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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. )

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  • Masanao Aoki

    (Department of Economics, UCLA)

Abstract

This paper discusses non-exponential growth patterns of macroeconomic models. More specifically, the paper discusses asymptotic growth patterns of the numbers of clusters and of components of partition vectors, that is, the number of clusters of specific sizes, of one-andtwo-parameter Poisson-Dirichlet models as the model sizes grow towards infinity. As the model sizes become large, the coefficients of variaation of the cluster sizes and components of the partition vector tend to zero in one-parameter Poisson-Dirichlet model, but they remain positive in the two-parameter version. Furthermore, the two-parameter version of the model exhibits power-law behavior, while the one-parameter versiondoes not. The growth behavior of the two-parameter models is shown to be expressed in terms of generalized Mittag-Leffler distributions. The paper ends with preliminary discussion of the effects of demand pattern management policies on growth patterns of models that endogenize the parameters of the two-parameter Poisson-Dirichlet model.

Suggested Citation

  • 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.
    • Handle: RePEc:cfi:fseres:cf085
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    References listed on IDEAS

    as
    1. 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.
    2. Aoki, Masanao, 2008. "Thermodynamic limits of macroeconomic or financial models: One- and two-parameter Poisson-Dirichlet models," Journal of Economic Dynamics and Control, Elsevier, vol. 32(1), pages 66-84, January.
    3. De Fabritiis, G. & Pammolli, F. & Riccaboni, M., 2003. "On size and growth of business firms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 38-44.
    4. 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.
    5. 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.
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