Operating efficiency assessment of commercial banks with Cooperative-Stackelberg hybrid two-stage DEA

The two-stage Data Envelopment Analysis (DEA) is widely applied to assess the efficiency of commercial banks in recent years. Even though this approach well simulates the sequence of bank’s production process, the independent operations within sub-stage are generally ignored, and the cooperative or non-cooperative relations between sub-stages are usually investigated separately. Commercial banking production system, however, has complex internal structure within which parallel and series structure can co-exist, and cooperative relations may concurrently occur with non-cooperative ones. In this paper, we develop a hybrid two-stage DEA to simultaneously consider the series-parallel internal structure and the cooperative-Stackelberg relations between sub-stages. The data of 19 Chinese listed commercial banks are used to show the abilities of the proposed models. This approach represents a powerful and flexible efficiency measurement implement that can be applied when the system in question has a complex internal structure in terms of both sub-systems features and sub-systems relations.