The Hölder Distance Functions: Economic Inefficiency Decompositions

Data Envelopment Analysis can determine both a technical efficiency score and benchmarking information on how to change inputs and outputs to reach the efficient frontier if the firm under evaluation is technically inefficient. All measures studied in this book resort to the determination of benchmarking information through the calculation of the farthest targets for the evaluated DMU—“farthest” in the sense that the measure corresponds to the maximum value of the sum of slacks of the corresponding model or some variation. In the case of the (weighted) additive model discussed in Chap. 6 , for example, this is clearly shown in the objective function of program (6.1). The objective function of this mathematical model consists of the weighted sum of the slack in each dimension (input and output), i.e., the difference between the target located on the strongly efficient frontier and the evaluated unit. In the case of the radial measures, i.e., the Farrell measure of technical efficiency, the situation is not so evident. In DEA, it is not strange to apply a second stage when the radial model is utilized in order to determine Pareto-efficient targets from the projection point. This second stage exploits the additive model. Consequently, we are also maximizing slacks. This means that most of the traditional measures in DEA generate the farthest targets. In other words, they yield the targets that are the most difficult ones to be achieved for the firm/organization in the short run.