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Exchangeability and non-self-averaging

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  • U. Garibaldi
  • P. Viarengo

Abstract

To pass from a deterministic dynamics of aggregate quantities to a probabilistic dynamics of a system of microvariables that describe the individual strategies of a population of economic agents, the route is that of Boltzmann’s kinetic theory at the half of XIX century (more suitable than that of Gibbs’ statistical mechanics), that is the introduction of n “elements” (molecules, agents,…), submitted to some microdynamics, wherefrom to derive the macroscopic behavior. The macrovariate is interpreted as a (time) mean of the average (on all elements) of the individual study-property at time t. The micro-derivation looks unproblematic if means and averages tend to constant values in the limit n → ∞. If this property, defined “self-averaging” in some recent papers by Aoki, holds, it would separate a deterministic result from fluctuations; consequently well defined macroeconomic deterministic relations prevail. However it is easy to show that in most cases in economy this property does not hold, due to long-range correlation existing among economic agents. If individual agents are not independent but exchangeable, also in the limit n → ∞ the coefficient of variation of the macrovariable is finite, which tends to a random limit rather than a constant. Finally the term “indistinguishable agent” is criticized, and the alternative “exchangeable agent” is discussed. Copyright Springer-Verlag 2012

Suggested Citation

  • U. Garibaldi & P. Viarengo, 2012. "Exchangeability and non-self-averaging," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 7(2), pages 181-195, October.
    • Handle: RePEc:spr:jeicoo:v:7:y:2012:i:2:p:181-195
    DOI: 10.1007/s11403-012-0090-9
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    References listed on IDEAS

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    1. Masanao Aoki & Hiroshi Yoshikawa, 2012. "Non-self-averaging in macroeconomic models: a criticism of modern micro-founded macroeconomics," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 7(1), pages 1-22, May.
    2. Alan Kirman, 1993. "Ants, Rationality, and Recruitment," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 108(1), pages 137-156.
    3. Masanao Aoki & Hiroshi Yoshikawa, 2007. "Non-Self-Averaging in Macroeconomic Models: A Criticism of Modern Micro-founded Macroeconomics," CIRJE F-Series CIRJE-F-493, CIRJE, Faculty of Economics, University of Tokyo.
    4. Garibaldi,Ubaldo & Scalas,Enrico, 2010. "Finitary Probabilistic Methods in Econophysics," Cambridge Books, Cambridge University Press, number 9780521515597, October.
    5. Costantini, D. & Donadio, S. & Garibaldi, U. & Viarengo, P., 2005. "Herding and clustering: Ewens vs. Simon–Yule models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 355(1), pages 224-231.
    6. U. Garibaldi & D. Costantini & P. Viarengo, 2007. "The two-parameter Ewens distribution: a finitary approach," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 2(2), pages 147-161, December.
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    Cited by:

    1. Imre Kondor & István Csabai & Gábor Papp & Enys Mones & Gábor Czimbalmos & Máté Sándor, 2014. "Strong random correlations in networks of heterogeneous agents," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 9(2), pages 203-232, October.

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