A statistical test for nested radial data envelopment analysis models

Some problems in economics, operations research, and engineering may be approached by means of a pair of radial DEA models that are nested, i.e., that the set of constraints of one of them is included in that of the other. In this paper we have focused on analyzing the marginal role of a given variable, called candidate, with respect to the efficieny measured by means of a DEA model. First, we have defined a new efficiency contribution measure (ECM), which finally compares the efficiency scores of the two radial DEA models differing in the candidate. This can be either one input or one output. Then, based on ECM, we have also approached the problem from a statistical point of view. To be precise, we have developed a statistical test that allows us to evaluate the significance of the observed efficiency contribution of the candidate. Eventually, solving this test may provide some useful insights in order to decide the incorporation or the deletion of a variable into/from a given DEA model, on the basis of the information supplied by the data. Two procedures for progressive selection of variables were designed by sequentially applying the test: a forward selection and a backward elimination. These can be very helpful in the initial selection of variables when building a radial DEA model.