Abstract: DEA (data envelopment analysis)is an empirical method which is used to evaluate the relative effectiveness of decision-making units (DMUs). The DEA has long been applied to assess operational performance in public and private sectors and a two-stage DEA method has been developed. Relative to the traditional DEA approach, two-stage DEA method has the advantage that it can not only provide the overall efficiency values of the evaluated objects, but also the values of each stage. But because of the existence of intermediate elements, two-stage DEA method can not follow the way which the traditional method does to adjust the inputs and outputs of the optimization process to project onto the effective frontier. Based on two-stage DEA method, by adding "virtual intermediate elements",we embed a "virtual stage" into the stages. Thus we can not only improve the logical structure of two-stage DEA, but also yield a frontier projection successfully. We apply the method to accomplish empirical analysis of operating performance of listed banks in China stock market. The empirical results surprise us that the operating performances of state-owned commercial banks are superior than the joint-stock banks.

Key words: two-stage DEA, effective frontier, virtual intermediate elements, virtual stage