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

  • Aoki, Masanao

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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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
Contact details of provider: Web page: http://www.elsevier.com/locate/jedc

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  1. Masanao Aoki, 2000. "Cluster Size Distribution of Economics Agents of Many Types in Market," UCLA Economics Online Papers 102, UCLA Department of Economics.
  2. repec:cup:cbooks:9780521637695 is not listed on IDEAS
  3. Zhi-Feng Huang, Sorin Solomon*, 2001. "Power, Levy, Exponential and Gaussian Regimes in Autocatalytic Financial Systems," Computing in Economics and Finance 2001 12, Society for Computational Economics.
  4. Philippe Aghion & Peter Howitt, 1990. "A Model of Growth Through Creative Destruction," NBER Working Papers 3223, National Bureau of Economic Research, Inc.
  5. 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.
  6. Devroye, Luc, 1993. "A triptych of discrete distributions related to the stable law," Statistics & Probability Letters, Elsevier, vol. 18(5), pages 349-351, December.
  7. De Fabritiis, Gianni & Riccaboni, Massimo & Pammolli, Fabio, 2003. "On Size and Growth of Business Firms," MPRA Paper 15866, University Library of Munich, Germany.
  8. repec:cup:cbooks:9780521606196 is not listed on IDEAS
  9. 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.
  10. Masanao Aoki, 2002. "Open Models of Share Markets with Two Dominant Types of Participants," UCLA Economics Online Papers 107, UCLA Department of Economics.
  11. 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.
  12. 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.
  13. 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.
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