The duality of Shephard’s weakly disposable technology

Hervé Leleu and Albane Tarnaud

No 2016-EQM-06, Working Papers from IESEG School of Management

Abstract: A part of the recent literature on the treatment of undesirable outputs by weakly disposable models advocates for the use of the Kuosmanen approach to weak disposability. It defines the minimum extrapolation technology satisfying the disposability assumptions specific to weakly disposable models under three different assumptions on convexity: convexity of the technology set, convexity of output sets only and no convexity at all. We contribute to this taxonomy by adding the case of assuming both input and output sets convex, restoring the classical Shephard approach to weak disposability on the output correspondence. After defining the technology through the definition of a directional distance function, we also linearize the corresponding program and show how the application of duality results in a clear, intuitive, and economically relevant interpretation of the assumption of weak disposability on outputs. Finally, we provide an original proof of the existing relationship between weak disposability and returns to scale.

Keywords: Undesirable output; weak disposability; duality; convexity; data envelopment analysis (search for similar items in EconPapers)
Pages: 13 pages
Date: 2016-03
New Economics Papers: this item is included in nep-eff
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Citations: View citations in EconPapers (1)

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