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The generation of unintended residuals when producing intended outputs is the key factor behind our serious problems with pollution. The way this joint production is modelled is therefore of crucial importance for our understanding and empirical efforts to change economic activities in order to reduce harmful residuals. Estimation of efficiency and productivity when producing both intended and unintended outputs has emerged as an important research strand. The most popular models in the field are based on weak disposability of the two types of outputs together and null-jointness introduced by Shephard. The purpose of the paper is to show that these model types are built on some questionable assumptions. An alternative model based on the production theory of Frisch introduces technical jointness for the case when the unintended output is unavoidable. The materials balance based on physical laws tells us that when material inputs are used unintended outputs are unavoidable. The modelling of joint production must therefore reflect this. The production of the two types of outputs occurs simultaneously. It is the maximisation of intended outputs for given inputs that engineers are striving at to achieve. The production functions for intended and unintended outputs are linked through common use of inputs. However, separate functions for the two types of output can be estimated because the intended outputs are independent of the unintended ones and vice versa, facilitating calculating separate efficiency and productivity measures using non-parametric DEA methods.

Performance measurement and joint production of intended and unintended outputs