Developing two dynamic Malmquist-Luenberger productivity indices: An illustrated application for assessing productivity performance of Indian banks

In the presence of undesirable output(s) in the production process, the Malmquist-Luenberger productivity index (MLPI) has emerged as a standard tool to measure total factor productivity change and its distinct components, namely efficiency change and technical change. Notwithstanding, the standard version of MLPI has certain genuine downsides, particularly the commonness of infeasibility while computing cross-period directional distance functions with negative data values and the black-box representation of the production technology. For overcoming these downsides, this paper advances two extensions of the standard MLPI. Specifically, we propose dynamic Malmquist-Luenberger and dynamic sequential Malmquist-Luenberger productivity indices to measure the productivity change in a system that can be represented by a dynamic network production structure. The proposed indices take a holistic view of production technology that connects several divisions internally by intermediate processes and use the carryovers flow over time to add a temporal dimension to it. To exhibit the capability of the proposed extensions of MLPI, we model a three-stage dynamic network structure for Indian banks and compute the indices of productivity change, efficiency change, and technical change for forty-two banks for the period from 2010 to 2017. The empirical findings elucidate that the observed productivity growth in the Indian banking industry is primarily driven by technical progress.