Good Modelling of Bad Outputs: Pollution and Multiple-Output Production

The materials-balance principle points to the crucial role of material inputs in generating residuals in production processes. Pollution modelling must be of a multi-output nature. The most flexible transformation function in outputs and inputs used in textbooks is too general to make sense in pollution modelling. Specifying bads <italic>as if</italic> they are inputs, although may be defendable on a macro level as a reduced form, hides explicit considerations of various modification activities. Applying a non-parametric efficiency approach extended to cover bads as outputs, assuming weak disposability of the bads, has serious formal weaknesses as well as not accounting satisfactorily for abatement. Factorially determined multi-output production may be used to model generation of bads by making them being functions of the same set of inputs as in the production of good outputs. A complete taxonomy of inputs as to the impact on both residuals and marketed products as joint outputs is then derived. Factorially determined multi-output production can also be used to model end-of-pipe purification, observing the materials-balance principle, thus providing detailed information for choice of policy instruments.