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

  • Masanao Aoki

    (Department of Economics, UCLA)

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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File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2006/2006cf444.pdf
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Paper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-445.

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Length: 21pages
Date of creation: Oct 2006
Date of revision:
Handle: RePEc:tky:fseres:2006cf445
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  1. Aghion, P. & Howitt, P., 1989. "A Model Of Growth Through Creative Destruction," Working papers 527, Massachusetts Institute of Technology (MIT), Department of Economics.
  2. Aoki,Masanao, 1998. "New Approaches to Macroeconomic Modeling," Cambridge Books, Cambridge University Press, number 9780521637695.
  3. Zhi-Feng Huang & Sorin Solomon, 2000. "Power, Levy, Exponential and Gaussian Regimes in Autocatalytic Financial Systems," Papers cond-mat/0008026, arXiv.org.
  4. 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.
  5. 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.
  6. 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.
  7. Devroye, Luc, 1993. "A triptych of discrete distributions related to the stable law," Statistics & Probability Letters, Elsevier, vol. 18(5), pages 349-351, December.
  8. Aoki,Masanao, 2001. "Modeling Aggregate Behavior and Fluctuations in Economics," Cambridge Books, Cambridge University Press, number 9780521781268.
  9. 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.
  10. Masanao Aoki, 2000. "Cluster Size Distribution of Economics Agents of Many Types in Market," UCLA Economics Online Papers 102, UCLA Department of Economics.
  11. Masanao Aoki, 2002. "Open Models of Share Markets with Two Dominant Types of Participants," UCLA Economics Online Papers 107, UCLA Department of Economics.
  12. 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.
  13. 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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