Heterogeneity as a Natural Source of Randomness

Tinbergen Institute Discussion Paper No. 2003-073/1

30 Pages Posted: 22 Nov 2003

See all articles by Cees G. H. Diks

Cees G. H. Diks

University of Amsterdam - Faculty of Economics and Business (FEB); Tinbergen Institute

Roy van der Weide

University of Amsterdam - Faculty of Economics and Business (FEB)

Date Written: September 2003

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.

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

JEL Classification: C00, D84, G12

Suggested Citation

Diks, Cees G. H. and van der Weide, Roy, Heterogeneity as a Natural Source of Randomness (September 2003). Tinbergen Institute Discussion Paper No. 2003-073/1, Available at SSRN: https://ssrn.com/abstract=452381 or http://dx.doi.org/10.2139/ssrn.452381

Cees G. H. Diks (Contact Author)

University of Amsterdam - Faculty of Economics and Business (FEB) ( email )

Roetersstraat 11
Amsterdam, 1018 WB
Netherlands
+31 20 525 53 29 (Phone)
+31 20 525 4349 (Fax)

Tinbergen Institute ( email )

Gustav Mahlerplein 117
Amsterdam, 1082 MS
Netherlands

Roy Van der Weide

University of Amsterdam - Faculty of Economics and Business (FEB) ( email )

Roetersstraat 11
Amsterdam, 1018 WB
Netherlands

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