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

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  • Masanao Aoki

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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Paper provided by UCLA Department of Economics in its series UCLA Economics Online Papers with number 391.

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Handle: RePEc:cla:uclaol:391

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  1. Aghion, P. & Howitt, P., 1990. "A Model Of Growth Through Creative Destruction," DELTA Working Papers 90-12, DELTA (Ecole normale supérieure).
  2. De Fabritiis, Gianni & Riccaboni, Massimo & Pammolli, Fabio, 2003. "On Size and Growth of Business Firms," MPRA Paper 15866, University Library of Munich, Germany.
  3. Masanao Aoki, 2002. "Open Models of Share Markets with Two Dominant Types of Participants," UCLA Economics Online Papers 107, UCLA Department of Economics.
  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, 1998. "New Approaches to Macroeconomic Modeling," Cambridge Books, Cambridge University Press, number 9780521637695.
  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. Zhi-Feng Huang & Sorin Solomon, 2000. "Power, Levy, Exponential and Gaussian Regimes in Autocatalytic Financial Systems," Papers cond-mat/0008026, arXiv.org.
  8. 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.
  9. 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.
  10. Aoki,Masanao, 2001. "Modeling Aggregate Behavior and Fluctuations in Economics," Cambridge Books, Cambridge University Press, number 9780521781268.
  11. Devroye, Luc, 1993. "A triptych of discrete distributions related to the stable law," Statistics & Probability Letters, Elsevier, vol. 18(5), pages 349-351, December.
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Cited by:
  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. 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.

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