Variable selection in Data Envelopment Analysis

The selection of inputs and outputs in Data Envelopment Analysis (DEA) is regarded as an important step that is normally conducted before the DEA model is implemented. In this paper, we introduce cardinality constraints directly into the DEA program in order to select the relevant inputs and outputs automatically, without any previous statistical analysis, heuristic decision making or expert judgement (though our method is not incompatible with these other approaches and indeed may help to choose among them). The selection of variables is obtained solving a mixed integer linear program (MILP) which specifies the maximal number of variables to be used. The computational time of the program is fast in all practical situations. We explore the performance of the method via Monte Carlo simulations. Some empirical applications are considered in order to illustrate the usefulness of the method.