A Comparative Study On Cross-efficiency Evaluation And Empirical Analysis

Data Envelopment Analysis (DEA) is introduced by Chames, Cooper andRodes in1978. It is a nonparametric method of measuring the efficiency ofdecision-making units (DMUs) with the same multiple inputs and multipleoutputs in the absence of market prices. The concept of cross-efficiency evaluationwas first proposed by Sexton，Silkman and Hogan in1986. Since it requests eachDMU not only to be self-evaluated but also to be peer-evaluated, it is an extension ofthe DEA basic methodology and can evaluate the performances of decision-makingunits better.In this paper, we introduce the basic knowledge of data envelopment analysisfirstly. Then we introduce some cross-efficiency models including the aggressivecross-efficiency model and the benevolent cross-efficiency model that are proposedby Doyle and Green in1994, the Game cross-efficiency model proposed by LiangLiang and Jie Wu in2008, and the neutral cross-efficiency model proposed byYing-Ming Wang and Kwai-Sang Chin in2010, conduct a comparative study on themand reveal their advantages and disadvantages. To make up their deficiencies wepropose two improvement measures, and then establish the double-frontier dataenvelopment analysis aggressive zero weights restricted cross-efficiency model, thedouble-frontier data envelopment analysis zero weights restricted benevolentcross-efficiency model, and the double-frontier data envelopment analysis gamezero weights restricted cross-efficiency model, and provide a simple numericalexample to validate them. Finally, we use the double-frontier data envelopmentanalysis aggressive zero weights restricted cross-efficiency model and thedouble-frontier data envelopment analysis zero weights restricted benevolentcross-efficiency model to evaluate the performances of12listed commercial banks inchina.