The statistics of firm growth rates

Whether one uses the sales, the number of employees or any other proxy for firm "size", it is well known that this quantity is power-law distributed, with important consequences to aggregate macroeconomic fluctuations. The Gibrat model explained this by proposing that firms grow multiplicatively, and much work has been done to study the statistics of their growth rates. Inspired by past work in the statistics of financial returns, I present a new framework to study these growth rates. In particular, I will show that they follow approximately Gaussian statistics, provided their heteroskedastic nature is taken into account. I will also elucidate the size/volatility scaling relation, and show that volatility may have a strong sectoral dependence. Finally, I will show how this framework can be used to study intra-firm and supply chain dynamics.

Joint work with JP Bouchaud and Angelo Secchi.