Modeling undesirable factors in efficiency evaluation: Comment

In a recent paper in this journal Seiford and Zhu propose using data translation as a means of integrating undesirable outputs and inputs into data envelopment analysis (DEA) models. By ‘reversing’ the bad outputs, they can be readily included in the standard DEA output increasing model, and the usual scaling will actually reduce the bad outputs. This recognizes the fact that increases in those outputs and inputs are not desirable, yet does not resort to the usual ad hoc treatment of undesirable outputs as inputs. Here we suggest an alternative approach which allows us to explicitly model a joint environmental technology and gauge performance in terms of increased good output and decreased undesirable output. This is achieved by adopting a directional distance function which may be estimated using the usual linear programming techniques employed in DEA.