Scaling laws to explore innovative behavior of transnational investment

In this research, we use scaling laws to explore the “innovative behavior” of transnational investment in the French system of cities, as cities are the major recipients of economic activities. As the Foreign Direct Investment operated by transnational firms abroad from their countries of origin have reached an unprecedented level (the amount of global FDI inflows reached many hundred billion US dollars annually since the 1990’s) and show a high concentration in some cities according to literature (e.g. “global cities” [Beaverstock & Taylor, 1999]), we suggest that we can consider it as an innovation. Scaling laws are therefore used by analogy to the proposal of an evolutionary theory for interpreting urban scaling laws that links urban activity, city size and innovation cycles [Pumain et al., 2006]; a scaling exponent higher or lower than 1 would disclose an innovative or more mature behavior of transnational investment, linked firstly to a higher concentration in biggest cities of the system or secondly to its diffusion from the biggest to the smallest cities.
As inward FDI stocks and FDI inflows cannot be located at a suitable level (they are designed at a national one), we use two databases regarded as both kind of FDI: employment in foreign-controlled companies (original database built by combining three main sources [Finance, 2015]) and employment in cross-border investment projects. We compare inward FDI stocks and FDI inflows to understand and compare the long-term and short-term attractiveness of French cities and the possible concentration of both kinds of investments in the biggest or smallest cities. This will reveal the distinct innovative or more mature nature of these two types of investments.
While inward FDI stocks show a clear supra-linear scaling parameter, concentrated in the biggest French cities, FDI inflows show a more linear distribution, according to the size of the cities. While the long-term investments have benefited to the biggest cities, the more recent ones show a distribution which is more proportional to the size of the cities. This could indicate a banalization of the transnational investment process in urban systems.