Essays on Microfoundations, Macroeconomic Applications and Economic History in Honor of Axel Leijonhufvud
Edited by Roger E.A. Farmer
Chapter 6: Growth Patterns of Two Types of Macro-Models: Limiting Behavior of One- and Two-Parameter Poisson–Dirichlet Models
6. Growth patterns of two types of macro-models: limiting behavior of one- and two-parameter Poisson–Dirichlet models Masanao Aoki* INTRODUCTION 6.1 This chapter discusses a new class of simple stochastic multi-sector growth models composed of clusters, where a cluster is a collection of agents of the same or similar characteristics in some sense. Depending on the context, these clusters may be sectors of the macroeconomy, or ﬁrms of some sector of the economy, and so on. As time passes, the total number of agents in the model increases stochastically, either because a new agent (factors of production) joins one of existing clusters or because a new cluster is created by the new agent. We focus on the total numbers of clusters, that is, on the number of distinct types of economic agents in the model, and on the number of clusters of some speciﬁed sizes.1 These models are not stochastic growth models familiar to economists. They are, however, growth models because innovations occur in an existing cluster or new clusters are created by innovations which cause the size of models to grow unboundedly. We then examine whether the coeﬃcients of variation of some extensive variables, such as the number of sectors or number of clusters of some speciﬁed size, converge to zero or remain positive in the limit of total number of units in the model tending to inﬁnity.2 If the limit of the coeﬃcient of variation is not zero, then the model behavior is...
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