CIRJE-F-445 | "Thermodynamic Limits of Macroeconomic or Financial Models: One-and Two-Parameter Poisson-Dirichlet Models" |
Author Name | Aoki, Masanao |
Date | October 2006 |
Full Paper | PDF file |
Remarks | Forthcoming in Journal of Econmic Dynamics and Control, 2007. |
Abstract |
This paper examines asymptotic behavior of two types of economic or financial
models with many interacting heterogeneous agents. They are oneparameter
Poisson-Dirichlet models, also called Ewens models, and its extension
to two-parameter Poisson-Dirichlet models.
The total number of clusters, and the components of partition vectors
(the number of clusters of specified sizes), both suitably normalized by some
powers of model sizes, of these classes of models are shown to be related to
the Mittag-Leffler distributions.
Their behavior as the model sizes tend to infinity (thermodynamic limits)
are qualitatively very different. In the one-parameter models, the number of
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 zero as model sizes becomes
large.
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