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Heterogeneity as a Natural Source of Randomness

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  • 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.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 03-073/1.

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Date of creation: 16 Sep 2003
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Handle: RePEc:dgr:uvatin:20030073

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Web page: http://www.tinbergen.nl

Related research

Keywords: Expectation formation; Heterogeneity; Continuous beliefs; Expectations feedback; Endogenous noise; Random dynamical systems;

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References

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Citations

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Cited by:
  1. 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, Elsevier, vol. 29(4), pages 741-763, April.
  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. "Optimal Monetary Policy under Heterogeneous Expectations," Macroeconomics, EconWPA 0409023, EconWPA.
  4. Massaro, Domenico, 2013. "Heterogeneous expectations in monetary DSGE models," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 37(3), pages 680-692.
  5. 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.
  6. Orlando Gomes, 2004. "A Continuous-Time Asset Pricing Model with Boundedly Rational Heterogeneous Agents," Finance, EconWPA 0409055, EconWPA.

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