Analysing cost-effectiveness in dynamic network DEA: a directional distance function approach

Dynamic data envelopment analysis (DEA) provides an efficiency estimation of the decision-making units (DMUs) across interconnected periods accounting for carryovers. Value-based cost efficiency evaluation is a well-known tool for estimating the cost-effectiveness of DMUs with heterogeneous input prices. This study introduces a value-based cost-efficiency approach within a directional DEA setup, addressing the significance of carryovers and varying input prices. It offers a network framework that incorporates inputs, outputs (both desirable and undesirable), and shared resources to dynamically measure the cost efficiency of DMUs at the system, period, and division levels. The proposed approach adheres to the principles of unit invariance provided links and carryovers are division-specific (not shared). It also satisfies the properties of translation invariance, and strict monotonicity with regard to input costs and allows for the selection of appropriate direction vectors to manage negative data in practical applications. To validate the efficacy of the proposed approach, it has been employed to assess the dynamic cost efficiency of domestic banks in India over a span of three consecutive periods. The results suggest that banks should concentrate on improving the cost efficiency in the process of deposit generation (division 1), followed by improvements in the income generation process (division 3) and then the lending and investment process (division 2). Moreover, the significance of the proposed approach is demonstrated through comparisons with an existing approach and a static approach.