A new Malmquist productivity index with an application to commercial banks

Management-led productivity improvements are crucial for achieving sustainable development, and the Malmquist productivity index is known to be useful in relevant contexts. This study aims to extend such index by using non-parametric mathematical modeling of production processes. Specifically, and in the spirit of the existing index, we introduce the directional distance function to develop a new one applicable to the joint production of desirable and undesirable outputs. Furthermore, we decompose the new index into two constituent components to provide more intuitive explanations when revealing the root sources of productivity changes over time. Under the cost minimization assumption, the new index is applicable when producers implement resource allocation management, and the input–output quantities and the micro-level input prices are known. The index emphasizes that the allocative efficiency should be regarded as an important aspect of productivity assessment like the technical efficiency. As a practical benchmarking tool, it can offer valuable information and provide appropriate strategies for managerial decision-making. The index’s application and usefulness is demonstrated in the commercial bank sector in China.