Dynamic Metafrontier Malmquist–Luenberger Productivity Index in Network DEA: An Application to Banking Data

Recent advances in the study of dynamic network data envelopment analysis (DNDEA) have shown to provide better insight into the system to improve the efficiency and productivity of a decision-making unit (DMU). A network structure of a DMU takes a holistic view of the production technology that connects several divisions internally by intermediate products and uses the carryovers flow over time to add a temporal dimension to it. In this paper, we propose a dynamic metafrontier Malmquist–Luenberger productivity index (DMMLPI) in the DNDEA framework to measure the total factor productivity change of a DMU when the data involves negative values and undesirable features. The DMMLPI decomposes the productivity change index into three indices: efficiency change, best-practice change, and technology gap change. To demonstrate the capability of the proposed index, we work on a balanced panel data of sixty Indian banks from 2013 to 2017. The sample banks are grouped into three categories: public banks, private banks, and foreign banks. The banks across the categories face heterogeneous production technology, business strategies, and operating environments. We assume that the underlying production architecture of each bank is a three-stage dynamic network. Our empirical analysis shows that foreign banks outperform their counterparts in terms of productivity change measured by the DMMLPI in the considered period.