Herding and Clustering in Economics: The Yule-Zipf-Simon Model

Abstract

The clustering of agents in the market is a typical problem discussed by the new approaches to macroeconomic modelling, that describe macroscopic variables in terms of the behavior of a large collection of microeconomic entities. Clustering is often described by Ewens Sampling Formula (ESF), that admits a very nice interpretation in terms of rational vs herding behavior. Focusing on the evergreen problem of the size of firms, we discuss the incompatibility between empirical data and ESF. An alternative model is suggested, inspired to Simon's approaches to the firm size problem. It differs from the Ewens model both in destruction and in creation. In particular the probability of herding is independent on the size of the herd. This very simple assumption destroys the exchangeability of the random partitions, and forbids an analytical solution. Simple computational simulations look to confirm that actually the mean number of clusters of size i (the equilibrium distribution) follows the corresponding Yule distribution. Finally we introduce a Markov chain, that resembles the marginal dynamics of a cluster, which drives the cluster to the right-censored Yule distribution.