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Non-parametric Analysis of Multi-output Production with Joint Inputs


  • We thank the Editor Rachel Griffith and two anonymous referees for constructive comments, which substantially improved the article. We are also grateful to David Saal for generously providing us with the data for our empirical application. Laurens Cherchye gratefully acknowledges financial support from the Research Fund K.U.Leuven through the grant STRT1/08/004. Thomas Demuynck thanks the Fund for Scientific Research – Flanders (FWO-Vlaanderen) for his postdoctoral fellowship. Bram De Rock gratefully acknowledges the European Research Council (ERC) for his Starting Grant.


We focus on analysing cost minimising production behaviour in multi-output settings. We distinguish between two approaches for modelling the use of joint inputs. The cooperative approach assumes cost minimisation at the aggregate firm level, while the non-cooperative approach assumes cost minimisation at the level of the individual output division. Our framework extends the existing non-parametric framework for analysing single output production. An empirical application to the English and Welsh drinking water and sewerage sector shows the practical usefulness of our framework. Specifically, we compare the empirical validity of the cooperative and non-cooperative models for describing the observed production behaviour.