Gibrat's law redux: Think profitability instead of growth

The basic philosophy behind Gibrat's rule of proportionate effect has been to find some common mechanism in the growth process of business firms, based on the idea that growth rates are independent of size and drawn from the same distribution. After decades of research, however, it seems fair to say that the 'law' fails to provide a universal mechanism for the growth of firms. Here we take the position that it is more plausible for Gibrat's approach to apply to firm profitability rather than firm growth, in line with the classical idea of economic competition as a dynamic process of capital reallocation. Considering a sample of more than five hundred long-lived US corporations from virtually all sectors, we compare the statistical properties of growth and profit rates over a time span of thirty years, and find that profit rates and their volatilities are independent of size, which is not true of growth rates. We also find that the empirical densities of both profitability and growth can be described by exponential power (or Subbotin) distributions, but there are pronounced differences in their parameterizations and autocorrelation structures. We argue that a recently proposed diffusion process not only reproduces the cross-sectional distribution of profit rates, but is also consistent with the empirical time series of individual firms and their autocorrelations. In the natural sciences such a situation is commonly referred to as a statistical equilibrium, while econometricians speak of ergodicity and stationarity. Our economic interpretation of this property is that all surviving firms are subject to the same competitive pressures of capital reallocation, irrespective of their industry or particular line of business. They all face the same profitability benchmark and volatility, while their idiosyncratic efforts merely have an effect on the persistence of abnormal profits. In other words, survivors have to participate in the same game and can only choose to do so at different 'speeds'. We conclude with the empirical observation that the speed of convergence from abnormal profits to the system-wide average depends negatively on firm size, diversification, and capital intensity.