Efficiency evaluation for banking systems under uncertainty: A multi-period three-stage DEA model

Efficiency evaluations are vital for banks so that they can determine their future development and enhance their competitiveness. To comprehensively explore a bank’s internal structures and identify the specific reasons for any inefficiencies, three stages of banking systems need to be examined; capital organization, capital allocation, and profitability. To measure the efficiencies over consecutive periods, this paper developed a multi-period, multi-stage DEA model, in which unused assets were carried over to subsequent periods, fixed assets and employee salaries were regarded as shared inputs for all three stages, and non-performing loans, which were characterized using triangular type-2 fuzzy numbers, were introduced as undesirable outputs to reflect credit risk. The developed model was applied to a case study to evaluate the efficiencies of listed Chinese commercial banks from 2014 to 2016, from which a disparity in efficiencies was found; that is all banks were found to be generally inefficient; however, the inefficiencies occurred in different stages for different types of banks. Varying optimistic-pessimistic attitudes were applied to identify the overly sensitive banks and comparisons were conducted to provide managerial insights and verify the superiority of the proposed model. It was concluded that to enhance overall efficiency, banks need to have a reasonable business scale, that adopting a three-stage analytical framework can better identify efficiencies and the weaker stages, and that neglecting carryovers can overestimate bank performance.