A spatial microeconometric model for firm demography
A spatial model for firm demography
In this section we will introduce a class of testable models to help explain the concentration of firms in space. The formalism is taken from Arbia (2001) and derives from a model proposed by Rathbun and Cressie (1994) for the spatial diffusion of vegetation. Our modelling framework also shares a particular resemblance with the methodology employed by Van Wissen (2000) to simulate the dynamics of firm demography in space. However, even if the set-up of the model is similar, we must emphasize that in Van Wissen’s approach (as in other recent works on firm demography, see Bade and Nerlinger 2000; Van Dijk and Pellenbarg 2000), the aim is to model firm behavior within regions. Our goal, however, is to explain why a firm locates (develops and dies) at a certain point in space. Indeed, the stochastic point processes theory presented in Part III is at the basis of possible firm demography models which account for the links of spatial interactions amongst individual economic agents. By treating the spatial distribution of the economic activities as the result of a dynamic process which occurs in space and time, the observed micro-geographical patterns can be modeled as realizations of a marked space-time survival point processes (see Chapter 6), where firms are created at some random location and at some point in time and then they operate, grow and attract (or repulse) other firms in their neighborhood. Following the reductionist approach already exploited by Arbia (2001), in this section we formalize three different model components:
i a birth model,
ii a growth model and
iii a death/survival model.
Such an approach can prove very useful in that the model parameters can provide indications of how to validate the different paradigmatic economic-theoretical cases, such as the presence of spatial spillover effects, the effects of positive spatial externalities or hypotheses concerning the spatial inhibition processes among economic agents.