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Growth Patterns of Two Types of Macro-Models: Limiting Behavior of One-and Two-Parameter Poisson-Dirichlet Models

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  • Masanao Aoki

    (Department of Economics, UCLA)

Abstract

This paper uses novel growth models composed of clusters of heterogeneous agents,and shows that limiting behavior of one-and two-parameter Poisson-Dirichlet models are qualitatively very different. As model sizes grow unboundedly, the coefficients of variations of extensive variables, such as the number of total clusters, and the numbers of clusters of specified sizes all approach zero in the one-parameter models, but not in the two-parameter models. In the calculations of the coefficients of variations Mittag-Le?er distributions arise naturally. We show that the distributions of the numbers of the clusters in the models havepower-lawbehavior.

Suggested Citation

  • Masanao Aoki, 2006. "Growth Patterns of Two Types of Macro-Models: Limiting Behavior of One-and Two-Parameter Poisson-Dirichlet Models," CIRJE F-Series CIRJE-F-446, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2006cf446
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    References listed on IDEAS

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    1. Scalas, Enrico, 2006. "The application of continuous-time random walks in finance and economics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 362(2), pages 225-239.
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    3. Scalas, Enrico & Gorenflo, Rudolf & Mainardi, Francesco, 2000. "Fractional calculus and continuous-time finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 284(1), pages 376-384.
    4. 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.
    5. Aoki,Masanao & Yoshikawa,Hiroshi, 2011. "Reconstructing Macroeconomics," Cambridge Books, Cambridge University Press, number 9781107634206, September.
    6. Mainardi, Francesco & Raberto, Marco & Gorenflo, Rudolf & Scalas, Enrico, 2000. "Fractional calculus and continuous-time finance II: the waiting-time distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 468-481.
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