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This paper deals with the evolution of firms, as part of a population of interacting entities (an industry).
Firms' growth dynamics have commanded a continuous attention in the economic literature, at least since Gibrat proposed his simple multiplicative stochastic model in the 30s. In his model, the size of any given firm is described as the result of a sequence of stochastic multiplicative shocks, which are thought to be independent both of the characteristics of the firm itself, and of what happens to all other firms in the market.
Multiplicative models have nourished because they offer a simple but realistic description of what happens at an individual firm level. After all, it is not that easy to predict whether a given firm will grow or shrink in the future. Success and failure contain without any doubts some stochastic elements, and it appears reasonable to think of them as multiplicative shocks, where big firms variations in size are in absolute value larger than small firms variations. Moreover, multiplicative models lead very easily to nice aggregate distributions of firm size. Lognormal and power-law distributions are easily obtained. They both imply a very large number of small firms, and a small number of very large firms, a feature observed in the real world. However, multiplicative models lead to very unreasonable aggregate dynamics, with the number and the size of firms either collapsing to zero or increasing without limits. In this paper I develop an agent-based simulation model in order to encompass and extend the results produced in the literature. My question is: ``which modifications to the standard models should be made in order to produce more 'reasonable' dynamics?'' I show that in order for a multiplicative model of firm growth to exhibit a stationary distribution of firm size for a wide range of average growth rate, we have either to assume that growth rates depend on firm size (i.e. relaxing the strong Gibrat assumption that growth rates are i.i.d.), or to include entry and exit mechanisms. With respect to the latter point, I show that stochastic multiplicative models of firm size that abstract completely from considering firm interaction fail to exhibit the desired stationary properties. I then test a number of different entry and exit mechanisms, dividing them in two broad classes. Non-threshold mechanisms imply there is no reference to an exogenous threshold in determining the entry and exit of firms, i.e. the model has no anchorage, except for the 'natural' floor at 0 for firms' size. They thus do not consider firm interaction. In threshold mechanisms on the contrary entry and exit are determined with reference to an exogenously defined demand (i.e. to an exogenous maximum capacity of the market), and therefore explicitly consider the fact that firms interact in their market. 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 where overcapacity penalizes all firms (i.e. both small and large firms), lead to 'reasonable' distributions of firms size even when the growth rate is independent of size, given a non-zero minimum threshold for firm size. Not considering interaction, on the other side, makes it impossible to reach the stationary distributions looked for. |