Introduction

Over the past four decades, China has made great progress in its social and economic development. Since the Chinese “Reform and Opening Up” in 1978, China’s economy has developed rapidly. According to official statistics, China’s gross domestic product (GDP) reached 83.2 trillion yuan (RMB) in 2017, a 33-fold increase over 1978. However, China’s rapid economic growth is based on the cost of high energy consumption and high pollution emissions (Kadoshin et al. 2000; Wu et al. 2013b; Wu et al. 2014). According to BP World Energy statistics, China surpassed the United States as the world’s largest energy consumer in 2010, which was also the year when China overtook Japan to have the world’s second-largest economy. In 2017, China consumed 4.56 billion tons of standard coal, eight times that of 1978. The huge increase of energy consumption has also resulted in some serious consequences, such as energy shortages, energy crisis and environmental pollution (Li and Oberheitmann 2009). China has become not only a huge engine driving global economic growth, but also the largest energy consumption driver. The contradiction between economic development and environmental protection is increasingly prominent (An et al. 2017; Song et al. 2012). China must pay attention to sustainable societal development (Zhu et al. 2020a). Therefore, energy use has become an important concerned research issue in recent years (Bian et al. 2016). Although China has carried out various plans and policies to save energy and enhance energy efficiency, such as increasing investment, adjusting energy consumption structure or improving energy conversion rate, the effectiveness of the implemented action is not significant. China must explore more detailed energy efficiencies to make more effective energy policies.

The operational structure of China’s economic system can help us effectively evaluate energy and environmental efficiencies of China if we understand it well. In China, the economic system can be divided into three industries, i.e., primary, secondary and tertiary industries. Similarly, the economic system of each province in China has the same structure. The uneven development economy has resulted in uneven energy consumption and different energy efficiencies. Therefore, it is necessary to calculate the energy efficiencies of three industries and the whole economic system’s efficiency rather than the single economic system. Based on this thought, we want to know the comprehensive energy efficiency of each province considering the internal subsystems. And for each province, which industry has led to the inefficiency of the whole economic system? We also want to further know the dynamic change of energy and environmental performance of China in recent years. We believe that this thought mentioned above might provide more detailed efficiency information of energy use and helpful to improve energy efficiencies.

Data envelopment analysis (DEA), a nonparametric approach proposed by Charnes et al. (1978), has been widely used to evaluate performance. In contrast to another traditional approach, i.e., stochastic frontier analysis (SFA), DEA allows the group of homogenous decision making units (DMUs) to have multiple inputs and multiple outputs (Zhu et al. 2021). Another more important advantage is that DEA does not need to have a predictive form for the production function, which may be too subjective. (Cooper et al. 2007; Zhu, 2004; Saen et al. 2005). Because of these advantages, DEA can well evaluate the performance of DMUs, so it has been applied in many areas like environmental performance evaluation (Wang et al. 2013a; Song et al. 2018), supply chains of enterprises (Mahdiloo et al. 2012), and allocation of resources (Li et al. 2017; Wu et al. 2013a; Lozano and Villa 2004). Therefore, in this paper, we select DEA as the main approach to analyze energy and environmental efficiency.

In the area of energy and environmental efficiency performance evaluation, there are many mature theories. In terms of energy efficiency, Hu and Wang (2006) used DEA to calculate the energy efficiencies of 29 administrative regions in China for the period 1995-2002 and proposed a new index called TFEE. Song et al. (2013) borrowed a super-SBM model to measure and calculate the efficiency of BRIC countries. Bian et al. (2016) proposed a parallel slacks-based measure approach to calculate the energy efficiency of the economic system in China from 1986 to 2012. However, their models did not take undesirable output like CO2 into account. Due to environmental issues, Rezaei et al. (2018) believed that it is necessary to find influential factors on CO2 emission. For this goal, they proposed a new model to predict CO2 emissions in four Nordic countries by applying group method of data handling (GMDH). Ahmadi et al. (2019b) pointed out that one of the most concerned issues of mankind is greenhouse gas emissions in the current society, especially CO2 emissions. Therefore, they used connectionist models to predict CO2 emissions and found that most research objects have invested in renewable energy R&D activities. Ghazvini et al. (2020) analyzed CO2 emissions related to energy. For energy systems can notably influence CO2 emissions, Ahmadi et al. (2019a) modeled CO2 emissions at the national level based on the energy sources utilized by a country. They used Artificial Neural Network (ANN) and GMDH approaches to determining the total amount of CO2 emissions produced from various energy sources. Guler et al. (2021) used DEA and promethee (the Preference Ranking Organization Method for Enrichment Evaluation) methods to evaluate the sustainable energy performance of OECD countries. Considering the environmental variable, Zhou et al. (2008) discussed the environmental DEA technologies for situations including nonincreasing returns to scale (NIRS) and variable returns to scale (VRS) and evaluated the carbon emission performance of eight world regions. Zhou and Ang (2008) measured economy-wide energy efficiency performance within a joint production framework using both desirable and undesirable outputs, applying the proposed model to the 21 OECD countries. Wang et al. (2013b) employed the nonradial directional distance function approach to evaluate energy efficiency and productivity. Song and Wang (2014) proposed a DEA decomposition approach based on a search algorithm to measure China’s environmental efficiency, and they decomposed the score from the perspective of government regulations and technological progress. Huang et al. (2014) created a new slack-based model to investigate the dynamics of regional eco-efficiency in China from 2000 to 2010. Li and Lin (2015) investigated the effects of technological progress on carbon intensity in China. Song et al. (2018) introduced the polar theory to DEA modeling and structured a ray slack-based model to analyze the provincial environmental efficiencies in China from 2004 to 2012.

Surveying previous research work, we find many papers on the energy and environmental efficiency of Chinese provinces, but most of those studies treated the economic systems of Chinese provincial-level regions as an entirety. That is, they commonly analyzed a unit’s energy and environmental efficiency by treating it like the “black box” (Färe et al. 1997), they did not consider the production processes within the units. The conventional model of efficiency evaluation only included the external total input and output of the evaluated unit, and such efficiency measurement might not be reasonable and fair for a unit with independent internal subsystems. To open the black box, experts and scholars have done much effective work (e.g., Liang et al. 2010; Song et al. 2014; Cui and Li 2014; Bian et al. 2015; Liu et al. 2016; Li et al. 2018).

However, no one has yet opened the black boxes of Chinese provinces. As we mentioned above, the economic systems of regions include primary industry, secondary industry, and tertiary industry. Based on research published by Kao (2012), DMUs can be considered in a parallel structure if each DMU has the same number of different processes and each corresponding process performs the same function. Therefore, in this situation, each region of China can be seen as a parallel system with three types of industries, which are called subsystems in this paper. Following Bian et al. (2016), in the specific system, we assume that each industry consumes the same type of resources (such as labor, energy, and capital) to produce the same outputs (such as GDP, CO2). Through this decomposition, provincial managers can easily identify inefficient subsystems and take appropriate measures to improve subefficiency, thus improving overall energy efficiency. The basic structure of the economic systems of Chinese provincial-level regions is described in Fig.1.

Fig. 1
figure 1

A parallel system with three subsystems

Full size image

As shown in Fig.1, this paper selects energy, labor, capital stock as the subsystem’s inputs (Chang and Hu 2010). To accurately model reality, Li et al. (2016) chose water as a nonnegligible input, so this paper also picks water as a new input. Similarly, GDP is selected as the desirable output, and from the perspective of environmental protection, we view the CO2 emission as the undesirable output (Wang et al. 2011). We can easily derive the energy and labor input of each subsystem from provided statistics, along with the GDP and CO2 emission output. Unfortunately, we cannot accurately determine the proportion of water and capital inputs for each subsystem, but we can get overall inputs for the whole parallel system, so it is feasible to consider the capital and water as the shared inputs. In many parallel production scenarios, a shared resource is considered, defined as an input used by more than one department (Yu 2008; Chen et al. 2010; Castelli et al. 2010).

Comparing with previous papers, three main improvements have been made in this paper. First, the existing studies commonly have analyzed regional energy efficiencies by treating them as “black box”, but in this paper three subsystem industries are considered simultaneously in a parallel system to reflect the energy and environmental performance of the province. Then, by comparing the efficiencies of three subsystems, the subsystem which performs worse than others will be found. Second, the model allows the DMUs to obtain their own proportions of shared resources, while not needing to follow the proportions for the evaluating DMU. Third, we use the Malmquist productivity index (MPI) to serve as a measure of changes in performance, which can represent the dynamic energy and environmental efficiency evaluation. In addition, most studies calculate the subsystems’ efficiencies by means of efficiency aggregation, not efficiency decomposition.

The structure of this paper is as follows. The following section, “Methodology”, introduces the model we propose in detail. Section “Data source” introduces the data in detail. The next section, “Empirical results and analysis”, uses the model to analyze an application involving the energy and environmental efficiencies of economic systems of 30 regions in China. The last section summarizes the paper.

Methodology

Efficiency evaluation model

In this subsection, a parallel DEA model is constructed to evaluate the energy and environmental efficiency of 30 provincial-level regions in China. Each region is regarded as an individual DMU, and we assume an input-oriented perspective since we need to save energy and reduce undesired output to protect the environment (Cui and Li 2014).

To measure the energy and environmental efficiency of Chinese provincial-level regions, we here denote each region as DMUj (j = 1, …, 30). As shown in Fig.1, each DMU comprises three subsystems, denoted as subsystem p (p = 1, 2, 3). Subsystem p consumes \({\mathrm{X}}_{ij}^p\) (Capital and Water, i = 1, 2), \({E}_{1j}^p\) (Energy), and \({R}_{1j}^p\) (Labor) to produce desirable output \({Y}_{1j}^p\) (GDP) and undesirable output \({F}_{1j}^p\) (CO2). Note that, for each DMUj, its total amounts of inputs and outputs are equal to the sum of those of the three subsystems. In this paper, Xij(i = 1, 2) denote the shared resources, and \({\alpha}_{ij}^p\) are the splitting variables that denote the proportion of shared inputs to be assigned to the three subsystems. Since we need to connect the subsystems through the splitting variables, hence it should be noticed that \({\alpha}_{ij}^1+{\alpha}_{ij}^2+{\alpha}_{ij}^3=1\).

In the following article, DMU0 represents the object we are evaluating. For that DMU, E0, E10, E20, E30 represent the whole system efficiency and three subsystem efficiencies, respectively. The model proposed is based on the assumption of variable returns to scale (Banker et al. 1984) because that model is more in line with reality. Given that what we want to derive is the overall efficiency of the DMU, we let the convex combination of the subsystem efficiency scores be the overall efficiency score. The model is formulated as follows:

$${\displaystyle \begin{array}{c}\operatorname{Max}\kern0.5em {E}_0={W}_1{E}_{10}+{W}_2{E}_{20}+{W}_3{E}_{30}\\ {}\mathrm{s}.\mathrm{t}.\kern0.75em {E}_{1j}=\frac{\varphi_1{Y}_{1j}^1-{\pi}_1{F}_{1j}^1+{u}_1}{\eta_1{E}_{1j}^1+{\rho}_1{R}_{1j}^1+{\sum}_{i=1}^2{v}_i{\alpha}_{ij}^1{X}_{ij}}\le 1,j=1,\dots, 30\\ {}\begin{array}{c}{E}_{2j}=\frac{\varphi_1{Y}_{1j}^2-{\pi}_1{F}_{1j}^2+{u}_2}{\eta_1{E}_{1j}^2+{\rho}_1{R}_{1j}^2+{\sum}_{i=1}^2{v}_i{\alpha}_{ij}^2{X}_{ij}}\le 1,j=1,\dots, 30\\ {}\begin{array}{c}\begin{array}{c}{E}_{3j}=\frac{\varphi_1{Y}_{1j}^3-{\pi}_1{F}_{1j}^3+{u}_3}{\eta_1{E}_{1j}^3+{\rho}_1{R}_{1j}^3+{\sum}_{i=1}^2{v}_i{\alpha}_{ij}^3{X}_{ij}}\le 1,j=1,\dots, 30\\ {}{\sum}_{p=1}^3{\alpha}_{ij}^p=1\\ {}{\varphi}_1,{\pi}_1,{\eta}_1,{\rho}_1,{v}_{1,2}\ge 0\end{array}\\ {}{u}_p\ free\ in\ {\operatorname{sign}},\kern0.5em p=1,2,3\\ {}{L}_i^p\le {\alpha}_{ij}^p\le {U}_i^p,\kern0.5em i=1,2\kern0.5em j=1,\dots, 30\kern0.5em p=1,2,3\end{array}\end{array}\end{array}}$$
(1)

We draw attention to one feature in model (1): the same factor has the same multiplier regardless of the process to which it corresponds. This feature means that no matter what the subsystems are, they all belong to the unit. To better understand model (1), we need to explain some variables. First of all, we choose between two ways to deal with the undesirable output. One action is, from the point of view of pollution that could have been avoided, to translate the undesirable output through subtracting its values from a number greater than the maximum of all observed values (Seiford and Zhu 2002). Another action is more direct: the undesirable output should be decreased in the production process (Korhonen and Luptacik 2004; Amirteimoori 2013). In this paper, we choose the second approach, so the sign of the outputs \({F}_{1j}^p\) is negative. Secondly, we use the weights W1, W2, and W3 to reflect the relative importance of the three subsystems. These weights can be chosen in any way, as long as the sum of weights is 1; the choices depend on the preferences of the decision makers. Because this paper adopts the input-oriented model, one logical and appropriate selection of the weight of each subsystem is the proportion of the total resources allocated to each subsystem, which reflects the relative size and importance of each subsystem (Chen et al. 2010). Finally, \({L}_i^p\) and \({U}_i^p\) are the lower and upper bounds for the shared resources, set to avoid extreme bias toward one of the subsystems (Wu et al. 2016). Hence, the weights for any given DMUj can be defined as follows:

$${\displaystyle \begin{array}{c}{W}_1=\frac{\eta_1{E}_{1j}^1+{\rho}_1{R}_{1j}^1+{\sum}_{i=1}^2{v}_i{\alpha}_{ij}^1{X}_{ij}}{\eta_1{E}_{1j}+{\rho}_1{R}_{1j}+{\sum}_{i=1}^2{v}_i{X}_{ij}}\\ {}{W}_2=\frac{\eta_1{E}_{1j}^2+{\rho}_1{R}_{1j}^2+{\sum}_{i=1}^2{v}_i{\alpha}_{ij}^2{X}_{ij}}{\eta_1{E}_{1j}+{\rho}_1{R}_{1j}+{\sum}_{i=1}^2{v}_i{X}_{ij}}\\ {}\ {W}_3=\frac{\eta_1{E}_{1j}^3+{\rho}_1{R}_{1j}^3+{\sum}_{i=1}^2{v}_i{\alpha}_{ij}^3{X}_{ij}}{\eta_1{E}_{1j}+{\rho}_1{R}_{1j}+{\sum}_{i=1}^2{v}_i{X}_{ij}}\end{array}}$$
(2)

By this definition, the overall efficiency E0 can be translated into the following form:

$${E}_0={W}_1{E}_{10}+{W}_2{E}_{20}+{W}_3{E}_{30}=\frac{\varphi_1{Y}_{10}-{\pi}_1{F}_{10}+{u}_1+{u}_2+{u}_3}{\eta_1{E}_{10}+{\rho}_1{R}_{10}+{\sum}_{i=1}^2{v}_i{X}_{i0}}$$
(3)

Up to now, many other papers still do not impose restrictions on weights. In our study, however, we must have a clear understanding of the weights, so they should be restricted to a certain range. In other words, we demand W1 ≥ a, W2 ≥ b and W3 ≥ c to determine reasonable values and avoid unreliable answers. We use a, b and c to represent the minimum weights for the three subsystems.

Replacing the objective function of model (1) by (3), we get a new model (4) by which we can measure the overall efficiency of the combined system.

$${\displaystyle \begin{array}{c}\begin{array}{c}\begin{array}{c}{\operatorname{Max}}\kern0.5em {E}_0=\frac{\varphi_1{Y}_{10}-{\pi}_1{F}_{10}+{u}_1+{u}_2+{u}_3}{\eta_1{E}_{10}+{\rho}_1{R}_{10}+{\sum}_{i=1}^2{v}_i{X}_{i0}}\\ {}\mathrm{s}.\mathrm{t}.\kern0.5em {E}_{1j}=\frac{\varphi_1{Y}_{1j}^1-{\pi}_1{F}_{1j}^1+{u}_1}{\eta_1{E}_{1j}^1+{\rho}_1{R}_{1j}^1+{\sum}_{i=1}^2{v}_i{\alpha}_{ij}^1{X}_{ij}}\le 1,j=1,\dots, 30\\ {}{E}_{2j}=\frac{\varphi_2{Y}_{1j}^2-{\pi}_1{F}_{1j}^2+{u}_2}{\eta_1{E}_{1j}^2+{\rho}_1{R}_{1j}^2+{\sum}_{i=1}^2{v}_i{\alpha}_{ij}^2{X}_{ij}}\le 1,j=1,\dots, 30\end{array}\\ {}{E}_{3j}=\frac{\varphi_1{Y}_{1j}^3-{\pi}_1{F}_{1j}^3+{u}_3}{\eta_1{E}_{1j}^3+{\rho}_1{R}_{1j}^3+{\sum}_{i=1}^2{v}_i{\alpha}_{ij}^3{X}_{ij}}\le 1,j=1,\dots, 30\\ {}{W}_1=\frac{\eta_1{E}_{10}^1+{\rho}_1{R}_{10}^1+{\sum}_{i=1}^2{v}_i{\alpha}_{i0}^1{X}_{i0}}{\eta_1{E}_{10}+{\rho}_1{R}_{10}+{\sum}_{i=1}^2{v}_i{X}_{i0}}\ge a\end{array}\\ {}{W}_2=\frac{\eta_1{E}_{10}^2+{\rho}_1{R}_{10}^2+{\sum}_{i=1}^2{v}_i{\alpha}_{i0}^2{X}_{i0}}{\eta_1{E}_{10}+{\rho}_1{R}_{10}+{\sum}_{i=1}^2{v}_i{X}_{i0}}\ge b\\ {}\begin{array}{c}\begin{array}{c}{W}_3=\frac{\eta_1{E}_{10}^3+{\rho}_1{R}_{10}^3+{\sum}_{i=1}^2{v}_i{\alpha}_{i0}^3{X}_{i0}}{\eta_1{E}_{10}+{\rho}_1{R}_{10}+{\sum}_{i=1}^2{v}_i{X}_{i0}}\ge c\\ {}{\sum}_{p=1}^3{\alpha}_{ij}^p=1,i=1,2\kern0.5em j=1,\dots, 30\\ {}{\varphi}_1,{\pi}_1,{\eta}_1,{\rho}_1,{v}_{1,2}\ge 0\end{array}\\ {}{u}_p\ free\ in\ {\operatorname{sign}},\kern0.5em p=1,2,3\\ {}{L}_i^p\le {\alpha}_{ij}^p\le {U}_i^p,\kern0.5em i=1,2\kern0.5em j=1,\dots, 30\kern0.5em p=1,2,3\end{array}\end{array}}$$
(4)

The above model is nonlinear, but we can transform the model into a standard linear problem by the Charnes-Cooper transformation (Charnes and Cooper 1962). Define \(\mathrm{A}={\eta}_1{E}_{1j}+{\rho}_1{R}_{1j}+{\sum}_{i=1}^2{v}_i{X}_{ij}\), and then let T = 1/A, \({\varphi}_1^{\prime }=T{\varphi}_1\), \({\pi}_1^{\prime }=T{\pi}_1\), \({\eta}_1^{\prime }=T{\eta}_1\), \({\rho}_1^{\prime }=T{\rho}_1\), \({v}_i^{\prime }=T{v}_i\), and \({u}_p^{\prime }=T{u}_p\). By this transformation, model (4) changes into model (5).

$${\displaystyle \begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}{\operatorname{Max}}\kern1.00em {E}_0={\varphi}_1^{\prime }{Y}_{10}-{\pi}_1^{\prime }{F}_{10}+{u}_1^{\prime }+{u}_2^{\prime }+{u}_3^{\prime}\\ {}s.t.\kern0.5em {\varphi}_1^{\prime }{Y}_{1j}^1-{\pi}_1^{\prime }{F}_{1j}^1+{u}_1^{\prime }-\left({\eta}_1^{\prime }{E}_{1j}^1+{\rho}_1^{\prime }{R}_{1j}^1+{\sum}_{i=1}^2{v}_i^{\prime }{\alpha}_{ij}^1{X}_{ij}\right)\le 0,j=1,\dots, 30\\ {}{\varphi}_1^{\prime }{Y}_{1j}^2-{\pi}_1^{\prime }{F}_{1j}^2+{u}_2^{\prime }-\left({\eta}_1^{\prime }{E}_{1j}^2+{\rho}_1^{\prime }{R}_{1j}^2+{\sum}_{i=1}^2{v}_i^{\prime }{\alpha}_{ij}^2{X}_{ij}\right)\le 0,j=1,\dots, 30\end{array}\\ {}{\varphi}_1^{\prime }{Y}_{1j}^3-{\pi}_1^{\prime }{F}_{1j}^3+{u}_3^{\prime }-\left({\eta}_1^{\prime }{E}_{1j}^3+{\rho}_1^{\prime }{R}_{1j}^3+{\sum}_{i=1}^2{v}_i^{\prime }{\alpha}_{ij}^3{X}_{ij}\right)\le 0,j=1,\dots, 30\\ {}{\eta}_1^{\prime }{E}_{10}^1+{\rho}_1^{\prime }{R}_{10}^1+{\sum}_{i=1}^2{v}_i^{\prime }{\alpha}_{i0}^1{X}_{i0}\ge a\end{array}\\ {}{\eta}_1^{\prime }{E}_{10}^2+{\rho}_1^{\prime }{R}_{10}^2+{\sum}_{i=1}^2{v}_i^{\prime }{\alpha}_{i0}^2{X}_{i0}\ge b\\ {}{\eta}_1^{\prime }{E}_{10}^3+{\rho}_1^{\prime }{R}_{10}^3+{\sum}_{i=1}^2{v}_i^{\prime }{\alpha}_{i0}^3{X}_{i0}\ge c\end{array}\\ {}{\eta}_1^{\prime }{E}_{10}+{\rho}_1^{\prime }{R}_{10}+{\sum}_{i=1}^2{v}_i^{\prime }{X}_{i0}=1\\ {}{\sum}_{p=1}^3{\alpha}_{ij}^p=1,\kern0.5em i=1,2\kern0.5em j=1,\dots, 30\end{array}\\ {}{\varphi}_1^{\prime },{\pi}_1^{\prime },{\eta}_1^{\prime },{\rho}_1^{\prime },{v}_i^{\prime}\ge 0,\kern0.5em i=1,2\\ {}{u}_p^{\prime }\ free\ in\ {\operatorname{sign}},\kern0.5em p=1,2,3\end{array}\\ {}{L}_i^p\le {\alpha}_{ij}^p\le {U}_i^p,\kern0.5em i=1,2\kern0.5em j=1,\dots, 30\kern0.5em p=1,2,3\end{array}}$$
(5)

By reviewing model (5), we can easily find that the model is still nonlinear since it has the variables \({v}_i^{\prime }{\alpha}_{ij}^1\). We also must point out that in each independent evaluation process, the splitting variables of different DMUs do not take the same values. That is to say, in one specific evaluation process, all DMUs will obtain their own variables α while not following the optimal allocation ratio of the evaluated unit (Wu et al. 2016). This approach is more realistic. To solve the nonlinear question, we need to set \({v}_i^{\prime }{\alpha}_{ij}^p={\xi}_{ij}^p\) (i = 1, 2, j = 1, …, 30, p = 1, 2, 3). Then model (5) can be expressed as model (6) below.

$${\displaystyle \begin{array}{c}\begin{array}{c}\begin{array}{c}{\operatorname{Max}}\kern0.5em {E}_0={\varphi}_1^{\prime }{Y}_{10}-{\pi}_1^{\prime }{F}_{10}+{u}_1^{\prime }+{u}_2^{\prime }+{u}_3^{\prime}\\ {}s.t.\kern1em {\varphi}_1^{\prime }{Y}_{1j}^1-{\pi}_1^{\prime }{F}_{1j}^1+{u}_1^{\prime }-\left({\eta}_1^{\prime }{E}_{1j}^1+{\rho}_1^{\prime }{R}_{1j}^1+{\sum}_{i=1}^2{\xi}_{ij}^1{X}_{ij}\right)\le 0,j=1,\dots, 30\\ {}{\varphi}_1^{\prime }{Y}_{1j}^2-{\pi}_1^{\prime }{F}_{1j}^2+{u}_2^{\prime }-\left({\eta}_1^{\prime }{E}_{1j}^2+{\rho}_1^{\prime }{R}_{1j}^2+{\sum}_{i=1}^2{\xi}_{ij}^2{X}_{ij}\right)\le 0,j=1,\dots, 30\end{array}\\ {}{\varphi}_1^{\prime }{Y}_{1j}^3-{\pi}_1^{\prime }{F}_{1j}^3+{u}_3^{\prime }-\left({\eta}_1^{\prime }{E}_{1j}^3+{\rho}_1^{\prime }{R}_{1j}^3+{\sum}_{i=1}^2{\xi}_{ij}^3{X}_{ij}\right)\le 0,j=1,\dots, 30\\ {}\begin{array}{c}\begin{array}{c}{\eta}_1^{\prime }{E}_{10}^1+{\rho}_1^{\prime }{R}_{10}^1+{\sum}_{i=1}^2{\xi}_{i0}^1{X}_{i0}\ge a\\ {}{\eta}_1^{\prime }{E}_{10}^2+{\rho}_1^{\prime }{R}_{10}^2+{\sum}_{i=1}^2{\xi}_{i0}^2{X}_{i0}\ge b\\ {}{\eta}_1^{\prime }{E}_{10}^3+{\rho}_1^{\prime }{R}_{10}^3+{\sum}_{i=1}^2{\xi}_{i0}^3{X}_{i0}\ge c\end{array}\\ {}{\eta}_1^{\prime }{E}_{10}+{\rho}_1^{\prime }{R}_{10}+{\sum}_{i=1}^2{v}_i^{\prime }{X}_{i0}=1\\ {}\begin{array}{c}{\sum}_{p=1}^3{\xi}_{ij}^p={v}_i^{\prime },\kern0.5em i=1,2\kern0.5em j=1,\dots, 30\\ {}{\varphi}_1^{\prime },{\pi}_1^{\prime },{\eta}_1^{\prime },{\rho}_1^{\prime },{v}_i^{\prime}\ge 0,\kern0.5em i=1,2\\ {}\begin{array}{c}{\xi}_{ij}^p\ge 0,\kern0.5em i=1,2\ j=1,\dots, 30\ p=1,2,3\\ {}{u}_p^{\prime }\ free\ in\ {\operatorname{sign}},\kern0.5em p=1,2,3\end{array}\end{array}\end{array}\end{array}\\ {}{L}_i^p{v}_i^{\prime}\le {\xi}_{ij}^p\le {U}_i^p{v}_i^{\prime },\kern0.5em i=1,2\kern0.5em j=1,\dots, 30\kern0.5em p=1,2,3\end{array}}$$
(6)

We call attention to the difference between models (5) and (6), in particular, the change in constraints. Note that \({\sum}_{p=1}^3{\xi}_{ij}^p={v}_i^{\prime }\) implies that \({\sum}_{p=1}^3{\alpha}_{ij}^p=1\), which guarantees that all shared inputs are fully distributed among the three subsystems. Once we have a method to solve model (6), we can obtain the optimal value of the overall efficiency of each DMU and subsystem’s efficiency score as follows:

$${\displaystyle \begin{array}{c}{E}_0^{\ast }={\varphi}_1^{\ast }{Y}_{10}-{\pi}_1^{\ast }{F}_{10}+{u}_1^{\ast }+{u}_2^{\ast }+{u}_3^{\ast}\\ {}{E}_{pj}^{\ast }={\varphi}_1^{\ast }{Y}_{1j}^p-{\pi}_1^{\ast }{F}_{1j}^p+{u}_p^{\ast }-\left({\eta}_1^{\ast }{E}_{1j}^p+{\rho}_1^{\ast }{R}_{1j}^p+{\sum}_{i=1}^2{\xi}_{ij}^{p\ast }{X}_{ij}\right),\kern0.5em p=1,2,3\end{array}}$$
(7)

where the superscript “*” denotes one of the optimal solutions of model (6). Note that model (6) may have multiple optimal solutions, but we can follow previous studies (e.g., Wu et al. 2016) to obtain the optimal efficiency of subsystems while maintaining the whole system’s efficiency.

Adjacent joint reference Malmquist-Luenberger productivity index

The energy and environmental efficiency calculated by the parallel DMU method created in the above section is a kind of relative efficiency. It reflects the differences in relative efficiency between DMUs in the same period, so this is a static performance evaluation study. The above research results are specific to the production technology of a certain event, but production is generally a long-term continuous process, so this will make it difficult to compare results between different years. Hence, we need to carry out a dynamic performance evaluation study. We adopt the Malmquist method to explore the changes in productivity. Färe et al. (1992, 1994) and Kao (2010) recommended taking the geometric average of the performance changes calculated for the two base periods as the Malmquist productivity index (MPI). Based on this groundbreaking work, MPI has received extensive attention and has been applied in many empirical studies. However, the conventional MPI does not take undesired output into account. In addition, the more severe problem is that the MPI is a special form of the super-efficiency model, which sometimes has no feasible solution.

To solve the problem in this paper, we select the approach called adjacent joint reference MPI (AJMPI), which uses data of two periods to construct an aggregate frontier. AJMPI is also called the biennial MPI (Pastor et al. 2011). Pastor and Lovell (2005) proposed the Global Malmquist productivity index (GMPI), and this index takes the sum of all periods as the productivity frontier to analyze the MPI. Therefore, AJMPI is a special form of the more general GMPI. In this paper, we propose a new adjacent joint reference Malmquist-Luenberger productivity index (AJMLPI) which takes undesired output into account. In the following study, we apply the method to dynamically evaluate the energy and environmental performance of Chinese provincial-level regions. To build the AJMLPI, we make the following definitions:

  • Definition 1. PPSt denotes the Production Possibility Set formed by all DMUs in the same period t.

  • Definition 2. PPSG denotes the Production Possibility Set formed by all DMUs in adjacent joint periods.

  • Definition 3. The optimal solution \({E}_0^{\ast }\) produced using PPSt is denoted Dt(x,y), and the optimal solution \({E}_0^{\ast }\) produced using PPSG is denoted DG(x, y).

In this paper, we decompose AJMLPI into two subindices named the technical efficiency change (EC) and the technological change (TC). The specific decomposition shows as follows:

$${\displaystyle \begin{array}{c}\begin{array}{c} AJMLP\mathrm{I}\left({x}^t,{y}^t,{x}^{t+1},{y}^{t+1}\right)\\ {}=\frac{D^G\left({x}^{t+1},{y}^{t+1}\right)}{D^G\left({x}^t,{y}^t\right)}\\ {}=\frac{D^{t+1}\left({x}^{t+1},{y}^{t+1}\right)}{D^t\left({x}^t,{y}^t\right)}\times \left(\frac{D^G\left({x}^{t+1},{y}^{t+1}\right)}{D^{t+1}\left({x}^{t+1},{y}^{t+1}\right)}\times \frac{D^t\left({x}^t,{y}^t\right)}{D^G\left({x}^t,{y}^t\right)}\right)\end{array}\\ {}= EC\times TC\end{array}}$$

where EC represents the change of efficiency of the same DMU in adjacent period t and period t + 1. EC tells us whether the DMU is being produced closer to the current production frontier and reflects the catch-up effect. TC measures the movement of the production frontier from period t to period t + 1, that is, the movement effect of the frontier. In other words, TC represents the change of the best practice gaps and reflects the technical innovation effect.

  1. (i)

    \(EC=\frac{D^{t+1}\left({x}^{t+1},{y}^{t+1}\right)}{D^t\left({x}^t,{y}^t\right)}\). If EC > 1 (<1), then the efficiency of the evaluated DMU increased (decreased). The increase (decrease) of efficiency means that in period t + 1, the DMU is closer to (farther from) the current technical benchmark and the efficiency improves (declines).

  2. (ii)

    \(TC=\frac{D^G\left({x}^{t+1},{y}^{t+1}\right)}{D^{t+1}\left({x}^{t+1},{y}^{t+1}\right)}\times \frac{D^t\left({x}^t,{y}^t\right)}{D^G\left({x}^t,{y}^t\right)}\). If TC > 1 (<1), then technological progress (retrogression) of the DMU is indicated. The progress (retrogression) means that the current productivity frontier in period t + 1 where the DMU is located is closer to (farther from) the global optimal frontier.

  3. (iii)

    AJMLPI(xt, yt, xt + 1, yt + 1) > 1 (<1) denotes the increase (decrease) of the total factor productivity.

Data source

We choose 30 provincial-level regions (interchangeably called “regions” and “provinces” in this study) in mainland China, excluding Tibet because its data is incomplete and unavailable. The input-outputs discussed in the preceding section and shown in Fig. 1 are summarized in Table 1 in detail.

Table 1 Kinds of Input-outputs
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In this paper, we take labor, capital, and water as three non-energy inputs, energy consumption as an energy input, and GDP as a financial input, CO2 as an undesirable output. Data for each region are obtained from the China Statistical Yearbook 2011-2018, China Energy Statistical Yearbook 2011-2018, China Compendium of Statistics 1949-2008, and China Statistical Abstract and Statistical Yearbook 2011-2018. Furthermore, we need to process the obtained original data to get the empirical data. There are no official data available for measuring China’s capital stock and CO2 emissions at the provincial level, especially at the three industries level. Therefore, in our research, we estimate the capital stock and CO2 emission through typical ways used in the literature.

For capital stock, we adopt the perpetual inventory method (PIM). The method is shown below.

$${K}_{j,t}=\left(1-\delta \right){K}_{j,t-1}+{I}_{j,t}={\left(1-\delta \right)}^{t-1991}{K}_{j,1991}+{\sum}_{s=1991}^t{\left(1-\delta \right)}^{t-s}{I}_{j,s}$$
(9)

In the above formula, Kj, t is the capital stock of the region, subscripts j and t represent the DMUj and the year, δ is the rate of depreciation, and I is the real value of the investment in fixed assets. What we need is to determine the depreciation rate δ and the base period with its initial value of capital stock. Following Li (2010), we set δ = 4% and assume it to be constant across provinces. The base period is 1991. The capital stock of the base period is calculated by the growth rate estimation method, which is based on the assumption of a balanced growth path (BGP) (Hall and Jones 1999; Henderson et al. 2007). Therefore, the initial capital stock for province j in 1991 is estimated as:

$${\displaystyle \begin{array}{c}{K}_{j,1991}=\frac{I_{j,1991}}{g_j+\delta}\end{array}}$$
(10)

where gj is the geometric mean of the growth rate of fixed-asset investment in the whole society of province j from 1991 to 2001.

For CO2 emission, we use the fuel-based carbon footprint model that has been successfully applied in many research efforts, such as Chen (2011) and Chang et al. (2013). Under the guidance of the Intergovernmental Panel on Climate Change guidelines (IPCC 2006) for National Greenhouse Gas inventories, we can calculate CO2 emissions roughly using the following equation:

$${\displaystyle \begin{array}{c}{CO}_2\ emission={\sum}_{i=1}^n{E}_i\times {NCV}_i\times {CEF}_i\times { CO F}_i\times \frac{44}{12}={\sum}_{i=1}^n{E}_i\times {\sigma}_i\times {\omega}_i\end{array}}$$
(11)

In model (11), Ei represents the actual energy consumption before conversion, and NCVi represents the net calorific value in IPCC (in China, it is also called the average low calorific value and is given in Appendix IV of the China Energy Statistical Yearbook). Further, CEFi represents the carbon emission factor, COFi represents the carbon oxidation factor, and 44 and 12 are the molecular weights of CO2 and carbon. For the sake of intuition and simplicity of calculation, we use σi and ωi to represent the conversion coefficient of standard coal for various energy sources and the carbon dioxide emission conversion coefficient estimated in this paper, respectively.

In most papers, only three primary sources of energy are taken to calculate CO2 emissions. There is no doubt that the result is not precise due to the differences in various energy sources. In this paper, we selected 17 energy sources with more detailed and representative data based on national and regional energy balance sheets. Details for the 15 remaining energy sources, which are used in model (11), are shown in Table 2.

Table 2 CO2 emission factors of major energy sources in the energy balance sheet
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After observing the energy conversion coefficients, we found that there is no conversion coefficient for heat and electricity, and their carbon dioxide emission coefficients are also difficult to obtain. In order to calculate the accuracy of the results, this paper is based on the data in the 2010-2017 energy balance sheet to obtain the energy conversion coefficient and carbon dioxide emission coefficient of heat and electricity, respectively. Table 3 shows the final results for the two special forms of energy.

Table 3 The coefficients σ and ω for Heat and Electricity
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The consumption of each energy resource by each provincial-level region can be collected using the approaches mentioned above, so CO2 emissions of all regions can be calculated according to formula (11). Thus, we can obtain all input/output data of all periods. We present the descriptive statistics for the input-output variables of the 30 regions in Table 4.

Table 4 Descriptive statistics for the inputs and outputs of 30 regions from 2010 to 2017
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Empirical results and analysis

In this section, we apply the proposed parallel DEA approach to evaluate the energy and environmental efficiency of Chinese provincial-level regions during 2010-2017. The index decomposition of AJMLPI is also demonstrated in this section.

Recalling models (1)–(6) again, we notice that the splitting variable alpha and the weights of the three subsystems need to be limited. In this paper, we impose lower and upper limits of 0.1 and 0.9 on the α that represents the proportion of the shared resource. Similarly, based on the real situation in Chinese provinces, we want each subsystem to have a weight at least 0.1, that is, a = b = c = 0.1. By plugging these values into the above models, we get the evaluated provincial results for 2010-2017. Table 5 contains the final results for 2017.

Table 5 The efficiencies of the 30 provincial-level regions in mainland China in 2017
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In Table 5, column 3 shows the optimal efficiency scores \({E}_j^{\ast }\) of the 30 economic systems in 2017. Columns 4, 5, and 6 show the efficiency scores \({E}_{1j}^{\ast }\), \({E}_{2j}^{\ast }\), and \({E}_{3j}^{\ast }\) for the subsystems of Primary Industry, Secondary Industry, and Tertiary Industry, respectively. Column 7 to column 12 display the alpha variables that describe the proportions of each shared inputs that are assigned to each subsystem. Note that, \({\alpha}_{1j}^1+{\alpha}_{1j}^2+{\alpha}_{1j}^3=1\) and \({\alpha}_{2j}^1+{\alpha}_{2j}^2+{\alpha}_{3j}^3=1\), conforming to the limitation stated above that all resources are allocated to the three subsystems. The last row of Table 5 displays the average efficiency scores and the average distribution ratios of evaluated units.

In this paper, we select data from the most recent year for our analysis. By analyzing Table 5, we can find only when all subsystems are efficient can the aggregate efficiency of a DMU attain the full 100% efficiency level. This tells us that if the efficiency of each subsystem is not 1, then the overall efficiency of the system will not be 1. For example, the secondary industry of Inner Mongolia is efficient, but the primary industry and the tertiary industry are not, so the overall efficiency score of Inner Mongolia is 0.6878. This is the advantage of our model that we can know the reasons which result in inefficiency. There are six regions reached full efficiency in 2017: Beijing, Tianjin, Shanghai, Hainan, Qinghai, and Ningxia. The rest of the provinces are inefficient. For Beijing, Tianjin and Shanghai, both of them are municipalities in China. They would not only get financial support from the Chinese government, but also policy support. Beijing as the political and cultural center of China, has strong economic development level and technological innovation level. Moreover, Beijing is also a pilot area for some environmental policies which make Beijing have a better environmental performance, like ‘Environmental protection and ecological construction plan for Beijing during the “13th Five-Year Plan” period’. There are two reasons accounting for the good environmental performance of Tianjin. The first is the economic volume. Although the GDP of Tianjin is not large, but its consumption of labor or energy is also low. The total number of three industrial labor and energy consumption are 900 ten thousand persons and 5960 ten thousand tce. The second is the speed of technological progress. Tianjin has introduced a large number of technologies which makes the rapid speed of technological progress (Zhu et al. 2020b). Shanghai is the center of economy which indicates the highest economic development in China. For Hainan, an island located in southern China, is famous for its fruit and the service industry. In 2010, the State Council planned to build Hainan into a world-class island resort for leisure and vacation by 2020 (Yu 2020). Qinghai and Ningxia are traditional backward areas in China, but when we take the environmental variable into account, they perform better than those which make much pollution, like Hebei and Guangxi. The results warn that China should not only work hard to develop the economy but also needs to pay attention to protecting the environment, especially under the reality that China has incorporated Ecological Civilization Construction into its Five-sphere Integrated Plan. Most of regions are inefficient. From Table 5, we know the average overall efficiency score of the 30 provincial-level regions is 0.6887, and 22 regions have less than the average score. This result indicates that China has the low energy efficiency (Dong et al. 2020).

When we turn our attention to the efficiency of each subsystem, we find a clear difference between them. For different provinces, the best performing subsystems are different. For example, Jiangsu performs well in subsystems 2 and 3, but not subsystem 1, whose efficiency score is only 0.2393. Jiangsu as a traditional grain producing province in China, is transforming its industrial structure. In 2017, the GDP of the primary industry was only 305.9 billion yuan, only 4% of the total GDP. However, its energy consumption ranked in the forefront of all provinces. For Liaoning, Jilin, and Heilongjiang, they are old industrial provinces in China, but all of them have not been efficient. The overall efficiency of each is lower than the average value. Among these three provinces, Heilongjiang has the best performance in subsystem 1 (efficiency score 0.6251), while Liaoning has the best performance in subsystem 2 (0.9069), and Jilin has the best performance in subsystem 3 (0.6793). From the perspective of the whole nation, the efficiency scores of the three subsystems are 0.5589, 0.7179, and 0.7722, respectively, which indicates that the Tertiary Industry subsystem in China’s economic system performed better than the other subsystems in 2017, and the Primary Industry subsystem needed to be improved.

From the optimal proportions of shared resources for the three industrial subsystems, we can achieve an answer to how each region can choose its optimal division of shared resources for its own individual subsystems. Let us take Beijing, the capital of China, as an example. The optimal proportions of capital and water for Beijing’s three subsystems are 0.15, 0.18, 0.67, 0.22, 0.25, and 0.53, respectively. Comparing the values, we find that the tertiary industry of Beijing should achieve more energy and water inputs. As the political and cultural center of China, such a result is to be expected. Although the optimal allocation ratios of shared resources vary greatly among provinces, the input difference among the three subsystems is very small from the perspective of the national average allocation ratio. This similarity tells us that China should not focus on just one industry; the appropriate is to allocate resources reasonably and give overall consideration to the three industries for balanced development.

Table 6 shows that five regions are efficient. As explained above, Beijing and Tianjin have good economic strength and technological innovation capabilities. Qinghai and Ningxia both consumed a small amount of energy. Considering the environmental variable CO2, they also only emited the least amount of carbon dioxide. This is mainly attributed to the strategy of establishing province by ecological way and the construction of recycling industry chains (Yu 2020). In addition, their GDP have grown rapidly because of the construction of the One Belt and One Road Initiative. Hainan as the impotant participator of the 21st-Century Maritime Silk Road, has realized DEA efficiency in recent years. By comparing with Table 5, Shanghai is not efficient. The inefficiency of Shanghai (0.9998) is caused by the inefficiency of the primary industry (0.9982). The main reason is that Shanghai is gradually reducing the input of the primary industry which has led to less GDP of the primary industry. Omitting changes of the efficient provinces, the average values of overall system efficiency and three subsystems are also different between Table 5 and Table 6. For example, the efficiency of the overall system in 2017 is 0.6887, lower than that (0.7559) in 2010-2017. This means that the overall energy efficiency in China has been reduced, and the situation of energy consumption has not improved. China’s rapid economic development is still dependent on huge energy consumption. Rehman et al. (2021) proved that fossil fuel energy consumption showed a constructive impact to economic progress. Another significant change is the relationship between \({E}_{2j}^{\ast }\) and \({E}_{3j}^{\ast }\). Over the entire study period, the average score of \({E}_{2j}^{\ast }\) is higher than the average score of \({E}_{3j}^{\ast }\), but in 2017, the average score of \({E}_{2j}^{\ast }\) is lower than the average score of \({E}_{3j}^{\ast }\). The result is reasonable beacuse in these eight years, although the secondary industry consumed a huge amount energy, it also has produced great amount of GDP. Among the three industries, the primary industry has the lowest efficiency in 21 provinces. Therefore, the inefficiency of the primary industry is the main reason for the inefficiency of most provinces in China. China always regards agricultural issues as the key point of the year’s work. From 2004 to 2017, China has issued the No.1 Central Document on the theme of agriculture, rural areas and farmers for 14 consecutive years. However, we still have paid more attention to the economic growth agricultural, ignoring the consumption of energy. The tertiary industries of Yunnan, Gansu and Xinjiang have the lowest efficiencies among three industries. All of them have a low level of economic development which mainly led to the inefficiency of the tertiary industry. From Table 6, we can also find energy efficiencies of provincial regions are different, so the central government should focus on balancing energy efficiencies of different regions and take more action to improve the energy efficiency of China (Chen et al. 2020).

Table 6 The average efficiencies of the 30 provincial-level regions in mainland China in 2010-2017
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To analyze the dynamic changes of energy and environmental performance, we have calculated the AJMLPI and its decomposition indexes. We still choose the most recent adjacent years for analysis. Table 7 shows the result.

Table 7 The AJMLPI and its decomposition indexes of 30 regions in 2016-2017
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Conclusions from Table 7 are as follows. First of all, from 2016 to 2017, the productivity index of 12 provinces has improved to some extent, 15 provinces’ AJMLPI values have a downward trend. In terms of specific provinces, the decline is most obvious in Guizhou (0.8909). Guizhou is one of the most backward regions in China which results in its bad performance. Because of the terrain, its geographical location does not have advantages and the traffic is also not developed (Du et al. 2019). In contrast to Guizhou, Chongqing (1.0511) and Jiangsu (1.0405) saw the largest increase in AJMLPI among all provinces. In general, we can find that the productivity indexes of economically developed areas are greater than 1. Liu and Tang (2012) also got the similar result. The main reason is that these regions will have a high level of research and development. From the perspective of the EC index, the EC of five regions increased, while six regions remained unchanged and the other 19 regions declined. This means that more than half of the provinces have a decline in the level of organization that use various inputs to generate output. Among them, Hainan (0.9375) performed worst in all regions. Please note that a higher EC does not mean a higher environmental efficiency, TC also affects the efficiency. Similarly, from the perspective of TC, 15 regions increased or remained unchanged, and the other 15 regions decreased. It is noteworthy that the AJMLPI, EC, and TC indices of three regions (Beijing, Tianjin, Qinghai) are equal to 1. Although this result may, at first, seem regrettable (these regions did not improve), the reason is that both of them were already maximally efficient in 2016 and 2017. We also consider the view of average values of AJMLPI, EC, and TC. Although all of them are very close to 1, they are not greater than 1. Comparing the values of EC and TC, we find that the decline in China’s total factor energy efficiency is mainly due to the decline in technical efficiency. This shows that with the development of China’s economy, the gap in energy utilization level of each province is further increased. The Chinese government needs to respond to this situation by strengthening the energy efficiency and management level of local governments and narrowing the local gaps. Moreover, in view of existing gaps in energy and environmental performance in different provinces, each province should formulate correspomding policies in accordance with the characteristics of specific region environmental development.

From Table 8, based on the average values of each period we can know China’s economic productivity is not sustainable when considering environmental issues. Another conclusion is that although some provinces in mainland China have achieved technical efficiency improvements and technological progress, in the whole of mainland China, the technical efficiency and technological progress are not optimistic. The productivity inefficiency is mostly due to the decline of technical efficiency, not the lack of technological progress. Figure 2 illustrates this conclusion.

Table 8 Changes in the AJMLPI of China’s economic system and its disaggregated indicators in 2010-2017
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Fig. 2
figure 2

Trends of EC, TC, MLPI in China in 2010-2017

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In Fig. 2, we can more clearly see the trends of the three indices. TC has maintained a trend of growth in the study years, except 2011-2012. In contrast, EC and AJMLPI had a downward trend in 2010-2014 and only gradually improved in the following years. Although the three indices showed an upward trend in recent years, the situation is still not optimistic. According to Du et al. (2019), the environmental total factor productivity has indicated that China is not efficient from 1997 to 2014. The technical efficiency and the productivity index were low. The government of China still needs to look for reasons for the low productivity in terms of energy. One potential reason is that with economic development, the consumption of electricity is increasing. In some previous literatures, the energy consumption and carbon dioxide emission related to electrical use are not considered. In fact, thermal power generation in China is still the mainstream source of electricity, and therefore electrical production emits a large amount of carbon dioxide. Therefore, China needs to increase investment in clean energy and improve the level of research and development.

Conclusions

Although China has surpassed Japan to have the world’s second-largest economy, it has also become the world’s largest energy consumer and the largest emitter of greenhouse gases. According to the Paris Climate Agreement and China’s ecological protection plan, China needs to drastically reduce its CO2 emissions. Therefore, it is necessary to research the energy and environmental efficiency of China’s economic system. However, previous papers mostly focus on the DMU’s overall system, ignoring its internal structure.

Addressing the lack of research on parallel systems of energy and environmental evaluation in China, in this paper, we select DEA to evaluate the performance of the economic systems of 30 provincial-level regions in mainland China from 2010 to 2017. The main contribution of this paper is that it is the first to create a parallel DEA method to analyze the efficiency by dividing the economic system into a parallel system with three subsystems: primary industry, secondary industry, and tertiary industry. Through considering this decomposition, local governments in different regions can better distinguish the weaknesses of their three subsystems, so specific policies can be implemented to improve the overall efficiency. In addition, we design a new Malmquist index to carry out the dynamic analysis of total factor energy efficiency changes.

The proposed approach is applied to measure the energy and environmental efficiency of the economic systems in 30 provincial-level regions in mainland China during 2010-2017. The following conclusions can be obtained based on the empirical study.

  1. (1)

    The overall energy efficiency of China is low, and the inefficiency of the economic system is mainly sourced from the low energy and environmental performance of the primary industry and the tertiary industry. From empirical results, we can know the average efficiencies of system and three subsystems are 0.7559, 0.6445, 0.8116 and 0.7768, respectively. Among three industries, the primary industry performed worst during the research period. Therefore, while the government strongly supports the development of agriculture, it must also pay attention to the energy efficiency of agriculture, especially after popularizing mechanized production which will result in a large amount of energy use.

  2. (2)

    The introduction of the environmental variable (CO2) leads to the increase of some backward areas’ efficiencies. Hainan, Qinghai and Ningxia although are not developed provinces in mainland China, but they all performed well during the research period. The one important reason is that we take the environmental variable CO2 into account (Du et al. 2019). Therefore, we cannot evaluate a province only considering GDP, especially after the ecological construction goals Chinese government proposed. Although for most regions, the development of its economy is still the most important problem, but reducing CO2 emissions and pollution are also the focus of government’s work.

  3. (3)

    The energy efficiencies of provincial regions are different, and most of them have their own inefficient industries. Our model’s biggest advantage is that it can distinguish the source of inefficiency. By considering internal structure of the economic system, we can find that the number of provinces with the lowest efficiency in the primary, secondary and tertiary industries are 21, 2 and 3, respectively. For most provinces, they need more efforts to improve the efficiency of the primary industry. We need to promote the planting area of high value-added crops and promote the application of hybrid rice in more regions. We also need to adjust the industrial structure of regions to balance the economic development of them. The backward provinces can reasonably undertake industrial transfer from the developed regions.

  4. (4)

    The total factor productivity of China is declining, mainly because of the decline of technical efficiency. The result indicates that the overall environmental performance during 2010-2017 did not improve significantly. China’s economic growth is still highly dependent on energy consumption, especially the real estate market has developed rapidly in recent years which has brought about a large amount of energy consumption and pollution emissions. For China, the economic development is still the subject of the future work. In this case, it needs to transform the pattern of economic development as soon as possible and increase investment in R&D to enhance the capacity of technological innovation. This will helpful for China to improve its manufacturing level from “made in China” to “created in China” and to “intelligent manufacturing in China”. Another feasible solution is to increase the use of clean energy, such as hydropower, wind power and photovoltaic power generation.

Due to the availability of data, we only calculated the energy efficiency of Chinese provinces from 2010 to 2017. In the future, once newer data is obtained, the latest energy and environmental performance of China could be determined by the method proposed in this paper. Another limitation is that, in this paper, we assume that all electricity comes from thermal power plants, ignoring other forms of energy generation such as photovoltaic power generation. Future research could take multiple electrical generation techniques into account. Lastly, this paper only calculates the MPI of the overall efficiency. We believe that the calculation of MPIs of subsystems and the research on the relationship of overall system MPI and subsystems MPIs may be a fruitful and meaningful extension of our research.