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Thermodynamic limits of macroeconomic or financial models: One- and two-parameter Poisson-Dirichlet models

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  • Aoki, Masanao

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.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Dynamics and Control.

Volume (Year): 32 (2008)
Issue (Month): 1 (January)
Pages: 66-84

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Handle: RePEc:eee:dyncon:v:32:y:2008:i:1:p:66-84

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  1. Devroye, Luc, 1993. "A triptych of discrete distributions related to the stable law," Statistics & Probability Letters, Elsevier, vol. 18(5), pages 349-351, December.
  2. Aghion, P. & Howitt, P., 1989. "A Model Of Growth Through Creative Destruction," UWO Department of Economics Working Papers, University of Western Ontario, Department of Economics 8904, University of Western Ontario, Department of Economics.
  3. Masanao Aoki, 2000. "Cluster Size Distribution of Economics Agents of Many Types in Market," UCLA Economics Online Papers 102, UCLA Department of Economics.
  4. 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.
  5. De Fabritiis, Gianni & Riccaboni, Massimo & Pammolli, Fabio, 2003. "On Size and Growth of Business Firms," MPRA Paper 15866, University Library of Munich, Germany.
  6. Masanao Aoki & Hiroshi Yoshikawa, 2006. "Stock Prices and the Real Economy: Power Law versus Exponential Distributions," Journal of Economic Interaction and Coordination, Springer, vol. 1(1), pages 45-73, May.
  7. 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.
  8. 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.
  9. 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. Aoki, Masanao & Yoshikawa, Hiroshi, 2007. "Non-Self-Averaging in Macroeconomic Models: A Criticism of Modern Micro-founded Macroeconomics," Economics Discussion Papers 2007-49, Kiel Institute for the World Economy.
  2. 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.
  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, vol. 3(37), pages 1-9.
  5. Alfarano, Simone & Milakovic, Mishael & Raddant, Matthias, 2011. "A Note on institutional hierarchy and volatility in financial markets," MPRA Paper 30902, University Library of Munich, Germany.
  6. 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, vol. 7(1), pages 1-22, May.
  7. 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.
  8. 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, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo CARF-F-085, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
  9. 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.

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