Gibrat’s law redux: think profitability instead of growth

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The core philosophy of Gibrat’s rule of proportionate effect seeks a common mechanism in the growth of business firms, suggesting that growth rates are independent of size and drawn from the same distribution. However, after extensive research, it appears that this "law" does not universally explain firm growth. We propose that Gibrat’s approach is more applicable to firm profitability than growth, aligning with the classical view of economic competition as a dynamic capital reallocation process. Analyzing over five hundred long-lived US corporations across various sectors over thirty years, we find that profit rates and their volatilities are independent of size, unlike growth rates. Both profitability and growth exhibit exponential power distributions, yet they differ significantly in parameterization and autocorrelation structures. We argue that a recently proposed diffusion process accurately reflects the cross-sectional distribution of profit rates and aligns with the empirical time series of individual firms. This scenario resembles statistical equilibrium in natural sciences, while econometricians refer to it as ergodicity and stationarity. Our interpretation suggests that all surviving firms face the same competitive pressures, regardless of industry, with a shared profitability benchmark and volatility. The idiosyncratic efforts of firms influence only the persistence of abnormal profits. Ultimately, we observe that t