Non-compensability in Composite Indicators: A Robust Directional Frontier Method

This paper follows the research mainstream aimed to link the efficiency frontier approaches and the composite indicators (CI) methods. More in detail, the main drawbacks of the CI methods based on Benefit of the Doubt (BoD) approach are the sensitivity to the outliers, the perfect compensability and the lack of consideration about the marginal rate of substitution between simple indicators. Following Simar and Vanhems (J Econ 166(2):342–354, 2012) results, we propose a weighting method that bypassing all previous shortcomings suggests a comprehensive approach to construct robust and non-compensatory composite indicators. This approach is based on the integration of BoD by a directional distance function. In order to better highlight the advantages and limitations of our approach we present two applications: in the first one we test our approach on simulated data, while in the second one we consider the supply level of the Italian national health service with the aim to analyse the regional differences and verify the robustness of the results.