The Luenberger indicator and directions of measurement : a bottoms-up approach with an empirical illustration to German savings banks

The Luenberger productivity indicator applies directional distance functions which allow to specifying in what direction (i.e. direction of measurement) the operating units will be evaluated. In the presence of a change in the direction of measurement, the standard components of the existing Luenberger productivity indicator may provide values which are not compatible with reality. In order to eliminate this pitfall, the so-called bottoms-up approach is used to revisit the definition of the indicator and its components. We start with a list of selected sources of productivity change, namely efficiency change, technical change and direction change, then examine the best possible way of measuring each of the sources and combine them to derive a new measure of productivity change. The proposed indicator will be illustrated by means of an empirical application to a panel of 417 German saving banks over the time period 2006-2012. The example explains how the proposed approach is able to properly measure efficiency change, technical change and direction change. The results also provide conclusive evidence about the effect of the change in direction of measurement on the results of the productivity over time in a centralized management scenario.