Statistical models for company growth

We study Suttonʹs ‘microcanonical’ model for the internal organization 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, whereas empirical results suggest that the kurtosis of the distribution increases with size. We also obtain the conditional distribution of the number and size of sub-sectors in Suttonʹs 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.