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Thermodynamic Limits of Macroeconomic or Financial Models: One-and Two-Parameter Poisson-Dirichlet Models (Forthcoming in "Journal of Economic Dynamics and Control", 2007. )

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  • Masanao Aoki

    (Department of Economics, UCLA)

Abstract

This paper examines asymptotic behavior of two types of economic or financial models with many interacting heterogeneous agents. They are one-parameter Poisson-Dirichlet models, also called Ewens models, and its extension totwo-parameter Poisson-Dirichlet models. The total number of clusters, and the components of partition vectors (the number of clusters of specified sizes),both suitably normalized by some powers of model sizes, of these classes of models are shown tobe related to the Mittag-Leffler distributions. Their behavior as the model sizes tend to infinity(thermodynamic limits) are qualitatively very different. In the one-parameter models, the number of clusters, and components of partition vectors are both self-averaging, that is, their coefficients of variations tend to zero as the model sizes become very large, while in the two-parameter models they are not self-averaging, that is, their coefficients of variations do not tend to zero as model sizes becomes large.

Suggested Citation

  • Masanao Aoki, 2006. "Thermodynamic Limits of Macroeconomic or Financial Models: One-and Two-Parameter Poisson-Dirichlet Models (Forthcoming in "Journal of Economic Dynamics and Control", 2007. )," CARF F-Series CARF-F-083, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    • Handle: RePEc:cfi:fseres:cf083
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    References listed on IDEAS

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    4. U. Garibaldi & D. Costantini & P. Viarengo, 2004. "A Finitary Characterization Of The Ewens Sampling Formula," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 7(02), pages 265-284.
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    Cited by:

    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. Luca Benati, 2008. "Investigating Inflation Persistence Across Monetary Regimes," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 123(3), pages 1005-1060.
    3. Masanao AOKI, 2007. "Patterns of Non-exponential Growth of Macroeconomic Models: Two-Parameter Poisson-Dirichlet Models," Rivista Internazionale di Scienze Sociali, Vita e Pensiero, Pubblicazioni dell'Universita' Cattolica del Sacro Cuore, vol. 115(1), pages 109-125.
    4. 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.
    5. Masanao Aoki, 2006. "Patterns of Non-exponential Growth of Macroeconomic Models: Two-parameter Poisson-Dirichlet Models (Forthcoming in "Rivista Internazionale di Scienze Sociali", cxv No.1, pp. 109-125, 2007. )," CARF F-Series CARF-F-085, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.

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