1. Introduction
With the shortage of energy and the increasingly severe environmental pollution in China, the issue of green development has aroused a growing attention from scholars. Implementing the green transformation for China entails very serious operations, especially for those resource-based cities [
1]. As an important cornerstone of China’s modern industrial system, resource-based cities have attracted a large number of heavy chemical enterprises with high energy consumption and high pollution because of their raw material advantages [
2]. They are not only the main suppliers of industrial raw materials and energy, but also the main undertakers of resource consumption and environmental damage. At present, China’s economy is in a critical period of transformation: upgrading industrial structure and moving towards a high-quality development level. Sustainable growth is one of the important internal requirements to achieve high-quality economic development. Therefore, the green transformation of resource-based cities is not only an important starting point for the transformation to high-quality development from a national level, but also an inevitable requirement for the sustainable development of cities themselves [
3]. The key lies in improving energy and environmental productivity, consuming less energy and discharging lower level pollutants as much as possible to achieve higher economic growth. Thus, in this context, scientifically measuring the energy environmental efficiency and productivity of resource-based cities, and exploring the linkages between energy consumption, economic output, and negative environmental impacts is of great significance to practice the transformation of green development mode, promote the sustainable development of resource-based cities, and encourage high-quality economic development.
Since the concept of total factor energy efficiency was put forward by Hu and Wang [
4], the measurement of energy efficiency in relevant researches has gradually changed from single factor indicators, such as energy intensity, to total factor indicators, in which comprehensive input factors such as capital and labor are also concerned. The main idea is to use the samples to build the technology frontier under the total factor framework, and therefore the gap between the actual input and potential minimum input of energy reflects inefficiency. There are often two methods to measure the inefficiency or efficiency: the stochastic function analysis (SFA) and data envelopment analysis (DEA); the latter is increasingly used in recent researches because of its deterministic frontier constructed and non-parametric characteristics, as well as its easy combination with the Malmquist index, by which the productivity can be evaluated further. At the same time, Chung et al. [
5] provided a viable approach to regard other bad outputs, such as environmental indicators, as undesirable outputs in the total factor framework, illustrating with the directional distance function (DDF) that it is feasible to measure energy environmental efficiency.
Combining different kinds of DEA and Malmquist models, a large number of papers have explored energy environmental efficiency and productivity, also called green efficiency and productivity [
6] or ecological efficiency and productivity [
7]. For environment quality assessment, Iram et al. [
8] utilized DEA to determine the efficiency of energy usage and its role in carbon dioxide emissions and economic-environmental efficiency for the economies of some Organisation for Economic Co-operation and Development (OECD) countries from 2013 to 2017. Bi et al. [
9] used slack-based DEA to investigate the relationship between fossil fuel consumption and the environmental regulation of China’s thermal power generation. Song et al. [
10] proposed a Ray slack-based model to evaluate provincial environmental efficiencies in China from 2004 to 2012. Halkos et al. [
11] integrated radial and non-radial efficiency measurements in DEA using the hybrid measure by considering good and undesirable outputs as separable and non-separable to estimate the efficiency of the power generation sector in the USA with the DEA window analysis. Wang and Feng [
12] evaluated the performance of China’s energy, environmental, and economic efficiency and its productivity growth therein from 2002 to 2011 by a developed slack-based measure based on global data envelopment analysis. Yang and Wei [
13] applied game cross-efficiency DEA to analyze the urban total factor energy efficiency of 26 Chinese prefectural-level cities from 2005 to 2015 under environmental constraints. Regarding research on resource-based cites, Li et al. [
14] used DEA model to evaluate the transformation development efficiency of Jiaozuo from 1999 to 2013. Based on the 2012 data from 116 resource-based cities in China, Li and Dewan [
15] measured efficiency in resource-based cities by using the Super-slack based model (SBM) model and analyzed its influence. Yan et al. [
16] analyzed the spatial variation in energy efficiency of 104 resource-based cities in China based on Super-SBM from an energy-economy-environment perspective. Tian et al. [
17] utilized the modified meta-frontier Epsilon-based measure (EBM) model to measure the CO
2 emission efficiency, comparing the performance between the Yangtze River Economic Belt (YREB) and non-YREB.
However, the models used in the aforementioned papers can hardly deal with the desirable output and the undesirable output asymmetrically in the efficiency measurement function. The hyperbolic distance function (HDF) is the exact one to solve this problem, but its non-parametric optimization model is non-linear, which is very difficult to solve especially with variable return scale assumption. Although Fare et al. [
18], the authors of this model, provide a rough estimation method, there are large errors in the results. In relevant studies [
19,
20,
21,
22]), the measurement of HDF is mainly solved by the parameter method, SFA, which is constructed based on transcendental logarithm function for regression estimation, depending on the model setting and hypothesis. That can also hardly analyze the scale effect. Fare et al. [
23] further proposed a linear iterative algorithm to estimate HDF using DDF, which improved the estimation accuracy under the original HDF model on the premise of satisfying the operational properties under the non-parametric DEA framework, but did not discuss the situation of including uncontrollable indicators and undesirable output. Zhang and Jiang [
24] argued that the relevant research on energy efficiency pointed out that some scholars failed to eliminate the influence of other factors such as capital and labor on the measurement of total factor energy efficiency, by which the measured efficiency can be also called both the total factor energy efficiency and the total factor capital and labor efficiency. That is to say, it failed to control the inputs other than energy in the model, which may lead to confusion on the concept.
Few studies have focused on the energy environmental efficiency of resource-based cities. Yu et al. [
25] applied a three-step material flow analysis (MFA) method to analyze the resource utilization efficiency, but only used Chengde in Hebei Province as a case. Li and Dewan [
15] used cross-sectional data for 2012 to measure the efficiency of China’s 116 resource-based cities but lacked analysis of time series. Wei et al. [
26] employed DEA model and Malmquist productivity index to measure the urban efficiencies of only 24 typical resource-based cities in China from 2000 to 2008. Related similar studies include those by Yan et al. [
16] and Liu and Meng [
27].
Most resource-based regions have suffered a lot from a series of development problems caused by the “resource curse”, such as experiencing long-term weak growth of gross domestic product (GDP), economic vulnerability, growing income gap in society, and more and more serious political corruption [
28,
29,
30,
31,
32]. In resource curse theory, resource dependence (RD) is the key conception to exert negative influence upon economic development, which reflects the importance of resource exploitation or resource industry in economic growth. In order to distinguish resource abundance, RD is commonly interpreted as the output elasticity coefficient of economic growth to resource input in the production function including resource factors [
33]. According to the “resource curse”, the energy environmental performance of cities may be affected by RD, implying cities with different RD should be treated differently when making policy. So how dose RD affect energy environmental efficiency in China?
Thus, in this paper, in order to measure the energy environmental efficiency and productivity changes scientifically and accurately, we propose a nonparametric linear estimation method of HDF model including uncontrollable index and undesirable output. To further provide empirical support for better policy-making for governments, by focusing on 107 resource-based cities in China, we divide the cities into three and four categories from the perspective of RD and region and discuss the performance of different types of cities.
The paper next is organized as follows: the research methodology applied in this research is illustrated in
Section 2, material is presented in
Section 3, followed by an empirical study in
Section 4, and the conclusions are presented in
Section 5.
2. Research Methodology
2.1. HDF Model with Environmental Technology
Assuming the production technology
T based on environmental technology which transforms a series of input vectors
into the desired output vectors
and the undesired output vectors
, the production possibility set
can be defined by
M,
S, and
L refer to the number of elements of
x,
g, and
b. Note that all elements of a vector which are shown in bold are non-negative real numbers. According to Cuesta et al. [
34], HDF based on environmental technology
:
can be set up as follows:
Taking DMU° as the decision making unit (DMU) under evaluation, is HDF technically efficient if and only if , while indicates its state of technical inefficiency which means increasing desirable output and reducing undesired output needed to improve efficiency. Having said that, cannot guarantee full Pareto–Koopmans efficiency because it is radially measured.
Traditional DDF measures the efficiency with the ray from the evaluated point to the projection point of the technological frontier, while HDF determines the projection point and measure efficiency along the hyperbolic path. There is also a difference between the two in the treatment of undesired outputs: Chung et al. [
5] proposed that the undesired outputs should meet the joint weak disposability constraints of the output combination in DDF, which indicates the reduction of undesired output must be at the cost of a reduction in desirable output, expressed as
, and it require an equal sign constraint on the undesired output in the optimal programming. The HDF model deals with the desirable output and the undesired output asymmetrically, which means that under the given input conditions, the HDF allows the output set to contain fewer desirable outputs and more undesired outputs, that is,
.
If the production set P(x) satisfies the usual axioms, has the following properties:
Approximate homogeneity: ;
Non-decreasing for weakly disposable desirable output: ;
Non-increasing for weakly disposable undesired outputs: ;
Non-increasing for strong disposable inputs: .
2.2. HDF for Energy Environmental Efficiency
In order to measure the efficiency including the energy factor, the energy input index
is introduced. The following technology sets
V can be defined by
When measuring the energy and environmental efficiency, the reducibility of other non-energy inputs should not be taken into account [
35]. The
EEE should be measured from three perspectives: reduction of energy input and undesirable output and expansion of desirable output. If non-energy input
x is set as strong disposable, energy input
e is set as weak disposable, and other indicators remain unchanged, then the
EEE can be defined by HDF
, which can be expressed as:
For DMU° which is under evaluation with the input-output vector
, the non-parametric DEA representation under variable return to scale (VRS)-based technology of
EEE can be represented as follows in optimal programming:
where
is the strength variable for constructing the convex combination of input-output indicators, and
is the ordinal number of DMUs. The model (5) measures the efficiency under the assumption of constant return on scale (CRS) when the convex combination constraint
is removed.
Note that the DEA model for measuring HDF distance is a non-linear programming, especially difficult to solve under the VRS assumption, and with no way to obtain the scale effect. Fare et al. proposed a non-parametric method of linear approximation to estimate HDF efficiency [
18], but Zofio and Lovell [
36] pointed out that the error of the approximation result will increase with the distance of the measured point from the technological frontier. That is to say, the lower the efficiency, the less reliable its approximate result. Fare et al. [
23] further proposed an iterative method based on linear approximation, using the approximate relationship between the DDF model and the HDF model, combining the characteristics of the dual model and the original constraints to perform iterative calculations, to control the error accuracy to obtain the final efficiency. Yet they only discuss the case where all indicators were weakly disposable, with no thought for uncontrollable variables and undesirable outputs. Following their idea, we will improve the approach to apply to the approximation of
EEE within the non-parametric framework of DEA.
2.3. An Improved Non-Parameters Approach for Estimating HDF
Model (5) can be expressed in a compact form as
where
represents the hyperbolic path with parameter
θ passing through DMU°, and
refers to the optimal solution of the model. Given
, it is well known that
by applying Taylor’s theorem. Accordingly, model (6) can be approximated using the following model
where
represents the straight path with parameter
passing through DMU°, and
refers to the optimal solution inside. In order to estimate
, we can utilize standard linear programming to rewrite the optimal model as follows:
where
.
Apparently this model (8) actually evaluates the DDF of DMU° with the particular directional vector . That is to say, HDF model is a special type of DDF model in a manner. With the help of relation between DDF and HDF, EEE the optimal solution based on HDF can be approximated by solving the DDF model. Yet the farther is to 0, the less accurate the approximated . In the light of Fare et al., an linear programming (LP)-based computational algorithm needs to be applied to obtain the exact value of .
The model (8) can be transformed into the following dual model:
where
refer to the transpose vectors of the shadow prices of
in turn, of which optimal values determine the gradient parameters of the supporting hyperplane of the technology set
V.
is a variable corresponding to convexity constraints, and its optimal value determines the type and size of returns to scale. By solving model (8) and model (9), a pair of dual solutions
and
can be obtained. Then
H1:
is a supporting hyperplane for
V at the projection point
; thereby, the equation for solving the intersection
of the hyperbolic curve
with hyperplane
H1 can be expressed as follows:
Let
, Equation (10) can be rewritten by:
The solutions of Equation (11) are as follows:
The next step is to test whether
can meet the constraint
Z1:
. Our approach is to start by constructing a non-parametric model for measuring DDF, as shown in model (12), where the original reference set
is used as the reference set,
represents the input-output vector of the unit
evaluated, and the direction vector of DDF is
.
The point is taken as the given input-output vector of the virtual to find the optimal solution of model (12). If γ∗ = 0, it means that the point is on the envelope of the technological frontier of V, and satisfies the constraint condition Z1, that is, is the final exact approximation of EEE. If , it indicates that does not satisfy the constraint condition Z1, and is outside the technology set, which means the following iteration algorithm needs to be implemented:
Reconstruct a new direction vector from DMU° to point : ;
Solving the DMU° for the DDF model (8) and its dual model (9) with d1 as the direction vector, we can get the second pair of dual solutions and , and then obtain another supporting hyperplane equation H2: for V;
Let the intersection of H2 and hyperbolic curve named , which satisfies the equation of the hyperplane H2, so we can get a model with the parameters and the unknown factor as the model (10). Then we solve the equation to obtain the value of ;
Constructing a new constraint test condition Z2: , which needs to test whether is the optimal HDF solution. If true, the iteration stops, otherwise it continues to reconstruct a new directional vector from DMU° to point , and returns to step 1.
2.4. Efficiency and Malmquist Index within Global Reference
Traditional DEA efficiency is evaluated by taking the DMU set of each year as the reference set, and there is a different technology frontier or reference standard for each year. Therefore, comparison of the efficiencies of the same DMU in different years can only reflect the relative distance change between the DMU and the technology frontiers of each year and cannot embody the absolute disparity of efficiency from year to year. In this paper, with reference to Pastor and Lovell [
37], the global energy and environmental efficiency (GEEE) is calculated, and the global Malmquist index is further calculated by GEEE to measure the change of energy and environmental productivity (EEP) under the framework of total factors.
To calculate GEEE, we only need to define the DMU sequence number set J in the DEA model as
, where
T is the number of periods of panel data and N is the number of DMUs per year. Unlike the geometric mean form of traditional Malmquist index, global Malmquist index takes the common frontier consisting of all DMUs each year as the reference set, and due to a single index, it satisfies the transitivity and can be multiplied cumulatively. The energy and environmental productivity changes (EEPC) from year t to year
t + 1 can be expressed as follows:
where
represents the energy and environmental efficiency of period
t under the global reference.
indicates that
has increased by
α% from
t to
t + 1 year, and also reflects absolutely the change of GEEE. In order to explore the internal causes of the change in EEP, EEPC under the CRS assumption can be decomposed according to Fare et al. [
38] as follows:
refers to the relative change of the technical efficiency within different frontiers each year, which reflects the changes in current technical application ability, resource organization, and management capabilities at the current scale.
represents the relative changes in the respective technological frontiers from year t to t + 1. It should be noted that the changes in technological frontiers here are measuring the change of the projection point of the DMU on the front surface, not the change of the overall front surface. Technological efficiency change (EC) (CRS) includes both changes in the practical capabilities of the current technology and changes in efficiency caused by changes in returns under scale changes. Therefore, EC (CRS) can be decomposed into two factors as follows:
refers to the pure technical efficiency after removing the scale effect, and represents the relative change in technical efficiency caused by scale factors.
3. Material
3.1. Subject Investigated
In 2013, the State Council of China issued the “National Resource-based City Sustainable Development Plan” (hereinafter referred to as the “2013 Plan”), which lists the 262 resource-based cities, and only distinguishes between mining and forestry, including 126 prefecture-level cities. This paper focuses on the cities based on exhaustible resources, selecting non-forest prefecture-level cities from the list, excluding the two special resource cities of Zigong (Salt) and Jingdezhen (Ceramics) and another city Bijie (promoted to a prefecture-level city in 2011); then 107 resource-based cities are identified as the subject investigated.
3.2. Data Sources and Description
In order to evaluate the GEEE and energy environmental productivity change (EEPC), we took capital stock and labor as non-energy input
x, energy consumption as energy input
e, actual regional GDP as desirable output
g [
16,
39], and three waste emissions as undesired output
b. The selection and processing of input-output indicators are as follows:
Capital stock (k). The capital stock of prefecture-level cities is estimated by using the perpetual inventory method. The basic formula is , where and are the nominal value of fixed investment and investment price index in the year t, and δ is the depreciation rate. Due to the lack of prefecture-level investment price index, we used the fixed asset investment price index of the province where the prefecture-level city is located as a substitute, and δ is defined by 5%. To calculate , the capital stock in the base year ( also needs to be evaluated, and it can be calculated by the formula , where refers to the investment in the base year and g is the average growth of real fixed asset investment from 2003 to 2016.
Labor input (l). We used the total number of employees at the end of the year, that is, the total number of employees in the unit of the city and the total number of private and individual employees in the city as the total labor input of the prefecture-level city.
Energy consumption (e). There is a high correlation between power consumption and energy consumption, and power consumption can be used as an alternative to regional energy consumption. Due to the limited data of the consumption of fossil energy such as coal and oil in all prefecture-level cities, the power consumption of prefecture-level urban areas is used as the approximate replacement of the city’s energy consumption. Unit: kilowatt-hour
Gross regional product (g). We took 2003 as the base year to carry out price adjustment and calculate the actual GDP of prefecture-level cities each year as the desirable output.
In terms of three wastes, the cities’ industrial sulfur dioxide emissions (s), wastewater emissions (w), and soot emissions (d) are selected as the measures of undesirable output with equal weight.
All data mainly comes from China Urban Statistical Yearbook, Easy Professional Superior (EPS) database, and Statistical Bulletin of National Economic and Social Development of cities. In addition, the data of abnormal changes between years and changes in some urban divisions during the investigation period are modified to ensure the reliability of the data. In this paper, R language is used to program the HDF iterative model mentioned above to evaluate GEEE and EEPC as well as the relevant decomposition results. Descriptive statistics of input-output variables from 2003–2018 are shown in
Table 1.
5. Conclusions and Enlightenment
Efficiency is a vital element in order to achieve the benefits of rich regional resources [
41]. The hyperbolic distance function (HDF), different from other DEA models, considers both the desirable output growth and the undesirable output reduction asymmetrically. Based on the idea of Fare et al. [
23], this paper proposes an LP iterative algorithm to estimate HDF, which includes undesirable output and uncontrollable index. The energy environment efficiency and productivity change and decomposition of resource-based cities are calculated under the global reference framework and are analyzed by the classification of RD and region. The main conclusions are as follows: (1) On the whole, the annual growth rate of energy and environmental productivity of resource-based cities in China is 2.6%, which is mainly due to technological changes. Work by Zhang et al. [
42] also show that technical changes are the dominant factors behind productivity change for China’s cities. The decline of relative technological efficiency hinders the further growth of productivity, and scale factor is the main reason for the decline of technological efficiency. (2) For the classification of RD, the energy and environmental efficiency of high-dependent group is significantly lower than that of the medium and low group. Using province-level data, Cheng et al. [
43] also found that the more abundant a province’s natural resources, the lower the green total factor productivity, similar as Wang et al. [
44]. The energy and environment productivity of the medium group has the highest growth. The regression of relative pure technical efficiency and scale diseconomy hinders the growth of productivity of the high-dependent group. (3) For classification of regions, the middle and west perform worse than the east and northeast. The east has the highest energy and environment efficiency, while the northeast has the fastest growth rate of productivity. Both the static efficiency and the dynamic change in the middle region show the phenomenon of “collapse in the middle”, and the great retreat of relative pure technical efficiency is the main reason for its low productivity growth. (4) The city division based on the static efficiency and the dynamic productivity change shows that the advantages and disadvantages of different resource-based cities in terms of energy and environmental productivity are obviously different, which needs to be concerned in the process of policy-making.
Based on the above research, this paper has come to the following conclusions: (1) The empirical results strongly show that since 2013, the supply side structural reform of China with the main purpose of improving TFP has achieved remarkable results, and the energy and environmental efficiency and productivity growth rate of resource-based cities have been greatly improved. But there is still much room for improvement, consistent with the findings of Yan et al. [
16]. We should continue to promote relevant reform unswervingly, but more attention needs to be paid to the practical application of technology and the insufficiency of resource allocation management efficiency. (2) Low relative technical efficiency and uneconomical scale are the main reasons for the poor performance of high-dependent cities in energy and environmental productivity, which also shows that RD may have a negative impact on energy and environmental efficiency. In addition, the problem of “middle collapse” also needs to attract the attention of governments. Similarly, Wang and Chen [
45] also found that the central and western regions have a significant “resource curse” effect in the context of eco-efficiency, in which natural resource endowment significantly inhibits the growth of regional eco-efficiency, mainly manifested by natural resource endowment to human capital and other industries. (3) Combining the classification of static efficiency and dynamic change is helpful to accurately understand the current situation of energy utilization and environmental protection efficiency of each resource-based city. Based on the classification and guidance of sustainable development of resource-based cities, it is necessary to further implement city-specific policies [
46].