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A remark on the definition of the Färe–Lovell measure for infeasible production vectors: implication for the Luenberger productivity indicator

Melle Agathe Stenger and Agathe Stenger

International Journal of Production Economics, 2017, vol. 184, issue C, 1-6

Abstract: In a recent paper Mahlberg and Sahoo (2011) introduced a non-radial Luenberger indicator in order to avoid the problem of slacks. They suggest to evaluate the Luenberger indicator by using a directional slacks-based measure. This paper demonstrates, by numerical examples, that directional slacks-based measures do not allow to characterize the technology. Along this line, it follows that a Luenberger indicator based upon a directional slacks-based measure may have some drawback. Mahlberg and Sahoo (2011) mention these problems and suggest to replace non-negative signs of the input-specific inefficiency factors by non-positive signs. In this paper an alternative formulation is proposed. It characterizes both the input (output) sets and the input (output) efficient subset. Its application to the construction of a suitable Färe–Lovell type productivity indicator is suggested.

Keywords: Debreu–Farrell efficiency measure; Färe–Lovell efficiency measure; Directional efficiency measures; Luenberger indicator; Non-radial Luenberger indicator (search for similar items in EconPapers)
JEL-codes: D21 D24 (search for similar items in EconPapers)
Date: 2017
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Handle: RePEc:eee:proeco:v:184:y:2017:i:c:p:1-6