Firms Growth, Distribution, and Non-Self Averaging Revisited

Abstract

During my last conversation with Masanao Aoki, he told me that the concept of non-self averaging in statistical physics, frequently appearing in economic and financial systems, has important consequences to policy implication. Zipf's law in firms-size distribution is one of such examples. Recent Malevergne, Saichev and Sornette (MSS) model, simple but realistic, gives a framework of stochastic process including firms entry, exit and growth based on Gibrat's law of proportionate effect, and shows that the Zipf's law is a robust consequence. By using the MSS model, I would like to discuss about the breakdown of Gibrat's law and the deviation from Zipf's law, often observed for the regime of small and medium firms. For the purpose of discussion, I recapitulate the derivation of exact solution for the MSS model with some correction and additional information on the distribution for the age of existing firms. I argue that the breakdown of Gibrat's law is related to the underlying network of firms, most notably production network, in which firms are mutually correlated among each other leading to the larger volatility in the growth for smaller firms that depend as suppliers on larger customers.