Thermodynamic Limits of Macroeconomic or Financial Models: One-and Two-Parameter Poisson-Dirichlet Models
AbstractThis 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-445.
Date of creation: Oct 2006
Date of revision:
Contact details of provider:
Postal: Hongo 7-3-1, Bunkyo-ku, Tokyo 113-0033
Web page: http://www.cirje.e.u-tokyo.ac.jp/index.html
More information through EDIRC
Other versions of this item:
- 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.
- Masanao Aoki, . "Thermodynamic Limits of Macroeconomic or Financial Models: One- and Two-Parameter Poisson-Dirichlet Models," UCLA Economics Online Papers 391, UCLA Department of Economics.
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Aghion, P. & Howitt, P., 1989.
"A Model Of Growth Through Creative Destruction,"
527, Massachusetts Institute of Technology (MIT), Department of Economics.
- Philippe Aghion & Peter Howitt, 1990. "A Model of Growth Through Creative Destruction," NBER Working Papers 3223, National Bureau of Economic Research, Inc.
- Aghion, P. & Howitt, P., 1990. "A Model Of Growth Through Creative Destruction," DELTA Working Papers 90-12, DELTA (Ecole normale supérieure).
- Aghion, P. & Howitt, P., 1989. "A Model Of Growth Through Creative Destruction," UWO Department of Economics Working Papers 8904, University of Western Ontario, Department of Economics.
- 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.
- Devroye, Luc, 1993. "A triptych of discrete distributions related to the stable law," Statistics & Probability Letters, Elsevier, vol. 18(5), pages 349-351, December.
- De Fabritiis, Gianni & Riccaboni, Massimo & Pammolli, Fabio, 2003.
"On Size and Growth of Business Firms,"
15866, University Library of Munich, Germany.
- 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.
- 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.
- 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.
- 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.
- Aoki, Masanao & Yoshikawa, Hiroshi, 2008.
"The Nature of Equilibrium in Macroeconomics: A Critique of Equilibrium Search Theory,"
Economics Discussion Papers
2008-37, Kiel Institute for the World Economy.
- 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.
- AOKI Masanao & YOSHIKAWA Hiroshi, 2007.
"Non-Self-Averaging in Macroeconomic Models: A Criticism of Modern Micro-founded Macroeconomics,"
07057, Research Institute of Economy, Trade and Industry (RIETI).
- 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.
- Alfarano, Simone & Milakovic, Mishael & Raddant, Matthias, 2011.
"A Note on institutional hierarchy and volatility in financial markets,"
30902, University Library of Munich, Germany.
- S. Alfarano & M. Milakovic & M. Raddant, 2013. "A note on institutional hierarchy and volatility in financial markets," The European Journal of Finance, Taylor & Francis Journals, vol. 19(6), pages 449-465, July.
- 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.
- 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.
- 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.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (CIRJE administrative office).
If references are entirely missing, you can add them using this form.