Global Malmquist and cost Malmquist indexes for group comparison

Abstract

The Malmquist index (MI) has demonstrated its usefulness in comparing the performances of Decision Making Units (DMUs) performances. The global MI (GMI) has been suggested as a means to overcome three drawbacks of the MI: non-circularity, disparate measurements, and infeasibility. Recently, it has appeared that the MI can also be used to compare groups of DMUs. While this new function of the index has also increased its usefulness, it presents the same drawbacks as the MI. In this paper, we define the global counterpart of the MI for group contexts. We also consider the case where DMUs have an economic optimization behavior by proposing a global cost MI (GCMI). The GCMI requires the observation of the input prices. As it may represent a strong assumption, we propose solutions. These two novel indexes equip the practitioners with a new toolkit. We illustrate the usefulness of our new indexes with the Chinese energy sector.