Geographic concentration of economic activities: on the validation of a distance-based mathematical index to identify optimal locations

The present study proposes a validation of a mathematical index Q able to identify optimal geographic places for economic activities, solely based on the location variable. This research work takes its roots in the 1970s with the statistical analysis of spatial patterns, or analysis of point processes, whose main goal is to understand if a resulting spatial distribution of points is due to chance or not. Indeed point objects are commonplace (towns in regions, plants in the landscape, galaxies in space, shops in towns) and the development of specific mathematical tools are useful to understand their own location processes. Spatial point deviations from purely random configurations may be analyzed either by quadrat or by distance methods. An interesting method of the second category – the cumulative function M – was developed recently for evaluating the relative geographic concentration and co-location of industries in a nonhomogeneous spatial framework. On this basis, and having quantified retail store interactions, The French physicist Pablo Jensen elaborated the Q-index to automatically detect promising locations. To test the relevance of this quality index, Jensen used location data from 2003 and 2005 for bakeries in the city of Lyon and discovered that between these two years, shops having closed were located on significantly lower quality sites. Here, using bankruptcy data provided by the Registrar of companies of the State of Valais in Switzerland and by the City Council of Glasgow in Scotland, we implemented a method based on univariate logistic regressions to systematically test for the relevance of the Q-index on the many commercial categories available. We show that the Q-index is reliable, although significance tests did not reach stringent levels. Access to trustable bankruptcy data remains a difficult task.