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 as if they are inputs, although may be defendable on a macro level as a reduced form, hides explicit considerations of various modification activities. Extending the non-parametric efficiency approach to cover bads as outputs, assuming weak disposability of the bads as the only change in the modelling of the technology, has serious weaknesses. A complete taxonomy of inputs as to the impact on both residuals and marketed products as joint outputs is derived, based on factorially determined multi-output production, thus providing information for choice of policy instruments.