A NEW MALMQUIST PRODUCTIVITY INDEX BASED ON SEMI-DISCRETIONARY VARIABLES WITH AN APPLICATION TO COMMERCIAL BANKS OF CHINA

The Malmquist productivity index studies productivity change, that is, the technical progress or regress together with the efficiency changes over time. In a nonparametric framework, the index can be estimated by data envelopment analysis (DEA). In this paper, first all inputs are divided into three groups, namely, discretionary variables, nondiscretionary variables, and semi-discretionary variables, and then a mixed integer linear model is proposed to deal with semi-discretionary variables. The proposed models consider not only the properties of semi-discretionary inputs, but also the relationship between them and other inputs. By introducing such a relationship and the preferences of decision-makers (DMs), the models aid DMs in generating efficiency scores and finding proper benchmarking points. Finally, the Malmquist productivity index combining the proposed model is computed and illustrated by an empirical application to the evaluation of 17 branches of Bank of China in Anhui Province. The results show a slight decrease in productivity during the year 2007/2008, and the productivity change positively during 2008/2009 due largely to efficiency increase.