Abstract:

The DEA-Malmquist index method combines the DEA method with the Malmquist index method， which does not need to set the specific form of the production function in advance， and is particularly suitable for the analysis of multi-input and multi-output production systems. Thus， this method has been widely used in total factor productivity measurement. However， for input-growth production systems， the missing data for some smaller or larger parts of inputs can cause the systematic bias in the DEA-Malmquist index measurement results. Therefore， from the perspective of production possibility set modification， it is important to study the techniques to modify and supplement missing data to modify the measurement bias of the DEA-Malmquist index method.In general， it is common that the input-output data of decision-making units （DMUs） keeps increasing with the continuous economic and social development. Moreover， the DEA-Malmquist index method is constructed based on the distance function， and the measure of the distance function has to be based on the C2R model， BC2 model and their corresponding inter-period comparison model. Therefore， when comparing DMUs across periods， there may be the cases of missing data for smaller inputs in the current period （data short tails） and missing data for larger inputs in the previous period （data short heads）. Among them， the missing data for smaller inputs will cause the problem of non-feasible solutions for the DEA-Malmquist index method， while the missing data for lager inputs will directly cause the overall bias of the calculation results of DEA-Malmquist index method. Therefore， in order to ensure the accuracy of the calculation results of DEA-Malmquist index method， it is necessary to construct a frontier restoration technique to modify the production possibility set in the traditional DEA-Malmquist index method.Through the empirical analysis， it is found that the method proposed in this paper can not only effectively modify the measurement bias of the traditional DEA-Malmquist index method， but also solve the problem that there is no feasible solution. In addition， the proposed method in this paper provides a new idea for the theoretical research of DEA-Malmquist index method， and also provides an effective tool for the measurement of total factor productivity.

Key words: DEA-Malmquist Index, total factor productivity, data envelopment analysis, short tail phenomenon of data, short head phenomenon of data