Memorandum,
Oslo University, Department of Economics

Abstract: 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 between the two types of outputs and null jointness introduced by Shephard. The purpose of the paper is to show that these model types are seriously flawed. 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. A key feature is that the two types of outputs should be separated using different production relations. This facilitates estimating two independent frontiers and calculating efficiency scores and Malmquist productivity changes for the two types using a non-parametric DEA model.

Keywords: Intended and unintended outputs; joint production; Materials balance; Technical jointness; pollution; weak disposability

JEL-codes: C14; D24; D62; Q50

42 pages, November 11, 2019

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