On multi-decomposition of the aggregate Luenberger productivity index

Abstract

The purpose of this note is twofold. First, it proposes a multi-decomposition of the Luenberger productivity index, that is, a combined decomposition both by attribute, which is characterized by technical change or efficiency change, and by firm. Second, it applies this technique to the European Union to measure the most important contributions to European productivity.

Acknowledgement

We thank Walter Briec for helpful comments. Any remaining errors are solely due to the authors.

Notes

¹ They show that aggregation holds for a linear technology and for a direction solely defined in the output space.

²More recently, Färe and Grosskopf (2004) studied various issues related to aggregation of efficiency and productivity measures.

³ See Shephard (1970) and Färe et al. (1985) for thorough analysis of their implications on technology.

⁴ Note that it is possible to bootstrap these relative contributions in order to gauge the significant changes over time (Simar and Wilson, 2000).

⁵ We choose the 15 countries of the European Union except the Netherlands for which the data are not available.