Target and technical efficiency in DEA: Controlling for environmental characteristics

In this paper we propose a target efficiency DEA model that allows for the inclusion of environmental variables in a one stage model while maintaining a high degree of discrimination power. The model estimates the impact of managerial and environmental factors on efficiency simultaneously. A decomposition of the overall technical efficiency into two components, target efficiency and environmental efficiency, is derived. Estimation of target efficiency scores requires the solution of a single large non-linear optimization problem and provides both a joint estimation of target efficiency scores from all DMUs and an estimation of a common scalar expressing the environmental impact on efficiency for each environmental factor. We argue that if the indices on environmental conditions are constructed as the percentage of output with certain attributes present, then it is reasonable to let all reference DMUs characterized by a composed fraction lower than the fraction of output possessing the attribute of the evaluated DMU enter as potential dominators. It is shown that this requirement transforms the cone-ratio constraints on intensity variables in the BM-model (Banker and Morey 1986) into endogenous handicap functions on outputs. Furthermore, a priori information or general agreements on allowable handicap values can be incorporated into the model along the same lines as specifications of assurance regions in standard DEA.