Efficiency and benchmarking with directional distances: a data-driven approach

In efficiency analysis the assessment of the performance of Decision-Making Units (DMUs) relays on the selection of the direction along which the distance from the efficient frontier is measured. Directional Distance Functions (DDFs) represent a flexible way to gauge the inefficiency of DMUs. Permitting the selection of a direction towards the efficient frontier is often useful in empirical applications. As a matter of fact, many papers in the literature have proposed specific DDFs suitable for different contexts of application. Nevertheless, the selection of a direction implies the choice of an efficiency target which is imposed to all the analysed DMUs. Moreover, there exist many situations in which there is no a priori economic or managerial rationale to impose a subjective efficiency target. In this paper we propose a data-driven approach to find out an 'objective' direction along which to gauge the inefficiency of each DMU. Our approach permits to take into account for the heterogeneity of DMUs and their diverse contexts that may influence their input and/or output mixes. Our method is also a data-driven technique for benchmarking each DMU. We describe how to implement our framework and illustrate its usefulness with simulated and real data sets.