volatility scaling, granularity, resource allocation

D40, L20

We revisit the size-volatility relationship in firm growth using administrative data on French manufacturing firms. Departing from the log-log linear decay commonly reported by other studies, we find a two-regime pattern: volatility declines steeply with size for small firms, but flattens for larger ones. We relate this new fact to the presence of resources misallocation as captured by imperfect correlation between size and productivity at the firm level. To explain the nexus between these two facts, we develop a stochastic model where firms face a number of risky business opportunities for which they compete. Two key features characterize this competition process. First, larger firms are more intensively exposed to competition dynamics. Second, firms with higher productivity are more likely to see business opportunities turning into positive, rather than negative, growth episodes. We analytically show that only when the correlation between firm size and productivity is lower than 1 the model is able to reproduce the volatility scaling we observed in the data. Simulations suggest that finite sample approximations of our asymptotic result are satisfactory in a reasonable portion of the parameter space. We conclude showing that in France industries populated by firms with higher correlation between size and productivity are associated with steeper average size-volatility decays consistent with the model's main prediction. Our findings suggest that the existence of resources misallocation, shaping the size-volatility relation, affects the relevance of the granularity channel in explaining aggregate fluctuations (Gabaix, 2011).