Statistical models for company growth
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.