Spatial–temporal distribution measurement of input–output efficiency of the water–energy–food nexus of the Yangtze River Economic Belt, China

Water, energy, and food are important factors affecting people’s lives and socio-economic development, and their production and consumption processes are closely related, so it is necessary to do research on input–output efficiency as a whole. The research is conducive to promoting the effective utilization and rational allocation of relevant resources in the Yangtze River Economic Belt, thereby promoting sustainable development. This study calculates the input–output efficiency of the water–energy–food (WEF) nexus of 11 provincial administrative regions in the Yangtze River Economic Belt utilizing the DEA-BCC model. Then, new indicators called area expansion degree and the subsystem’s influence degree are proposed with the aid of the standard deviation ellipse model to analyze the characteristics and trends of spatial–temporal distribution of input–output efficiency. The standard deviation ellipse model starts from the basic spatial elements, including point, line, and surface, and is used to study the spatial distribution and trend change of efficiency according to the center of gravity and area. The shift of the center of gravity shows the direction of significant improvement in the effect of resource allocation, and the change of area shows the differences in the speed of efficiency improvement between regions and the future development trend. The results mainly indicate that the resource allocation in the middle and lower reaches of the Yangtze River Economic Belt is more reasonable than that in the upper reaches, and the efficiency distribution is obviously concentrated in the northeast direction. It is suggested that the provincial administrative regions in the upper reaches should optimize the industrial structure, the regions in the middle and lower reaches should improve the resource structure, and the flow of talents and technology of regions should be promoted.