A model for scaling in firms’ size and growth rate distribution

• We introduce an agent-based model for firm growth.
• Competition for a resource accounts for the dynamics of the system.
• Its firm size distribution in its stationary state is heavy-tailed.
• Aggregate growth rate distribution is tent-shaped.
• The variance of firms’ growth rate distribution is size-dependent.

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.