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Thermodynamic Limits of Macroeconomic or Financial Models: One-and Two-Parameter Poisson-Dirichlet Models

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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 manyinteracting 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 (thenumberof clustersofspecified sizes),both suitably normalizedby some powers of model sizes, of these classes of models are shown tobe related to the Mittag-Letter distributions. Theirbehavior as the model sizes tend to infinity(thermodynamic limits) are qualitatively very different.Inthe one-parametermodels,thenumberof 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 zeroasmodel sizesbecomes large.

Suggested Citation

  • Masanao Aoki, 2006. "Thermodynamic Limits of Macroeconomic or Financial Models: One-and Two-Parameter Poisson-Dirichlet Models," CIRJE F-Series CIRJE-F-445, CIRJE, Faculty of Economics, University of Tokyo.
  • Handle: RePEc:tky:fseres:2006cf445
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    1. Aghion, Philippe & Howitt, Peter, 1992. "A Model of Growth through Creative Destruction," Econometrica, Econometric Society, vol. 60(2), pages 323-351, March.
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    3. Sutton, John, 2002. "The variance of firm growth rates: the ‘scaling’ puzzle," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 312(3), pages 577-590.
    4. Aoki, Masanao, 2002. "Open models of share markets with two dominant types of participants," Journal of Economic Behavior & Organization, Elsevier, vol. 49(2), pages 199-216, October.
    5. Zhi-Feng Huang & Sorin Solomon, 2000. "Power, Levy, Exponential and Gaussian Regimes in Autocatalytic Financial Systems," Papers cond-mat/0008026, arXiv.org.
    6. Masanao Aoki & Hiroshi Yoshikawa, 2006. "Stock Prices and the Real Economy: Power Law versus Exponential Distributions," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 1(1), pages 45-73, May.
    7. Iwai, Katsuhito, 2000. "A contribution to the evolutionary theory of innovation, imitation and growth," Journal of Economic Behavior & Organization, Elsevier, vol. 43(2), pages 167-198, October.
    8. Canning, D. & Amaral, L. A. N. & Lee, Y. & Meyer, M. & Stanley, H. E., 1998. "Scaling the volatility of GDP growth rates," Economics Letters, Elsevier, vol. 60(3), pages 335-341, September.
    9. Masanao Aoki, 2000. "Cluster Size Distribution of Economics Agents of Many Types in Market," UCLA Economics Online Papers 102, UCLA Department of Economics.
    10. Devroye, Luc, 1993. "A triptych of discrete distributions related to the stable law," Statistics & Probability Letters, Elsevier, vol. 18(5), pages 349-351, December.
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    Cited by:

    1. AOKI Masanao & YOSHIKAWA Hiroshi, 2007. "Non-Self-Averaging in Macroeconomic Models: A Criticism of Modern Micro-founded Macroeconomics," Discussion papers 07057, Research Institute of Economy, Trade and Industry (RIETI).
    2. Albrecht Irle & Jonas Kauschke & Thomas Lux & Mishael Milaković, 2011. "Switching Rates And The Asymptotic Behavior Of Herding Models," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 14(03), pages 359-376.
    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. Aoki, Masanao & Yoshikawa, Hiroshi, 2009. "The nature of equilibrium in macroeconomics: A critique of equilibrium search theory," Economics - The Open-Access, Open-Assessment E-Journal, Kiel Institute for the World Economy (IfW), vol. 3, pages 1-9.
    5. Ted Theodosopoulos, 2016. "Hierarchical economic agents and their interactions," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 11(2), pages 345-377, October.
    6. S. Alfarano & M. Milakovic & M. Raddant, 2013. "A note on institutional hierarchy and volatility in financial markets," The European Journal of Finance, Taylor & Francis Journals, vol. 19(6), pages 449-465, July.
    7. Aoki, Masanao & Hawkins, Raymond J., 2010. "Non-self-averaging and the statistical mechanics of endogenous macroeconomic fluctuations," Economic Modelling, Elsevier, vol. 27(6), pages 1543-1546, November.
    8. Charles S. Tapiero, 2015. "A financial CCAPM and economic inequalities," Quantitative Finance, Taylor & Francis Journals, vol. 15(3), pages 521-534, March.
    9. Alfarano, Simone & Milaković, Mishael & Raddant, Matthias, 2009. "Network hierarchy in Kirman's ant model: fund investment can create systemic risk," Economics Working Papers 2009-09, Christian-Albrechts-University of Kiel, Department of Economics.
    10. Masanao Aoki, 2006. "Patterns of Non-exponential Growth of Macroeconomic Models: Two-parameter Poisson-Dirichlet Models," CIRJE F-Series CIRJE-F-449, CIRJE, Faculty of Economics, University of Tokyo.
    11. 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.
    12. 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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