a dynamic feedback setting. Beliefs distributions are defined on a beliefs space representing a continuum of possible strategies agents can choose from. Agents base their choices on past performances, re-evaluating strategies as new information becomes available. The distribution of beliefs among agents is updated using a continuous choice model. This leads to price dynamics in which the beliefs distribution evolves together with realized prices. By considering individual choices as random variables, which is natural in a random utility framework, heterogeneity can be seen to act as a 'natural source of randomness'. Allowing for modeling the dynamics explicitly, our framework gives rise to a random dynamical system (RDS), the stochastic properties of which are directly related to the time varying beliefs distribution. We consider some asset pricing examples and discuss several conditions (dependence among agents, unequal market impact) under which the randomness persists even as the number of agents tends to infinity.

Suggested Citation

  • Cees Diks & Roy van der Weide, 2003. "Heterogeneity as a Natural Source of Randomness," Tinbergen Institute Discussion Papers 03-073/1, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20030073
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Hommes, C.H. & Wagener, F.O.O., 2008. "Complex evolutionary systems in behavioral finance," CeNDEF Working Papers 08-05, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    2. Anastasios Xepapadeas & William Brock, 2005. "Optimal Control and Spatial Heterogeneity: Pattern Formation in Economic-Ecological Models," Working Papers 2005.96, Fondazione Eni Enrico Mattei.
    3. Orlando Gomes, 2004. "A Continuous-Time Asset Pricing Model with Boundedly Rational Heterogeneous Agents," Finance 0409055, University Library of Munich, Germany.
    4. Diks, Cees & van der Weide, Roy, 2005. "Herding, a-synchronous updating and heterogeneity in memory in a CBS," Journal of Economic Dynamics and Control, Elsevier, vol. 29(4), pages 741-763, April.
    5. Orlando Gomes, . "Volatility, Heterogeneous Agents and Chaos," The Electronic Journal of Evolutionary Modeling and Economic Dynamics, IFReDE - Université Montesquieu Bordeaux IV.
    6. 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.
    7. Orlando Gomes, 2004. "Optimal Monetary Policy under Heterogeneous Expectations," Macroeconomics 0409023, University Library of Munich, Germany.
    8. Massaro, Domenico, 2013. "Heterogeneous expectations in monetary DSGE models," Journal of Economic Dynamics and Control, Elsevier, vol. 37(3), pages 680-692.
    9. 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.
    10. Schmitt, Noemi & Westerhoff, Frank, 2015. "Managing rational routes to randomness," Journal of Economic Behavior & Organization, Elsevier, vol. 116(C), pages 157-173.
    11. Michele Berardi, 2021. "Discrete beliefs space and equilibrium: a cautionary note," Journal of Evolutionary Economics, Springer, vol. 31(2), pages 505-532, April.
    12. Kai Li, 2014. "Asset Price Dynamics with Heterogeneous Beliefs and Time Delays," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 13, July-Dece.
    13. Kai Li, 2014. "Asset Price Dynamics with Heterogeneous Beliefs and Time Delays," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2014.
    14. Park, Beum-Jo, 2011. "Asymmetric herding as a source of asymmetric return volatility," Journal of Banking & Finance, Elsevier, vol. 35(10), pages 2657-2665, October.

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    More about this item

    Keywords

    Expectation formation; Heterogeneity; Continuous beliefs; Expectations feedback; Endogenous noise; Random dynamical systems;
    All these keywords.

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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