Statistical models for company growth

TL;DR

This paper compares two statistical models for company growth, analyzing their predictions for growth rate distributions and sector size distributions, and discusses implications for empirical data at company and country levels.

Contribution

It introduces an alternative power-law sector size model and compares its predictions with Sutton's microcanonical model for company growth.

Findings

Sutton's model predicts Gaussian growth rate distributions, contrary to empirical data.

The power-law sector size model predicts non-Gaussian, anomalous scaling behavior.

Both models offer testable predictions to distinguish their applicability.

Abstract

We study Sutton's `microcanonical' model for the internal organisation of firms, that leads to non trivial scaling properties for the statistics of growth rates. We show that the growth rates are asymptotically Gaussian in this model, at variance with empirical results. We also obtain the conditional distribution of the number and size of sub-sectors in this model. We formulate and solve an alternative model, based on the assumption that the sector sizes follow a power-law distribution. We find in this new model both anomalous scaling of the variance of growth rates and non Gaussian asymptotic distributions. We give some testable predictions of the two models that would differentiate them further. We also discuss why the growth rate statistics at the country level and at the company level should be identical.