The Weighted Additive Distance Function (WADF): Economic Inefficiency Decompositions

After the introduction in the Data Envelopment Analysis literature of the radial measures, other approaches and ways of measuring the distance from a firm to the efficient frontier were defined, with the aim of solving certain drawbacks of the radial ones. On the one hand, radial measures are too restrictive in the sense that each assessed unit is evaluated keeping the input or the output mix constant, depending on the selected orientation. However, as Chambers and Mitchell (2001) pointed out, firms routinely consider changes in outputs that are not “radial” in nature. Indeed, the firm’s very reason to change its output vector may be to change its mix. For example, the firm may want to partially phase out a product while increasing the production of another output. Therefore, it seems interesting to identify non-radial changes as a way of reducing technical inefficiency since this type of movements could be more realistic than those implied by the radial approach. Additionally, standard radial models are subject to the input or the output orientation, neglecting a global consideration of all the decision variables (resources and products). Again, the introduction of a more flexible framework became necessary. On the other hand, the classical Pareto-Koopmans definition of technical efficiency (Koopmans, 1951) is not taken into account by the radial measures, meaning that certain inefficiency that comes from the slacks of the optimization model is overlooked.