The standard analysis in macroeconomics depends on the assumption of the representative agent. However, when the degree of uncertainty becomes significant, we cannot ignore a simple fact that the macroeconomy consists of a large number of heterogeneous agents. In this paper, we demonstrate the...

Using a simple stochastic growth model, this paper emonstrates that the coefficient of variation of aggregate output or GDP does not necessarily go to zero even if the number of sectors or economic agents goes to infinity. This phenomenon known as non-self-averaging implies that even if the...

This paper uses novel growth models composed of clusters of heterogeneous agents,and shows that limiting behavior of one-and two-parameter Poisson-Dirichlet models are qualitatively very different. As model sizes grow unboundedly, the coefficients of variations of extensive variables, such as...

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...

This paper outlines the applications of one-and two-parameter Poisson-Dirichlet distributions to describe stationary statistical distributions of clus-ters of agents by types. We discuss how the notion of residudal allocation processes in statistics and population genetics literature also arises...

When the coefficient of variation, namely the standard deviation relative to mean approaches zero as the number of economic agents becomes large, the system is called self-averaging. Otherwise, it is non-self-averaging. Most economic models take it for granted that economic system is...

This paper presents a model of the dconomy with many sectors which face demand (quantity) constraints. Depending on the sign of the sectoral excess demand, the size of each sector either increases or decreases stochastically. We assume that reallocation of resources is not instantaneous, and,...

This paper discusses non-exponential growth patterns of macroeconomic models. More specifically, the paper discusses asymptotic growth patterns of the numbers of clusters and of components of partition vectors, that is, the number of clusters of specific sizes, of one-andtwo-parameter...

This paper discusses a symptotic behavior of one-and two-parameter Poisson-Dirichlet models, that is, Ewens models and its two parameter extensions by Pitman, and show that their a symptotic behavior arevery different. The paper shows asymptotic properties of a class of one-and two-parameter...