Generalizing Gibrat. Reasonable Multiplicative Models of Firm Dynamics

Multiplicative models of firm dynamics ‘à la Gibrat’ have become a standard reference in industrial organization. However, some unpleasant properties of their implied dynamics – namely, their explosive or implosive behaviour (firm size and number collapsing to zero or increasing indefinitely) - have been given only very little attention. In this paper I investigate which modifications to the standard multiplicative model of firm dynamics lead to stable (and reasonable) distributions of firm size. An agent-based simulation study is performed, and a methodology is proposed to recover the (aggregate) laws governing the system by estimating the reduced form, i.e. the local data generating process, on the artificial data resulting from a number of artificial experiments. I show that in order to obtain stable systems for a wide range of average growth rate, either heteroskedasticity in the growth rates has to be assumed, or entry and exit mechanisms included. While other particular, ad hoc, entry and exit mechanisms could be imagined, I show that combining the broad class of threshold entry mechanisms and the more restricted class of threshold exit mechanisms with overcapacity penalizing all firms (where entry and exit are determined with reference to an exogenously defined total capacity of the market), lead to stable distributions even in the case of growth rate homoskedasticity, given a non-zero minimum threshold for firm size.