On the inconsistency of the Malmquist–Luenberger index

On the inconsistency of the Malmquist–Luenberger index

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Article ID: iaor20133172
Volume: 229
Issue: 3
Start Page Number: 738
End Page Number: 742
Publication Date: Sep 2013
Journal: European Journal of Operational Research
Authors: , ,
Keywords: productivity, Malmquist index
Abstract:

Apart from the well‐known weaknesses of the standard Malmquist productivity index related to infeasibility and not accounting for slacks, already addressed in the literature, we identify a new and significant drawback of the Malmquist–Luenberger index decomposition that questions its validity as an empirical tool for environmental productivity measurement associated with the production of bad outputs. In particular, we show that the usual interpretation of the technical change component in terms of production frontier shifts can be inconsistent with its numerical value, thereby resulting in an erroneous interpretation of this component that passes on to the index itself. We illustrate this issue with a simple numerical example. Finally, we propose a solution for this inconsistency issue based on incorporating a new postulate for the technology related to the production of bad outputs.

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