The directional profit efficiency measure: on why profit inefficiency is either technical or allocative
The directional distance function encompasses Shephard’s input and output distance functions and also allows nonradial projections of the assessed firm onto the frontier of the technology in a preassigned direction. However, the criteria underlying the choice of its associated directional vector are numerous. When market prices are observed and firms have a profit maximizing behavior, it seems natural to choose as the directional vector that projecting inefficient firms towards profit maximizing benchmarks. Based on that choice of directional vector, we introduce the directional profit efficiency measure and show that, in this general setting, profit inefficiency can be categorized as either technical, for firms situated within the interior of the technology, or allocative, for firms lying on the frontier. We implement and illustrate the analytical model by way of Data Envelopment Analysis techniques, and introduce the necessary optimization programs for profit inefficiency measurement.
KeywordsDirectional distance function Profit efficiency Technical efficiency Allocative efficiency
JEL ClassificationC61 D21 D24
We are grateful to the participants and discussants at the International Workshop on Efficiency and Productivity in honor of Prof. Knox Lovell (October 4–5, 2010, Elche, Spain). We acknowledge financial support from the Ministerio de Ciencia e Innovacion, Spain, and the Conselleria de Educacion, Generalitat Valenciana, for supporting this research with grants MTM2009-10479 and ACOMP/2011/115, respectively. Finally, we are also indebted to two referees for their comments and suggestions that have contributed to improving this paper.
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