A Model for Scaling in Firms' Size and Growth Rate Distribution

TL;DR

This paper presents an agent-based model explaining key empirical stylized facts about firm size and growth rate distributions, linking them through competition for scarce resources and analyzing their scaling relationships.

Contribution

The paper introduces a simple, probabilistic competition-based model that captures the fat-tailed size distribution and tent-shaped growth rate distribution of firms, relating them through scaling laws.

Findings

Model reproduces empirical size and growth rate distributions.

Shows the relationship between size and growth rate variance.

Discusses effects of data binning on analysis.

Abstract

We introduce a simple agent-based model which allows us to analyze three stylized facts: a fat-tailed size distribution of companies, a `tent-shaped' growth rate distribution, the scaling relation of the growth rate variance with firm size, and the causality between them. This is achieved under the simple hypothesis that firms compete for a scarce quantity (either aggregate demand or workforce) which is allocated probabilistically. The model allows us to relate size and growth rate distributions. We compare the results of our model to simulations with other scaling relationships, and to similar models and relate it to existing theory. Effects arising from binning data are discussed.