A statistical equilibrium model of competitive firms

Abstract

We find that the empirical density of firm profit rates, measured as returns on assets, is markedly non-Gaussian and reasonably well described by an exponential power (or Subbotin) distribution. We start from a statistical equilibrium model that leads to a stationary Subbotin density in the presence of complex interactions among competitive heterogeneous firms. To investigate the dynamics of firm profitability, we construct a diffusion process that has the Subbotin distribution as its stationary probability density. This leads to a phenomenologically inspired interpretation of variations in the shape parameter of the Subbotin distribution, which essentially measures the competitive pressure in and across industries. Our findings have profound implications both for the previous literature on the ‘persistence of profits’ as well as for understanding competition as a dynamic process. Our main formal finding is that firms' idiosyncratic efforts and the tendency for competition to equalize profit rates are two sides of the same coin, and that a ratio of these two effects ultimately determines the dispersion of the equilibrium distribution.