Identification of spatial regimes of the production function of Italian hospitals through spatially constrained cluster-wise regression

Building on the idea that different hospitals may operate with different technologies, the objective of this paper is a spatial characterization of the production function of hospital services through the identification of different spatial regimes. We introduce an original methodology to identify spatially constrained regimes, namely spatially constrained portions of territory in which the production units are maximally homogeneous in functional terms. The empirical algorithm can be described as a k-means cluster-wise regression procedure in which the units are belonging to a proximity graph and where distance is assessed in regressive terms. The analysis is implemented, first, on simulated data and, then, on output and input data of Italian hospitals for the year 2010. Our results, besides their methodological value, allow to shed light on the working of the hospital sector in Italy. The heterogeneity of the identified technological regimes can be associated to spatial heterogeneity of relevant aspects, like demand, internal organization, clinical and managerial governance, etc., and consequential policy implications can be, therefore, gathered.