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Weak Disposability in Nonparametric Production Analysis with Undesirable Outputs Timo Kuosmanen Wageningen University, The Netherlands 14th EAERE Annual Conference, June 2005, Bremen, Germany

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Background Production activities typically generate some environmentally detrimental undesirable outputs as side-products emissions, waste, noise, etc. The treatment of undesirable outputs in nonparametric production analysis has recently attracted debate: Hailu and Veeman, AJAE 2001 Färe and Grosskopf, AJAE 2003 Hailu, AJAE 2003

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This paper Shows that conventional formulations of weak disposability implicitly and unintentionally assume that all firms apply uniform abatement factors. It is usually cost efficient to abate emissions in those firms where the marginal abatement costs are lowest. Presents an alternative formulation of weak disposability that allows for non-uniform abatement factors

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Notation Firms transform inputs to (good) outputs, which causes undesirable side-products (bads). Input quantities Output quantities Environmental bads Production technology characterized by output set

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Weak Disposability Definition (Shephard, 1970): Outputs are weakly disposable if and =>

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Nonparametric production analysis (also known as Activity Analysis or Data Envelopment Analysis (DEA)) Assume a sample of K observations Estimate output set P(x) by a set of output vectors that consists of all observed output vectors output vectors that are feasible by the maintained production assumptions and no other vectors

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Nonparametric production analysis Maintained assumptions inputs x and (good) outputs v are freely disposable bad outputs w are weakly disposable outputs sets P(x) are convex for all x

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Illustration 3 observations, the same amounts of inputs w v

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Illustration Feasible set spanned by convexity w v

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Illustration Feasible set spanned by convexity and free disposability of v w v

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Illustration Feasible set spanned by convexity, free disposability of v, andweak disposability w v

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Shephards formulation – uniform abatement outputs bads inputs VRS intensity weights abatement factor

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outputs bads inputs VRS intensity weights K abatement factors Generalized formulation

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Partition the intensity weights as where represents the part of firm ks output that is abated through scaling down of activity level, i.e., represents the part of firm ks output that remains active, i.e., Linearization

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outputs bads inputs VRS intensity weights Linearized formulation

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Numerical example Firm AFirm BFirm C v835 w641 x514

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Output sets: w not disposable

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Output sets: weak disposability - Shephard

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Output sets: weak disposability – this paper

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Empirical significance Static environmental efficiency analysis Measurement of total productivity over time Estimation of abatement cost functions Etc...

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Methodological significance Production assumptions interact The fundamental minimum extrapolation principle by Banker et al. (Management Science 1984) can fail The minimum set that satisfies the maintained assumptions and contains all observations may exclude production vectors that are feasible by the same set of assumptions => Need to reconsider the main principle of data envelopment analysis

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Further details... Paper accepted for publication in American Journal of Agricultural Economics Questions / comments are welcome to Thank you for your attention!

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