Abstract
This paper introduces a model to construct composite indicators for performance evaluation of decision making units, which is based upon the determination of the least distance from each assessed unit to a frontier estimated by data envelopment analysis. This generates less demanding targets from a benchmarking point of view. The model also makes it possible to account for the existence of slacks in all the considered dimensions (sub-indicators), playing with the notion of Pareto efficiency. Additionally, our approach satisfies units invariance, translation invariance and strong monotonicity and ensures that the weights used for the aggregation of the sub-indicators are always strictly positive. All previous approaches based on data envelopment analysis have failed to satisfy at least one of these properties. We also implement a new version of the Russell output measure of technical efficiency working with full-dimensional efficient facets. Finally, the new approach is illustrated by an application to the sphere of corporate social responsibility, showing the main empirical implications of the theoretical properties.
Highlights
Data envelopment analysis (DEA) is a methodology based on mathematical programming for the assessment of technical efficiency of a set of decision making units (DMUs), which allows a data-driven construction of a piece-wise frontier, enveloping the data cloud of observations and, at the same time, the determination of the distance from each DMU to this frontier
From a benchmarking viewpoint, it is worth mentioning that traditional DEA models can yield targets that are determined by the “furthest” efficient projection to the assessed DMU; see [9]
To get the optimal targets for each DMU0, we have to solve the linear system of Eqs. (20), where through the first equation we consider all the feasible projection points, which are on the optimal hyperplane determined by (20), and, through the second equation, we are sure that Y0∗ Y0 + s0∗ is the point where NCImEXinFA(Y0) is achieved:5 s μr∗0 yr0 + sr0 + ψ0∗
Summary
Data envelopment analysis (DEA) is a methodology based on mathematical programming for the assessment of technical efficiency of a set of decision making units (DMUs), which allows a data-driven construction of a piece-wise frontier, enveloping the data cloud of observations and, at the same time, the determination of the distance from each DMU to this frontier. DEA has been recently linked to the construction of composite indicators in social science through the notion of the Benefit-of-the-Doubt (BoD) model; see [11,12,13] This is a DEA model without real inputs [14], where sub-indicators are all treated as outputs to generate an overall and objective aggregated indicator for each assessed DMU through the determination of its efficiency. As far as we are aware, no previous contribution to the definition of composite indicators by BoD in DEA has applied the PLA, when determining the final aggregated indicator for each unit, neglecting the potentiality of the approach as a benchmarking tool for the evaluated DMUs. Previous research has used the variety of.
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