Spatial Solution to Measure Regional Efficiency — Introducing Spatial Data Envelopment Analysis

When investigating healthcare efficiency at the regional level, the problem of interactions between neighbouring locations arises. The health of the population in a given region is related to the healthcare in other areas through a medical tourism, a limited number of highly specialised institutions, competition between institutions, etc. Ignoring these inter-regional links may result in a systematic bias in the efficiency analysis. Similar issues may hinder any regional studies. Hence, the main purpose of this paper is to introduce a new approach to measuring efficiency in regional studies through spatial data envelopment analysis (SDEA). The paper offers a proper mathematical formulation of the new methodology and highlights differences between classic data envelopment analysis (DEA) and the newly developed method. The motivation for seeking a new solution to the problem of spatially adequate assessment of regional efficiency is derived from the literature review and a discussion of the presented theoretical examples. The classic DEA allows for multidimensional analysis of the performance of homogenous independent decision-making units. However, in regional studies, an area where DEA has gained popularity, the assumption of the isolation of decision-making units seems to be unfounded. In the SDEA approach, the region-specific spatial context is incorporated into the analysis via the W matrix and spatial interactions are reflected in the model through spatially weighted inputs and outputs. Therefore, in our paper, we verify the hypothesis that spatial interactions are an indispensable factor of regional efficiency analysis. A study of healthcare efficiency in European regions is presented as an illustration of the utility of the new methodology. Furthermore, we compare the results of the classic DEA approach with those of the SDEA, which is augmented with the spatial equivalents of inputs and outputs. Our results suggest that classic DEA undervalues regional healthcare efficiency by underestimating the region-specific spatial context.2 Researchers may find the introduced SDEA method useful in all space related fields when investigated phenomenon exhibits spatial autocorrelation. In particular, the new approach may deepen the regional efficiency analysis of innovation, development, logistics, tourism, etc.