Composite Indicators based on the Principle of Least Action and Data Envelopment Analysis. An application to Corporate Social Responsibility Data

Abstract

This paper introduces a model to construct composite indicators that is based upon the determination of the least distance from each assessed unit to a frontier estimated by Data Envelopment Analysis (DEA). The model also allows accounting for the existence of slacks in all the considered dimensions (sub-indicators), playing with the notion of Pareto-efficiency. All previous approaches based on DEA for building composite indicators maximize in some sense the sum of these slacks, determining the furthest and less credible targets and peers for the set of evaluated units. In contrast, the new model applies the Principle of Least Action (PLA), which ultimately determines the closest targets on the efficient frontier. Additionally, in order to assure the satisfaction of a set of important properties (units invariance, translation invariance, Pareto-efficiency, strong monotonicity), the model implements a new version of the Russell output measure of technical efficiency working with full dimensional efficient facets (FDEFs). This also guarantees that the weights used for the aggregation of the sub-indicators are always strictly positive. Finally, the new approach is illustrated by an application to the sphere of Corporate Social Responsibility (CSR).