Revisiting Granular Models of Firm Growth

We revisit "granular models of firm growth" that have been proposed in the literature to explain the anomalously slow decrease of growth volatility with firms size and how this phenomenon shapes the distribution of their growth rates. In these models, firms' sales are viewed as collections of independent "sub-units", and these non-trivial statistical properties occur as a direct result of the fat-tailed distribution of the number or sizes of these sub-units. We present and discuss new theoretical results on the relation between firm size and growth rate statistics. Our results can be understood by noting that granular models imply the existence of three types of firms: well-diversified firms, with a size evenly distributed among several sub-units; firms with many sub-units but with their total size concentrated on only a handful of them, and lastly firms which are poorly diversified simply because they are made up of a small number of sub-units. We establish new empirical facts about growth rates and their relation with size. As predicted by the model, the distribution of growth rate volatilities is to a good approximation {independent of firm size}, once rescaled by the average size-conditioned volatility. However, the tail of this distribution is much too thin to be consistent with a granular mechanism. Moreover, the moments of growth volatility scale with size in a way that is at odds with theoretical predictions. We also find that the distribution of growth rates rescaled by firm-specific volatility, which is predicted to be Gaussian by all the models we consider, remains very fat-tailed in the data, even for large firms. This paper, in ruling out the granularity scenario, suggests that the overarching mechanisms underlying the growth of firms are not satisfactorily understood, and argues that they deserve further theoretical investigations.