The Biennial Malmquist Index in the of Negative Data

We purpose the range directional model (RDM), a particular case of the directional distance function, is used for computing efficiency in the presence of negative data. We use RDM efficiency measures to arrive at a Malmquist-type index which can reflect productivity change. We illustrate how the biennial Malmquist index can be used, not only for comparing the performance of a unit in two time periods, but also for comparing the performance of two different units at the same or different time periods. The proposed approach is then applied to a sample of bank branches where negative data were involved. In this paper, we introduce a biennial Malmquist index of productivity change that can be used with negative data.