Scientific determination of energy and environmental efficiency and productivity is the key foundation of green development policy-making. The hyperbolic distance function (HDF) model can deal with both desirable output and undesirable output asymmetrically, and measure efficiency from the perspective of "increasing production and reducing pollution". In this paper, a nonparametric linear estimation method of an HDF model including uncontrollable index and undesirable output is proposed. Under the framework of global reference, the changes of energy environmental efficiency and productivity and their factorization of 107 resource-based cities in China from 2003 to 2018 are calculated and analyzed. With the classification of resource-based cities by resource dependence (RD) and region, we discuss the feature in green development quality of those cities. The results show that: (1) On the whole, the average annual growth rate of energy and environmental productivity of resource-based cities in China is 2.6%, which is mainly due to technological changes. The backward of relative technological efficiency hinders the further growth of productivity, while the scale diseconomy is the main reason for the backward of relative technological efficiency. (2) For the classification of RD, the energy and environmental efficiency of the high-dependent group are significantly lower than the other two, and the growth of productivity of the medium-dependent group is the highest. (3) In terms of classification by region, the energy and environmental efficiency of the eastern region is the highest, and that of the middle and western regions is not as good as that of the eastern and northeastern regions. The middle region shows the situation of "middle collapse" in both static efficiency and dynamic productivity change, and the main reason for its low productivity growth is the retreat of relatively pure technical efficiency. This conclusion provides practical reference for the classification and implementation of regional energy and environmental policies.
Keywords: HDF; data envelopment analysis (DEA); energy and environmental productivity; green development; hyperbolic distance function; resource-based city.