Bank efficiency estimation considering enterprise risk: entropy meta two parallel three-stage dynamic DDF model

This research sets up a new DEA model, Entropy Meta Two Parallel Three-Stage Dynamic DDF, to evaluate the efficiency of 42 banks in China over the period 2019–2023. Different from other studies, we integrate enterprise risk into the efficiency analysis framework, account for the stage characteristics of banks (enterprise risk, operation, sustainability, and market), exploring the changes in heterogeneous bank efficiency. The findings are as follows. (a) Most banks show positive growth in total efficiency. (b) The enterprise risk stage efficiency generally rises with a slight fluctuation, the operation stage efficiency is at a relatively high level, 70% of banks have superior performance in sustainability stage, and 80% of banks still have not achieved superior market efficiency. (c) There is a negative correlation between enterprise risk and operational stage efficiency and a positive correlation between sustainability stage and market stage efficiency. The systems exhibit a high degree of coupled coordination. (d) Most banks have higher operational efficiency than sustainability efficiency and higher sustainability efficiency than market efficiency. State-owned commercial banks have the strongest risk resistance and perform optimally in different stages. Lastly, we note that joint-stock commercial banks must pay attention to the sustainability stage and market stage efficiencies, urban commercial banks should target to improve market stage efficiency, and rural commercial banks need to focus on enhancing enterprise risk stage efficiency.