Weight assurance region in two-stage additive efficiency decomposition DEA model: an application to school data

Abstract

In this paper we use the additive efficiency decomposition approach in two-stage data envelopment analysis. Initially, we evaluate the variable returns to scale version and face a structural difficulty of the model. In an extreme case, weights xi(1) or xi(2) which represent the relative importance of the performance of the first and second stages, respectively, become zero for a number of decision making units (DMUs). As a result, individual stage efficiencies for these DMUs are undefined. We propose a weight assurance region model to restrict xi(1) and xi(2), which ensures that both weights are always positive, and therefore individual stage efficiency is always defined. Furthermore, the proposed model is appropriate for policy making in the presence of a priori information about the relative importance of each stage in the overall process. We employ the new model to evaluate the efficiency of secondary education in 65 countries and construct an overall 'school efficiency' index. In the first stage we measure the 'learning environment efficiency' and in the second we measure the 'student's performance efficiency'.