On model selection in data envelopment analysis: a multivariate statistical approach

This paper addresses an important issue in DEA: the selection of inputs and outputs to be included in a model. A two-stage methodology is suggested. The first stage applies a methodology based on comparing reduced models that do not include a particular input/output with extended models that include it. The second stage uses the tools of multivariate statistical analysis to visualize important aspects of the models considered. In this way model selection combines mathematical tools, statistical analysis, and the exercise of judgment. The methodology has the advantage of explaining why some Decision Making Units (DMUs) appear to be efficient under some models and inefficient under other models. It is also possible to produce rankings of DMUs that are a consensus over all the models. The methodology is illustrated with the help of a case study: the efficiency of Spanish banks. It is found that, in this case, there are various defensible definitions of efficiency, and it is suggested that a variety of models should be estimated.