Conditional versus unconditional industrial agglomeration: disentangling spatial dependence and spatial heterogeneity in the analysis of ICT firms' distribution in Milan

A series of recent papers have introduced some explorative methods based on Ripley's K-function (Ripley in J R Stat Soc B 39(2):172-212, 1977) analyzing the micro-geographical patterns of firms. Often the spatial heterogeneity of an area is handled by referring to a case-control design, in which spatial clusters occur as over-concentrations of firms belonging to a specific industry as opposed to the distribution of firms in the whole economy. Therefore, positive, or negative, spatial dependence between firms occurs when a specific sector of industry is seen to present a more aggregated pattern (or more dispersed) than is common in the economy as a whole. This approach has led to the development of relative measures of spatial concentration which, as a consequence, are not straightforwardly comparable across different economies. In this article, we explore a parametric approach based on the inhomogeneous K-function (Baddeley et al. in Statistica Nederlandica 54(3):329-350, 2000) that makes it possible to obtain an absolute measure of the industrial agglomeration that is also able to capture spatial heterogeneity. We provide an empirical application of the approach taken with regard to the spatial distribution of high-tech industries in Milan (Italy) in 2001.