Water usage efficiency and productivity change: a non-convex metafrontier Malmquist index

This paper uses a non-convex metafrontier approach to study the temporal evolution and the productivity change in the water usage efficiency of 91 countries during the period 2015–2020. A circular three-stage Network Data Envelopment Analysis (NDEA) production process is considered. The non-radial Directional Distance Function (DDF) is used to compute the system efficiency as well as that of the three stages. Three sets of NDEA models are solved: contemporaneous group, intertemporal group and intertemporal metafrontier. The corresponding Malmquist index and its decomposition into efficiency change, best practice gap change and technology gap change is computed for each country and averaged for each world region. The results found indicate that water usage inefficiency seems to be limited to a relatively small number of countries and is due to shortfalls in the gross value added and treated municipal wastewater dimensions. The inefficiency in gross value added actually shows an upward trend. The inefficiency in the water withdrawal and treated municipal wastewater dimensions have remained approximately constant during this period while the inefficiency in produced municipal wastewater have decreased slightly. As regards productivity change, most regions had a negative evolution during this period. Central Asia and Middle East-Western Asia are the exception to this trend and their productivity improvement is mostly due to an improvement in their best practice gap and, to a lesser extent, in their technology gap ratios.