“Bad outputs as inputs”, reverse outputs and extended strong disposability

Abstract

In this paper we examine the relation between the “bad outputs as inputs” with other approaches of modeling undesirable outputs in non-parametric production analysis and we end up with six equivalencies among them. Based on these, we argue that the “bad outputs as inputs” is a valid modeling option as long as the assumption of extended strong disposability and thus of reverse outputs is reasonable in a particular setting. In this case, the “bad outputs as inputs” approach can easily be implemented by means of a conventional input-oriented DEA model with variable returns to scale where the translated additive inverse transformation is applied to undesirable output quantities.