Non-linear externalities in firm localization

This paper presents a model of firm localization allowing for non-linear, quadratic externalities. The model disentangles localization externalities from the intrinsic advantages of regions, while the inferential analysis on its parameters verifies whether externalities may have a non-linear shape. Specifically, the introduction of a quadratic term can accommodate both more-than-linear positive feedbacks as well as congestion effects. If the quadratic term is sufficiently negative, one location can reach the point in which the addition of an extra firm decreases the probability for that same location to further attract other firms. In this sense, the present model does not assume a priori that the localization choices of firms are characterized by positive interdependencies. Rather, the methodology allows to estimate whether or not this is actually the case. Our main result is that the quadratic term is virtually never found to be statistically different from zero across Italian sectors observed at the scale of commuting zones, so that localized externalities seem to be well approximated by a linear specification.