The problem of taking into account the quality attributes of different goods has a long tradition in economics A strand of literature deals with the environmental impacts in the measurement of efficiency and productivity growth. Färe et al. (1989) indeed started what has become now a relatively vast literature extending efficiency measurement when some outputs are undesirable. The central notion of this paper is that of weak disposability of outputs. To credit firms for their effort to cut off on pollutants, technology is modeled so that it can handle the case when the reduction of some (bad) outputs requires the reduction of some of the other outputs and/or the increase of inputs.Besides the concept of output weak disposability, an interesting and useful idea for this setting is the directional distance function, a generalization of the radial distance function introduced to production economics by Chambers, Chung and Färe (1996). In this fashion it is possible to evaluate the performance of the firms that need to increase the production of the good outputs and decrease that bad outputs.
