The Theoretical Relationship between the CCR Model and the Two-Stage DEA Model with an Application in the Efficiency Analysis of the Financial Industry

Since Charnes, Cooper, and Rhodes introduced data envelopment analysis (DEA) in 1978, later called the DEA-CCR model, many studies applied this technique to different fields. Based on the original CCR model, many modified DEA models were developed by researchers. Since 1999, Seiford and Zhu presented a two-stage DEA model. Later, these models were widely used in many studies. However, the relationship between the efficiency scores that are obtained from the original CCR model and the two-stage DEA model remains unknown. To fill this gap, this study proposed a theoretical relationship between the efficiency scores that are calculated from the two-stage DEA model and those that are obtained from the original CCR model. How the sets of nonsymmetrical weights affected the efficiency scores were also investigated. Theorems regarding the relationship were developed, and then the model was utilized to evaluate the two-stage efficiency scores of the insurance companies (non-life) and bank branches. The results show that using a two-stage DEA model can get more information about operational efficiency than the traditional CCR model does. The findings from this study about the two-stage DEA technique can provide significant reasons for using this model to evaluate performance efficiency.