Heterogeneity as a Natural Source of Randomness
AbstractWe 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 03-073/1.
Date of creation: 16 Sep 2003
Date of revision:
Contact details of provider:
Web page: http://www.tinbergen.nl
Expectation formation; Heterogeneity; Continuous beliefs; Expectations feedback; Endogenous noise; Random dynamical systems;
Other versions of this item:
- 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
This paper has been announced in the following NEP Reports:
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Brock, W.A. & Hommes, C.H., 1996.
"A Rational Route to Randomness,"
9530r, Wisconsin Madison - Social Systems.
- Brock, William A & Durlauf, Steven N, 2001.
"Discrete Choice with Social Interactions,"
Review of Economic Studies,
Wiley Blackwell, vol. 68(2), pages 235-60, April.
- repec:att:wimass:9621 is not listed on IDEAS
- Brock, W.A. & Hommes, C.H. & Wagener, F.O.O., 2002.
"Evolutionary dynamics in markets with many trader types,"
CeNDEF Working Papers
02-10, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
- Brock, William A. & Hommes, Cars H. & Wagener, Florian O. O., 2005. "Evolutionary dynamics in markets with many trader types," Journal of Mathematical Economics, Elsevier, vol. 41(1-2), pages 7-42, February.
- Shiller, Robert J, 1981.
"Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends?,"
American Economic Review,
American Economic Association, vol. 71(3), pages 421-36, June.
- Robert J. Shiller, 1980. "Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends?," NBER Working Papers 0456, National Bureau of Economic Research, Inc.
- 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.
- Ziegler, Alexandre, 2002. "State-price densities under heterogeneous beliefs, the smile effect, and implied risk aversion," European Economic Review, Elsevier, vol. 46(8), pages 1539-1557, September.
- Dagsvik, John K, 1994. "Discrete and Continuous Choice, Max-Stable Processes, and Independence from Irrelevant Attributes," Econometrica, Econometric Society, vol. 62(5), pages 1179-1205, September.
- Karl B. Diether & Christopher J. Malloy & Anna Scherbina, 2002. "Differences of Opinion and the Cross Section of Stock Returns," Journal of Finance, American Finance Association, vol. 57(5), pages 2113-2141, October.
- repec:att:wimass:9506 is not listed on IDEAS
- Gallant, A Ronald & Rossi, Peter E & Tauchen, George, 1992. "Stock Prices and Volume," Review of Financial Studies, Society for Financial Studies, vol. 5(2), pages 199-242.
- Michael P. Keane & Kenneth I. Wolpin, 1994.
"The solution and estimation of discrete choice dynamic programming models by simulation and interpolation: Monte Carlo evidence,"
181, Federal Reserve Bank of Minneapolis.
- Keane, Michael P & Wolpin, Kenneth I, 1994. "The Solution and Estimation of Discrete Choice Dynamic Programming Models by Simulation and Interpolation: Monte Carlo Evidence," The Review of Economics and Statistics, MIT Press, vol. 76(4), pages 648-72, November.
- Lux, T. & M. Marchesi, . "Scaling and Criticality in a Stochastic Multi-Agent Model of a Financial Market," Discussion Paper Serie B 438, University of Bonn, Germany, revised Jul 1998.
- William A. Brock & Cars H. Hommes, 1995.
"Rational Routes to Randomness,"
95-03-029, Santa Fe Institute.
- Guesnerie, R., 1999.
"Anchoring Economic Predictions in Common Knowledge,"
DELTA Working Papers
1999-06, DELTA (Ecole normale supérieure).
- R. Guesnerie, 2002. "Anchoring Economic Predictions in Common Knowledge," Econometrica, Econometric Society, vol. 70(2), pages 439-480, March.
- Kandel, Eugene & Pearson, Neil D, 1995. "Differential Interpretation of Public Signals and Trade in Speculative Markets," Journal of Political Economy, University of Chicago Press, vol. 103(4), pages 831-72, August.
- Antonio Cabrales & Takeo Hoshi, 1993.
"Heterogeneous beliefs, wealth accumulation and asset price dynamics,"
Economics Working Papers
55, Department of Economics and Business, Universitat Pompeu Fabra, revised Jun 1993.
- Cabrales, Antonio & Hoshi, Takeo, 1996. "Heterogeneous beliefs, wealth accumulation, and asset price dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 20(6-7), pages 1073-1100.
- William A. Brock & Blake D. LeBaron, 1995.
"A Dynamic Structural Model for Stock Return Volatility and Trading Volume,"
NBER Working Papers
4988, National Bureau of Economic Research, Inc.
- Brock, William A & LeBaron, Blake D, 1996. "A Dynamic Structural Model for Stock Return Volatility and Trading Volume," The Review of Economics and Statistics, MIT Press, vol. 78(1), pages 94-110, February.
- LeBaron, Blake, 2000. "Agent-based computational finance: Suggested readings and early research," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 679-702, June.
- Michaely, Roni & Vila, Jean-Luc, 1996. "Trading Volume with Private Valuation: Evidence from the Ex-dividend Day," Review of Financial Studies, Society for Financial Studies, vol. 9(2), pages 471-509.
- John K. Dagsvik, 2002. "Discrete Choice in Continuous Time: Implications of an Intertemporal Version of the Iia Property," Econometrica, Econometric Society, vol. 70(2), pages 817-831, March.
- Anastasios Xepapadeas & William Brock, 2005.
"Optimal Control and Spatial Heterogeneity: Pattern Formation in Economic-Ecological Models,"
2005.96, Fondazione Eni Enrico Mattei.
- Brock,W.A. & Xepapadeas,A., 2005. "Optimal control and spatial heterogeneity : pattern formation in economic-ecological models," Working papers 11, Wisconsin Madison - Social Systems.
- 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.
- Diks, C.G.H. & Weide, R. van der, 2003. "Herding, A-synchronous Updating and Heterogeneity in Memory in a CBS," CeNDEF Working Papers 03-06, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
- Cees Diks & Roy van der Weide, 2003. "Herding, A-synchronous Updating and Heterogeneity in Memory in a CBS," Tinbergen Institute Discussion Papers 03-103/1, Tinbergen Institute.
- 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.
- Massaro, Domenico, 2013. "Heterogeneous expectations in monetary DSGE models," Journal of Economic Dynamics and Control, Elsevier, vol. 37(3), pages 680-692.
- Orlando Gomes, 2004. "Optimal Monetary Policy under Heterogeneous Expectations," Macroeconomics 0409023, EconWPA.
- Orlando Gomes, 2004. "A Continuous-Time Asset Pricing Model with Boundedly Rational Heterogeneous Agents," Finance 0409055, EconWPA.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Antoine Maartens (+31 626 - 160 892)).
If references are entirely missing, you can add them using this form.