The overall Malmquist index: a new approach for measuring productivity changes over time

This paper deals with a special case of the non-homogeneity problem related to the determination of the global benchmark technology when measuring productivity changes over time. The authors propose a new way of constructing the global framework of the Malmquist index which applies the minimum extrapolation principle on the aggregation of the experienced contemporaneous technologies. The proposed index, called overall Malmquist index, preserves the role of each contemporaneous technology in the determination of the newly-proposed best practice technology, whereby an acceptable level of discrimination between non-homogeneous observations is provided. With respect to both computational and test properties, the proposed index possesses the circularity property, generates a single measure of productivity change and is immune to infeasibility under variable returns to scale. Furthermore, unlike in the global form, previously computed results by the overall Malmquist index are more stable and less sensitive to changes in the shape of the best practice technology when a new time period is incorporated. Similar to traditional indices, it can be decomposed into various components such as efficiency change, scale efficiency change, and best practice change. The suggested index will be illustrated by means of a real-world example from banking. In particular, it will be compared to the contemporaneous and global forms of the Malmquist index introduced into the literature by Färe et al. (J Product Anal 3:85–101, 1992) and Pastor and Lovell (Econ Lett 88:266–271, 2005) , respectively.