1. Introduction
With globalization, China has accelerated melting into the world economy after entering World Trade Organization (WTO) and has become a world factory in international division with rapid economic growth. However, this growth is mainly driven by development within the energy-intensive industrial sector [
1]. According to the British Peroleum (BP) Statistical Review of World Energy 2017 [
2], China is currently the world’s largest energy consumer at 23% of the total global consumption and 27% of the demand growth of global energy consumption in 2016. However, China has paid a high price to the environment for such rapid advancement. Uncontrolled fossil fuel combustion has released harmful substances in various forms and led to all kinds of pollutions [
3], e.g., water contamination, acid rain, and haze (smog). Large loads of waste gases have been emitted into the atmosphere to create a severe decline in air quality.
China has suffered from a severe haze over many of its cities comprised of fine particulate matter less than 2.5 micrometers in diameter (PM
2.5), especially in winter months, since 2013 [
4,
5]. In 2016, only 84 Chinese cities had standard air quality—this amounts to merely 24.9% among the 338 monitored cities at or above the prefecture level (Report on the State of China’s Environment in 2016 [
6]). Pollution severely affects Chinese citizens’ daily living conditions and, ultimately, threatens their health. Epidemiological studies have revealed a strong association between exposure to fine particulate matter and mortality [
7,
8]. Many environmental laws and regulations have been enacted to combat this, including China’s State Council’s
Action Plan for Air Pollution Prevention and Control (One could refer to
http://www.gov.cn/zwgk/2013-09/12/content_2486773.htm for more details.) targeting air quality in September 2013. One goal of the Action Plan is to reduce the average concentration of fine particulate matter by 25% in the Beijing-Tianjin-Hebei region by 2017 against the 2012 level (80
). Measuring energy efficiency and environmental efficiency can provide quantitative information for energy and environmental policy analysis and decision-making. Cities are not only places of high energy consumption, but also form the main sources of various pollutants. Cities, to this effect, are the main area for controlling pollutant emissions. It is essential for administrators to understand the energy and environmental performance (EEP) of their cities to formulate scientific, strategic goals for energy conservation and emission reduction.
In recent years, the data envelopment analysis (DEA) linear programming method has become a popular approach to measuring energy and environmental efficiency to reduce energy consumption and control emissions. DEA was proposed by Farrell [
9] and developed by Charnes, et al. [
10] to automatically generate appropriate production functions to combine multiple inputs and multiple outputs. The principle of DEA is to enable data to “speak for itself” rather than require excessive artificial parametric assumptions for functions [
11]. With this approach, we only need to collect the values of variables for inputs and outputs to establish production frontiers without priori assumptions for functional forms. The automatically generated production frontiers make it possible to measure the distance from an observed decision-making unit (DMU) to projected production frontier, which determined by the efficient DMUs and with which the distance is defined as inefficiency measurement. Therefore, this advantage provides a simple way to measure the inefficiency of DMUs (i.e., ones which are under the production frontier) through measuring its distance to the referred production frontier. Many previous researchers have studied energy efficiency; Hu and Wang [
12], for example, first established the total factor energy efficiency (TFEE) concept by using DEA. Song, et al. [
13] used a bootstrap-DEA approach to find that China’s energy efficiency has maintained a slow upward trend from 1992 to 2010. Özkara and Atak [
14], and later Feng and Wang [
15], measured total-factor energy efficiency and energy savings potential in Turkey’s manufacturing industry and China’s provincial industrial sectors, respectively. Zhou, et al. [
16] proposed an output-specific energy efficiency estimating method. These researchers concentrated on static analysis without dynamic comparison. Honma and Hu [
17] investigated the dynamic changes in energy efficiency by introducing a Malmquist productivity index (MPI). Other researchers, such as Wang and Zhou [
18], Chang and Hu [
19], and Zhang, et al. [
20] have made dynamic analyses of energy efficiency as well.
Beside above energy efficiency evaluation models, researchers focused on securing as many desirable outputs as possible while minimizing the undesirable outputs which are inevitably produced by industrial production. Färe, et al. [
21] first proposed the concept of environmental DEA technology to incorporate undesirable outputs into efficiency evaluation frameworks. Kuosmanen and Kortelainen [
11] applied DEA to aggregate multiple undesirable outputs and emphasized the trade-off between economic production and environmental protection in regards to the impact of undesirable outputs on the economy. Kortelainen [
22] extended the static framework to a dynamic environmental performance analysis by using MPI; they decomposed the changes in environmental performance into two components: relative environmental efficiency change and relative environmental technological change.
Many previous researchers have used the radial DEA approach to measure environmental performance, where different undesirable outputs are adjusted by the same proportion. However, radial efficiency measures overestimate technical efficiency due to the existence of nonzero slacks. A series of non-radial DEA models have been developed to resolve this limitation. For example, Zhou, et al. [
23] employed a non-radial DEA approach to measure the environmental performance of OECD countries. Zhang and Choi [
24] explored total-factor carbon emission performance in China’s fossil fuel power plants using a metafrontier non-radial MPI. Rashidi and Saen [
25] calculated the pure eco-efficiency of OECD countries by a non-radial DEA model based on green indicators. Sueyoshi and Goto [
26] applied a non-radial DEA environmental assessment to evaluate the performance of coal-fired power plants in the northeast United States. Xie, et al. [
27] computed environmental efficiency based on a directional distance function with the radial and non-radial slacks of outputs.
There are two major approaches to estimating productivity or efficiency changes: the Malmquist productivity index and Luenberger productivity index. Some researchers assert that the Malmquist productivity index overestimates productivity changes compared to the Luenberger [
28,
29]. Further, the Luenberger productivity index is a difference-based index, so it is well applicable to measuring differences in EEP. Recent researchers have adapted the Luenberger productivity index to study dynamic changes in productivity or efficiency. For instance, Mahlberg and Sahoo [
30] applied non-radial decompositions of the Luenberger productivity index to analyze the eco-productivity performance behavior in 22 OECD countries. Based on a Luenberger environmental index, Azad and Ancev [
31] measured the relative environmental efficiency of agricultural water use to reveal substantial variations across different regions. Wang [
32] applied the Luenberger index to explore changes in energy and environmental productivity at the provincial level. Our research team developed a non-radial Luenberger productivity index to resolve the limitation of radial measurement [
33,
34]. Non-radial efficiency measures can help us identify specific effects and contributions of energy factor and specific undesirable outputs, while radial efficiency measures do not reflect the impact of emission structures on efficiency changes.
The aforementioned studies focused on single aspects of energy efficiency or environmental performance rather than integrated EEP measurements. A few researchers have investigated the integrated EEP by new DEA models. Wang, et al. [
35], for example, used DEA window analysis to find that EEP is highest in the eastern area of China compared to other regions. Zhou and Wang [
36] explored the energy and CO
2 emission performance for over 100 countries by using a new directional distance function (DDF). Zhou, et al. [
37], Vlontzos, et al. [
38], Meng, et al. [
39], Geng, et al. [
40], Wang and Zhao [
41], and Perez, et al. [
42] measured integrated EEP in their respective studies. The researchers mentioned above have tended to focus on the regional or national level and lack of research down to the city level, though cities play an important role in environmental governance. Cities are responsible for 75–80% of global greenhouse emissions [
43,
44]. Only a few researchers, e.g., Li, et al. [
45], Yuan, et al. [
46], Wang, et al. [
47], Zhou, et al. [
48], and Guo, et al. [
49] have explored environmental performance at the city level.
In the present study, we extended the existing research in two main aspects. In terms of methodology, we proposed an additive DEA model combined with a slack-based measure and non-radial directional distance function as first developed by Färe and Grosskopf [
50]. The Luenberger productivity index with an additive structure is used to measure changes in productivity (which differs from the Malmquist index with multiplicative structure). We established a biennial Luenberger index extended from biennial Malmquist index proposed by Pastor, et al. [
51] to avoid infeasible solution of DEA. In terms of indicator selection, we properly account for multi-undesirable outputs and compare these sub-performances. We also use the natural breaks method [
52] to identify break points by picking the class breaks which maintain the greatest similarity in one class but maximize the difference among different classes. Geographical location has a marked effect on the emission abatement potential, so we alter the traditional regression to geographically weighted regression (GWR) to allow our estimated coefficients of influencing factors to vary by location.
The current our study is different from that of Picazotadeo, et al. [
53], which focused on ecological-economic performance based on the Pressure Generating Technology (PGT) rather than environmental production technology. The current our study also differs from that of Wang and Wei [
33], which explored the energy and environmental productivity change at the provincial-level by using Luenberger index and decomposed the energy and environmental productivity into four sub-indicators: Luenberger pure efficiency change, scale efficiency change, pure change in technology and change in returns to scale of technology. They analyzed energy input-specific and environmental productivity change without taking the undesirable output-specific performance into consideration. The current our study also differs from that of Zhou, Wang, Su, Zhou and Yao [
48], which studied the change of industrial energy conservation and emission reduction according to the Malmquist index and only considered one undesirable output (CO
2). The three aforementioned research teams may not avoid infeasible solution of DEA when dealing with inter-temporal data. Our study first attempted to analyze undesirable outputs and energy inputs performances at the city level in China with a biennial Luenberger index to avoid infeasibility. The remainder of this paper is organized as follows.
Section 2 presents the non-radial DEA model, decomposition method, and GWR estimation.
Section 3 explains our data sources and presents our results with discussion.
Section 4 summarizes our main conclusions and makes policy recommendations based on empirical results.
2. Methodology
2.1. Biennial Energy and Environmental Production Technology
Consider a production process with the vectors of non-energy inputs (
), such as labor and capital input, and the vectors of energy inputs (
) to produce the vectors of desirable outputs (
) and undesirable outputs (
). The corresponding production set, called the energy and environmental production technology set, is:
In the energy and environmental production technology set
, inputs and desirable outputs are assumed to be strongly disposable.
satisfies two additional assumptions proposed by Färe, Grosskopf, Lovell and Pasurka [
21] to model a production technology that includes both desirable and undesirable outputs.
- (1)
Weak disposability assumption: If and , then . It means that we can not reduce undesirable outputs alone while keeping the desirable outputs constant. In practice, it is feasible to reduce the desirable outputs and undesirable outputs at the same time; undesirable outputs can be abated at the cost of a decrease in desirable output.
- (2)
Null-jointness assumption: If and , then . Production must cease entirely in order to fully eliminate undesirable outputs.
It is unlikely to find a concrete production function which depicts the energy and environmental production technology set
. Here, we use nonparametric DEA technology to approximately represent
with piecewise linear combinations of the observed data. On the assumption of constant returns to scale (CRS), the energy and environmental production technology
can be estimated as follows:
where
is the intensity variable that ensures the technology set
is bounded and closed. The first three inequality constraints indicate the strong disposability on inputs and desirable outputs (strong disposability means that increasing input will not decrease the output). To ensure technology set
satisfies the weak disposability and null-jointness assumptions, the equality constraint is imposed on undesirable outputs.
Technology is generally stable in the short run, so we neglect technological changes from period “
t” to “
t + 1”, and combine technology set
and
together as
, namely, biennial energy and environmental technology, which represents the comprehensive technology shared by periods “
t” and “
t + 1”. In order to estimate
, we use observations from periods “
t” and “
t + 1” to construct the biennial energy and environmental DEA technology
as-formed by following linear constraints:
Model (3) can avoid infeasible solutions to the DEA model when dealing with cross-period data. Based on
, we propose a biennial Luenberger productivity index derived from the concept of the biennial Malmquist productivity index [
51].
2.2. Biennial Luenberger Energy and Environmental Performance Index
The Luenberger productivity index deduced by directional distance function (DDF) was first proposed by Chambers, et al. [
54]. The DDF allowing the simultaneous evaluation of input contractions and output expansions can be defined as:
where
is the directional vector.
Based on the Luenberger productivity index, the EEP change can be decomposed into energy and environmental technical efficiency change (catch-up effect) and energy and environmental technological change (frontier-shift effect). For the biennial periods “
t” and “
t + 1”, we first select technology in the period “
t” as the benchmark and then examine the EEP change by the difference in DDFs from periods “
t” to “
t + 1” referred to technology set
. Energy and environmental performance index (EEPI) used to measure the EEP change is defined as follows:
Similarly, EEPI can be defined with regard to the technology of the period “
t + 1”:
We compute the simple arithmetic mean of Equations (5) and (6) to eliminate the bias derived from arbitrary period selection:
The energy and environmental technical efficiency is defined by the differences in DDFs from period “
t” to “
t + 1” with respect to their own technologies; this reveals the change in distances of one observation in two periods “
t” and “
t + 1” to the corresponding frontier of technologies “
t” and “
t + 1” respectively.
The energy and environmental technological change can be measured by comparing the distance from one observed data point in the period “
t” to the frontier of technology set of periods “
t” and “
t + 1” respectively, which measures the distance between two technologies “
t” and “
t + 1”.
Similar to Equation (9), the energy and environmental technological change can be defined by comparing one observed data point in the period “
t + 1” to the technology of period “
t” and “
t + 1”respectively:
We also compute the simple arithmetic mean of Equations (9) and (10) to eliminate the bias of period selection:
Equations (7), (8) and (11) can be combined into a comprehensive equation which reflects the additive structure of the Luenberger productivity index:
Per the definition of
or
, the biennial DDF based on
instead of
is:
Similar to the definition of above Luenberger productivity index, the biennial Luenberger productivity index has two components:
2.3. Energy and Environmental Performance Measurement with Non-Radial DEA Model
Based on the definitions of DDFs (Equations (4) and (13)) and estimated technology sets of
and
(Models (2) and (3)), the radial DDFs can be estimated by the following DEA models:
Traditional and biennial DDFs can be computed by Models (18) and (19), respectively.denotes the slack ratio (adjustment rate) or “inefficiency score”. If , then the corresponding DMU is considered to be efficient and with no improvement potential. indicates that the corresponding DMU is inefficient and has not yet achieved the relative optimization. Models (18) and (19) are regarded as radial DDFs with the same adjustment rate.
The radial DDF gives the same contraction (expansion) to all the inputs (outputs) and thus may have weak technical efficiency. Increasing desirable outputs and decreasing inputs and undesirable outputs can be further achieved under the current technical conditions, i.e., the radial DDF overestimates the efficiency. The non-radial DDF can further identify potential in increasing inputs and decreasing outputs, so we use a non-radial DDF model to measure EEP here. Mathematically, traditional and biennial radial DDFs can be improved by the following DEA models:
In Models (20) and (21),
,
,
, or
represents the ratio of the slack to a non-energy input, energy input, desirable output, or undesirable output respectively. If
, Models (20) and (21) are converted into Models (18) and (19). The non-radial DDF allows us to exploit slacks more exhaustively with stronger discrimination power than the radial DDF [
55]. We mainly focused on energy conservation and pollution reduction in this study, so the directional vector is set to
here. The DDF we used can be calculated by the following DEA linear programming models:
In Models (22) and (23), and represent the ratios of energy conservation and emission abatement, respectively. In Model (22), represents the specific energy performance while represents the specific undesirable output performance (wastewater, SO2 or soot performance). represents the energy and environmental inefficiency, so we can calculate EEP by
If input-output combination observed in the period “t” for two technologies in the period “t” and “t + 1” respectively, we can estimate and with Model (22). We can estimate and similarly. We can also estimate and by employing Model (23) with production activity observed in the period “t” and “t + 1” respectively.
To calculate the Luenberger EEPI which represents the EEP change, we need to calculate six DDFs (activities in “t” and “t + 1” refer to technologies in the period “t”, “t + 1” and pooled respectively) by Models (22) and (23). Given that different undesirable output structures impact the EEP, a non-radial efficiency measure can help us identify specific effects and contributions of energy factor and specific undesirable outputs. The total EEPI can be further decomposed into specific EEPIs to analyze the contributions of specific undesirable outputs and energy inputs on total EEPI.
2.4. Exploratory Spatial Data Analysis—Moran’s Index
The sample data we used contains abundant spatial information, so we sought to consider the spatial effects on EEP among different cities. We did so by applying Exploratory Spatial Data Analysis (ESDA) to describe the spatial distribution of the EEP. We used Moran’s
I statistic to measure the spatial correlation at the city level, including global spatial correlation and local spatial correlation [
56].
(1) Global Moran’s I statistics
The global Moran’s
I statistics reflect the similarity of attributes with their neighborhoods:
where
represents the observed value in the ith city;
n represents the number of the cities;
represents the spatial weight matrix which reflects the spatial adjacent relationship in the
ith and
jth cities. Global Moran’s
I ranges from −1 to 1: value less than 0 represents a negative correlation, 0 represents an uncorrelated relationship, and greater than 0 represents a positive correlation. As the global Moran’s
I moves towards −1, the spatial differences among cities become more obvious. If the obtained value of global Moran’s
I is near to 1, there are more intimate relations (e.g., high-value clusters or low-value clusters) among cities.
(2) Local Moran’s
I statistics
If is greater than 0, the th spatial unit is similar to its neighbors (i.e., “high-high” or “low-low”); , with a value lower than 0 represents dissimilarities to neighbors (“high-low” or “low-high”). We can also visually identify the high-value clusters and low-value clusters according to the map of local indicators of spatial association (LISA).
2.5. Geographically Weighted Regression Model
The spatial heterogeneity of our data means that explanatory variables have varying extent of influence on the explained variable in different areas. Under the traditional econometric regression model, regression parameters are same across whole regions and regional differences are neglected. The geographically weighted regression (GWR) model [
57,
58], which takes the regional difference into account, allows regression parameters to change along with the geographical position. Regression parameters in GWR are a data set rather than a fixed coefficient. The GWR model can be derived as follows:
where the vector
represents the explained variable; the vector
represents explanatory variables;
is the space coordinate (longitude and latitude) in the area
.
is the regression parameter for the
kth explanatory variable in the area
.
is random error; we assume that
and
. To estimate regression parameters, we assign
,
,
,
for the area
to represent influences from all other areas [
59]. According to the weighted least square method, we can then estimate the regression equation in
by minimizing the following equation:
with
We can then derive
. The spatial weighting function is the key to the above GWR model. Here, we use a Gaussian weighting function as the spatial weighting function [
59].
4. Conclusions
China is currently facing a trade-off between economic development and environmental protection. Chinese cities represent complete, independent administrative districts which implement environmental regulations; top administrators are held accountable for environmental damages. A given city’s energy utilization and environment regulation directly influence the amount to which it pollutes the environment, and to identify the best performer and regional difference on EEP will stimulate the cities to learn from each other. This paper proposed a new biennial Luenberger EEPI to avoid infeasibility problem in conducting data envelopment analysis. Changes in EEP were decomposed into technical efficiency change and technological change. To examine the contributions of specific undesirable outputs (e.g., SO2, soot, and wastewater) and energy inputs to the EEP, the total performance was divided into sub-performances via a non-radial measure. We empirically analyzed a sample of 283 cities from 2010 to 2014 accordingly and investigated the primary drivers of emission abatement potential based on the GWR model. Our main conclusions can be summarized as follows.
(1) The best performers are mainly located in the Guangdong, Shandong, Jiangsu, Jiangxi, Sichuan, and Hainan provinces, while the worst performers are mainly distributed in Heilongjiang, Guangxi, Ningxia, and Shanxi provinces. The best performers possess advanced service industries and either consume less energy or have inherently high ecological quality, while the worst performers depend on abundant coal and nonferrous metal resources to support economic development. Best performers tended to move from the coastal towards the inland area over time.
(2) At the national level, average EEP change, technical efficiency change, and technological change values are 2.38%, −1.57%, and 7.90%, respectively. China achieved remarkable progress in energy conservation and emission abatement over the study period. The deterioration of the technical efficiency is a relative deterioration caused by the fast technological progress. Changes in EEP are primarily attributable to technological progress, but said progress slowed down during the study period.
(3) At the regional level, the central area (2.97%) shows the greatest improvement in total performance followed by eastern (2.73%) and western (1.96%) areas. The northeastern area (0.50%) shows almost no change in EEP. The eastern area achieves the greatest technological progress (5.86%) but greatest decline in technical efficiency (−3.14%) among the four areas. The sub-performances all increased apart from soot emission performance. Deterioration in SO2 technical efficiency is the biggest driver of deteriorated technical efficiency in all four areas.
We used the ESDA method to find that EEP has obvious spatial agglomeration features. The high-high type clusters mainly exist in Shandong province and the southeast coast of China; high-high type clusters move from coastal areas towards the inland areas which have inherently better ecological quality. The factors that affect SO2 emission abatement potential exhibit significant spatial heterogeneity in different areas. The gross industrial output positively affects SO2 emission abatement potential in most cities. The strongest impact coefficients of gross industrial output are mainly distributed in the western area. Cities with the strongest positive effect of pollution intensity on SO2 emission abatement potential were mainly distributed in central and southern Liaoning province, Beijing-Tianjin-Hebei, and Shandong Peninsula areas (i.e., areas around the Bohai Gulf which are characterized by haze problems). The ratio of service industry to GDP has an uncertain effect on SO2 emission abatement potential, indicating that industrial structure is not the significant influencing factor of SO2 emission abatement potential in the study period.
Based on the empirical results, we make the following policy recommendations: First, the measurement of EEP is useful for the Chinese government to build an evaluation system of EEP of the industrial sectors at the city level. Second, the Chinese government should pay more attention to the cities with the worst EEP that have abundant mineral resources and encourage these cities to develop resource-processing industries then they can produce high value-added products instead of raw materials. Third, Cities that possess advanced service industries or have inherently high ecological quality achieve a high EEP. Therefore, the city government should encourage the development of service industry with low energy consumption and low pollution. Besides, they should pay attention to protecting ecological environment and avoiding the path of “pollution first, treatment later”. Fourth, the Chinese government should promote the exchange of advanced experience and technology relating to energy conservation and emission abatement in order to narrow the EEP gaps between different cities.