| Currently, environmental problems are becoming one of major problems to hinder socio-economic sustainable development. How to solve the environmental problems effectively and to stop the environment becoming worse has aroused great concerns from many experts and scholars worldwide. Therefore, the relevant technical issues of research and improvement of the environmental efficiency evaluation will promote the development of the academic frontier; meanwhile, it will provide support to realize the binding indicators of energy-saving and emission-reduction in China’s“Twelfth Five-year Plan”. As DEA method has the advantages of being simple, practical and it doesn’t need pre-determined the weight coefficient of input and output indicators, the international academic highly concerned about this topic since it was proposed in 1978. The practical DEA model has been developed and enriched all the time and DEA becomes more and more widely used in efficiency evaluation in all kinds of systems. And it has gradually been formed as a new area of cross research on mathematical, economics and management science and been well developed. Therefore, after the DEA-based environmental efficiency evaluation method was first proposed in 1989, many domestic and foreign scholars have taken it as an important research direction.In environmental efficiency evaluation, how to measure the undesirable outputs is a critical aspect, because the traditional DEA efficiency model assumptions on the maximization of output can’t be applied when we consider the undesirable outputs. However, some results in solving methods and handling the relationship among variables still have some shortcomings. Modifying and improving existed undesirable outputs of DEA model can increase the accuracy of evaluation results and broad the scope of model application, in order to serve the practice better. In addition, the existing DEA efficiency evaluation axiomatic framework fails to fully consider the parameters of structural features. The existing system only based on some of the most suitable natures (such as convexity and monotony etc.). Therefore, the effects of efficiency evaluation process are relatively insubstantial, which restricts the development of DEA method to a certain extent.Based on the axiomatic theory of productive efficiency, this article will provide a more stable and accurate DEA method for evaluation system of environmental efficiency, build a complete model of the statistical tests, and apply it in evaluation problems of environmental efficiency which is concerned worldwide and need to be solved. By combination of theory and practice, some researches are carried out in this article as following:(1) As one of front research fields of efficiency analysis, DEA efficiency model considering undesirable outputs has important and appropriate values to environmental efficiency assessment. This article, focusing on the theory of DEA efficiency model considering undesirable outputs and evaluation systems based on it, sort outs the research about environmental efficiency assessment at home and abroad. The article also reviews the progress of the theory and application of efficiency analysis, explores the achievements of the theoretical and objective basis of environmental policy analysis, and searches their possible shortcomings. The future research direction is forecast as well.(2) Production process of desirable outputs often produces by-products, which have harmful effects on the environment. However, traditional DEA models cannot measure efficiency evaluation of these undesirable outputs. This article gives an improved DEA-SBM model, named ISBM-DEA, and constructs an illustration to compare it with slacks-based measured DEA model. The results show that computing conclusions of the new model are highly related to the efficiency assessment of DEA-SBM model, and it has more focus on the affects of undesirable outputs on production efficiency than the latter, which means this new model has more extensive value for application.(3) Although CCR-SBM model achieves some good results in solving undesirable outputs, its still cannot settle the“congestion”problem of outputs. Based on the axiomatic theory of productivity, this article sets out a systematic research of the CCR-SBM model considering undesirable outputs and further expands the CCR-SBM model from the point of network analysis, by which the new model can not only carry out efficient evaluation considering undesirable outputs, but also solve the“congestion”problem of outputs. The illustration shows that the efficiency values obtained from network CCR-SBM model are lower than the classical SBM model, and can achieve a more profound analysis of the efficiency focusing on environmental impact.(4) It is one of the issues of current concern for international researches engaged in DEA that how to achieve more accurate results of environmental efficiency evaluation. A new DEA model on environmental efficiency evaluation considering non-radial and bi-objective is established, from which it is transformed as a single objective linear programming problem to find the maximum by linear weighted plus. The results illustrates that this new model can not only analyze the effectiveness of DEA and the relationship between it and Pareto Optimality, but also obtain adjustable volumes of inputs and outputs by using the“projection”of decision making units. The conclusions of subsequent empirical analyses are highly consistent with the very reality in China, which indicate that this new model promotes the accuracy of environmental efficiency evaluation.(5) To construct an improved non-parametric DEA efficiency model which considers undesirable output,shadow price and ineffective decision-making units, this article establishes a non-parametric DEA efficiency model which takes undesirable output into account, demonstrates the effective necessary and sufficient condition of DEA from the perspective of shadow price, and calculates improvable amount of invalid DMUs. Then, based on an example, this article makes an empirical analysis. Comparing the new model with the classical SBM model shows that their correlation coefficient is more than 0.9. At the same time, the new model has some excellent characteristics which are not owned by SBM model. This new non-parametric method can measure the level of environmental efficiency; also, it need not to establish the normative function form beforehand, nor need to consider measurement unit of index data, which means the method has unique advantages.(6) Production function of the desirable outputs and undesirable outputs are constructed in this article, and non-convex nonparametric least squares estimation considering undesirable outputs is studied. Whenαi 1 ,βi′1 ,αi2,βi′2 are given, explicit expression of f and g can be obtained. According to DEA considering undesirable outputs and CNLSUO, relationship between the two fitting curves can be calculated. For the actual outputs of each unit, the estimation of CNLSUO is never larger than that of DEA. Empirical analysis shows that the DEA estimation considering desirable and undesirable outputs is good. The analysis of statistical properties of methods for environmental efficiency evaluation, including least squares estimation of DEA considering undesirable outputs is bound to expand the scope of non-parameter statistical properties of DEA, which promote the further integration and development of Statistics and Operations.(7) This article is also doing some empirical analysis of quantitative relations among government regulation, technological progress and regional environmental efficiency of China. After calculating regional environmental efficiency of China in four time points, being 1992, 1999, 2007 and 2009, the concept of DEA decomposition and its calculating algorithm are first proposed. The article decomposes sub-provincial environmental efficiency of three setting periods from government regulation and technological progress. The results show that the efforts of government regulation on environmental efficiency spread from south area to north area, the efforts of technological progress spread from east area to west area. This is to verify the two propositions of the theoretical analysis. Therefore, government should take effective measures to increase government regulation on environmental issues in central and western provinces, and to promote advanced technology transfer from the eastern region to the central and western provinces as soon as possible in order to improve the overall efficiency of China’s environment. In addition, establishing statistical systems of multidisciplinary collaborative management of the environmental efficiency will accelerate this process.In addition to above research results, some frontier issues worthy of further study in this field have also been pointed out in this article. |
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