The Energy Efficiency and the Impact of Air Pollution on Health in China

The rapid growth of China’s economy in recent years has greatly improved its citizens’ living standards, but economic growth consumes many various energy sources as well as produces harmful air pollution. Nitrogen oxides, SO2 (sulfur dioxide), and other polluting gases are damaging the environment and people’s health, with a particular spike in incidences of many air pollution-related diseases in recent years. While there have been many documents discussing China’s energy and environmental issues in the past, few of them analyze economic development, air pollution, and residents’ health together. Therefore, this study uses the modified undesirable dynamic two-stage DEA (data envelopment analysis) model to explore the economic, environmental, and health efficiencies of 30 provinces in China. The empirical results show the following: (1) Most provinces have lower efficiency values in the health stage than in the production stage. (2) Among the provinces with annual efficiency values below 1, their energy consumption, CO2 (carbon dioxide), and NOx (nitrogen oxide) efficiency values have mostly declined from 2013 to 2016, while their SO2 efficiency values have increased (less SO2 emissions). (3) The growth rate of SO2 efficiency in 2016 for 10 provinces is much higher than in previous years. (4) The health expenditure efficiencies of most provinces are at a lower level and show room for improvement. (5) In most provinces, the mortality rate is higher, but on a decreasing trend. (6) Finally, as representative for a typical respiratory infection, most provinces have a high level of tuberculosis efficiency, indicating that most areas of China are highly effective at respiratory disease governance.


Introduction
The 2019 China Statistical Yearbook [1] shows that the country's total energy consumption in 2018 was 4.6 billion tons of standard coal, or 3.41 times that in 1998, with coal and oil consumptions to total energy consumption at 59% and 18.9%, respectively. Fossil fuels such as coal and petroleum produce huge amounts of air pollutants such as sulfur dioxide, nitrogen oxides, soot, and dust. The fine particles contained therein are able to penetrate into human organs such as the respiratory system and the cardiovascular system, thus reducing a person's immunity and increasing incidences of infectious and chronic diseases. Kim et al. [2] used Meta-AIR (metabolic and asthma incidence research) to analyze the effects of long-term and short-term exposures to air pollution on humans, showing how they are harmful to the human body's lipid metabolism.
Du et al. [33] explored CO 2 emission efficiencies in China's provinces from 2006 to 2012. Their findings are that economic activity (EAT) is the main driver of increased emissions, while potential energy intensity (PEI) changes, energy structure changes (EMX), and energy efficiency changes (EC) reduce CO 2 emissions in most provinces of China. Wang et al. [34] used the meta-frontier DEA model to explore the carbon emission efficiency of different countries, presenting results that the overall carbon emissions of Asia are lower than those of Europe and U.S. Qin et al. [35] employed the directional distance function model to explore the energy and environmental efficiencies of China's coastal areas from 2000 to 2012. The results presented that the level of economic development has a positive relationship with energy efficiency. Wang et al. [36] showed a negative correlation between resource richness and carbon emission efficiency in China from 2003 to 2016.
Li et al. [37] used the dynamic DEA model to analyze the energy and emissions efficiencies of 31 cities in China from 2013 to 2016, stating that Beijing, Guangzhou, Shanghai, Lhasa, and Nanning have the best emissions efficiency. Li et al. [38] employed the meta frontier dynamic Data Envelopment Analysis model to explore energy and emissions efficiencies in OECD countries and non-OECD countries from 2010 to 2017. The results exhibited that the efficiencies of the United Arab Emirates and Singapore are increasing year by year. Ren et al. [39] used the meta-frontier dynamic SBM model to explore the energy and emissions efficiencies of the Yangtze River Economic Belt (YREB) in China from 2014 to 2016. Their results showed that YREB's energy and emissions efficiencies are higher than those of non-YREB. Using the non-radial directional distance function model, Teng et al. [40] found that China's energy efficiency has great room for improvement. Zhou et al. [41] used the Super-SBM DEA model to analyze the emissions efficiency of China's construction industry from 2003 to 2016, noting that this industry has low carbon emissions.
Decision making is important for efficiency analysis, Kou et al. [42] used multiple criteria decision-making (MCDM) methods to classify small samples, and confirmed that the MCDM method can be effectively used for evaluation. Li et al. [43] used the group decision-making (GDM) method for integrating heterogeneous information and applied it to a numerical example of supplier selection. Zhang et al. [44] analyzed cost issue by GDM. Kou et al. [45] reviewed and classified 37 main literatures of pairwise comparison matrix (PCM) from 2010 to 2015, which helped to use PCM in measurements. Kou et al. [46] proposed an approach to resolve disagreements among MCDM methods based on Spearman's rank correlation coefficient, and the results showed that the differences between MCDM rankings were greatly reduced. Kou et al. [47] used multiple criteria decision making (MCDM) to analyze financial credit and bankruptcy risk, and the results showed that MCDM was effective in evaluating clustering algorithms.
(c) The literature on the negative effect of air pollutants on human health Schiavon et al. [48] used the AUSTAL2000 dispersion model to show that high concentrations of emissions that have occurred in Italy affect the human body. Fischer et al. [49] showed that long-term exposure to PM 10 and NO 2 is associated with mortality in the Netherlands. Lelieveld et al. [50] confirmed that the annual premature mortality rate of 3.3% globally is due to outdoor air pollution, mainly in Asian countries. Li et al. [51] explored the effects of exposure to air pollution on public health. Their results showed that PM 10 and SO 2 cause serious economic losses and increased human health-related problems. Wu et al. [52] studied the relationship between antioxidant activity and ambient air pollution, presenting that exposure to particulate air pollution can affect the body's circulating antioxidant enzymes. Yang et al. [53] noted that long-term exposure to ambient air pollution has an impact on hypertension. Vlaanderen et al. [54] explored how short-term exposure to air pollution affects human blood metabolism. Shen et al. [55] introduced the total air quality index (AAQI) and health risk air quality index (HAQI) to assess human health risks. According to the HAQI results, the current AQI system may significantly underestimate the health risks of air pollution, and the public may need stricter health protection measures to reduce their risk. Zhao et al. [56] explored the problems caused by air pollution in Beijing, China in 2015, which has a negative impact on the health of cyclists.
Dauchet et al. [57] explored two urban areas in northern France, presenting that an increase in O3 is associated with a rise in the blood eosinophil count. Kasdagli et al. [58] used a systematic review and meta-analysis to analyze the relationship between air pollution exposure and Parkinson's disease (PD), noting that there is insufficient evidence of air pollution and PD caused by traffic. Ljungmau et al. [59] used linear regression to analyze the relationship between long-term and short-term air pollution exposure and arterial stiffness, and their results showed that long-term exposure to PM 2.5 is not associated with arterial stiffness. Ngo et al. [60] employed hospitalization and emergency department data to analyze the incidences of patients with respiratory diseases and heart disease in California between 2005 and 2012. Heavy exposure to sandstorms is associated with an increase in human acute respiratory illness. Torres et al. [61] studied the adverse effects of exposure to air pollution in Alentejo and the Lisbon metropolitan area on human health. Their results showed that cardiovascular and respiratory disease-related mortalities occur mainly in the Alentejo and Algarve regions. Khaniabadi et al. [62] looked into human health problems caused by exposure to air pollution in developing countries. Exposure to air pollution caused a cardiovascular disease (CM) mortality of 4.96%, respiratory diseases (HA-RD) of 4.97%, cardiovascular disease (HA-CVD) of 5.55%, lung disease (HA-COPD) of 2.50%, and acute myocardial infarction (AMI) of 4.73%. Bayat et al. [63] used the Environmental Benefits Mapping and Analysis Program (BenMAP-CE) to explore the human health problems caused by exposure to air pollution in Tehran, Iran. The results showed that a total of 7146 adults with PM 2.5 exposure died of ischemic heart disease, stroke, lower respiratory tract infection, chronic obstructive pulmonary disease, and lung cancer. Huang et al. [64] examined the relationship between PM 2.5 and the social economy in Beijing, China, with household income and education negatively correlated with environmental air quality in 2014. Lua et al. [65] used a 1 km high-resolution annual satellite search for PM 2.5 data to analyze the concentration of PM 2.5 in China from 2001 to 2017 and its adverse health effects.

DEA Basis
DEA is a linear programming model that evaluates a decision making unit (DMU) based on Pareto's optimal solution, instead of finding the efficiency frontier with a preset function as an analysis of the relative efficiency relationship between DMUs. Farrell [66] used the frontier production function to measure the level of production efficiency of DMUs, connecting the most efficient production points to the theoretical production frontier. Here, the gap between any real production point and the theoretical production frontier indicates the degree of inefficient production. However, the problem of Farrell's theoretical model is that it can only be applied to a single input and a single output; it cannot meet the actual benefits of presenting multiple inputs and multiple outputs. Charnes et al. [67] proposed the CCR model in 1978, extending the Farrell model into a generalized mathematical linear programming model that can be used to measure the performance evaluation of multiple inputs and multiple outputs of constant returns to scale, naming it the data envelopment analysis method (DEA). Banker et al. [68] proposed the BCC model in 1984, revising the assumption of constant returns to scale to variable returns to scale (VRS). Since the CCR model and the BCC model measure radial efficiency, these two models assume that the input or output can be adjusted (increased or decreased) in equal proportions, but this assumption is not applicable in some cases. Tone [69] thus proposed the Slacks-Based Measure (SBM) model in 2001, which uses the difference variable as the basis for measurement, taking into account the difference between the input and output items (slack) and using the non-radial estimation method and a single value (scalar) to present SBM efficiency. The traditional DEA model uses input and output projections to perform an efficiency conversion between two variables, and the conversion process is identified as a "black box". Fare et al. [70] proposed the Network DEA model, noting that the production process is composed of many sub-production technologies, and regarded the sub-production technology as a sub-DMU that can be solved by the traditional CCR and BCC models. Zhu [71] described the value chain process as a "black box" and believed that it must contain some sub-processes that constitute the value chain system. To estimate the efficiency of a system, it is necessary to evaluate the efficiency of each of these sub-processes. Chen and Zhu [72], Kao and Hwang [73], and Kao [74] divided the whole business process into sub-processes and connected the stages through some intermediate outputs. They calculated the efficiency of each stage under different conditions and analyzed which sub-process caused efficiency loss to the system. Tone and Tsutsui [75] proposed the weighted slack-based measures network data envelopment analysis model. The linkage between the departments of the decision-making unit is used as the basis for the analysis of the Network DEA model, and each department is regarded as a sub-DMU, and thus one can use the SBM model to find an optimal solution. In the network DEA model, more and more studies in the literature are devoted to the research of the multi-stage production process and its efficiency evaluation. Castelli et al. [76] reviewed multi-stage models. The two-stage DEA also takes a dynamic approach in which DMUs are evaluated at different time periods and carry-overs are introduced to connect the various stages.

Measures Network DEA
Tone and Tsutsui [75] proposed the slack-based measures network DEA model, which is used to measure the overall efficiency of decision-making units and the efficiency of various departments. The SBM model is a non-radial measurement method that is suitable for the inputs and outputs that cannot be adjusted in equal proportions. The following part describes the non-oriented network DEA model, indicating the objective function, the department efficiency, and the solving process of a decision-making unit. Non-oriented model: If the input slack and output slack are considered at the same time, then non-oriented efficiency can be evaluated by Formula (1): According to (1), the definition of non-oriented department efficiency can be expressed as: Here, s k− * io and s k+ * ro are the optimal input slack and the optimal output slack, respectively. If ρ * k = 1, then DMU o 's k department has non-oriented efficiency; if ρ * o = 1, then DMU o has non-oriented overall efficiency. Whether it is input-oriented, output-oriented, or non-oriented, the assessed departmental efficiency and the overall efficiency of decision-making units have unit invariance.
Traditional DEA cannot analyze the efficiency of individual departments, and so we need to use Network DEA. At the same time, a company's operations might span several periods. Thus, a dynamic DEA model must be used. If one considers departments and time, then a combination of Network DEA and dynamic DEA is needed.
Many scholars research on Dynamic DEA such as Kloop [77], Malmquist [78], Fare et al. [79] Malmquist index. These research studies did not analyze the "the effect of carry-over activities" in two periods. Fare and Grosskopf [80] were the first to put inter-connecting activities into the dynamic model. Nemotoa and Goto [81] added some important insights on dynamic DEA, while Nemoto and Goto [82] proposed a method using dynamic DEA to instantly adjust to a quasi-fixed input at the optimal level. Sueyoshi and Sekitani [83] incorporated the concept of returns to scale into a dynamic DEA model. Amirteimoori [84] defined the DEA model to assess dynamic income efficiency, which was modified and extended by Färe and Grosskopf [80]. Tone and Tsutsui [85] extended the model to a dynamic analysis of slacks-based measures. Tone and Tsutsui [86] proposed the slack-based measures dynamic network DEA model. The linkage between various departments of the decision-making unit is used as the basis for the analysis of the network DEA model, and each department is regarded as a sub-DMU, and carry-over activities are used as the linkage. Carry-over activities can be divided into 4 types: (1) desirable, (2) undesirable, (3) discretionary, and (4) non-discretionary. We introduce the dynamic two-stage DEA model as follows. Non-oriented model: (a) Overall efficiency: ok l good k l = 1, . . . , ngood k ; ∀k; ∀t) Z    (b1) Period efficiency: (b2) Division efficiency: (b3) Division period efficiency: This model treats undesirable output as a two-stage link or carry-over link. In this paper, referring to Tone and Tsutsui [75], the output of the SBM model is divided into desirable output and desirable output. Based on the Tone and Tsutsui [86] dynamic network DEA model, a Modified Undesirable Dynamic Network Model is proposed.

Modified Undesirable Dynamic Network Model
Our model has two stages. Production is the first stage, and health treatment is the second stage. At the production stage, labor and energy consumed are the inputs, and GDP is the output indicator. CO 2 , SO 2 , and NO x are the variables linking production with health treatment. The health treatment stage uses health expenditures as input, and the outputs are birth rate, death rate, and phthisis. The carry-over variable is fixed assets.
Suppose there are n DMUs (j = 1, . . . ,n), with each having k divisions (k = 1, . . . ,K), and there are T time periods (t = 1, . . . ,T). Each DMU has an input and output at time period t and a carryover (link) to the next t + 1 time period.
We set m k and u k to represent the inputs and outputs in each division K, with (k,h) i representing divisions k to h and Lhk being the k and h division sets. The inputs, outputs, links, and carry-over definitions are outlined in the following paragraphs. The following is the non-oriented model. Overall efficiency: Subject to: ok l input k l = 1, . . . , ngood k ; ∀k; ∀t) s (t,(t+1)) ok l good ≥ 0,(∀k l ; ∀t) (8) where W t (∀ t) is the weight to period t and W k (∀ . k) is the weight to division k. These weights satisfy the condition: They are supplied exogenously. They are weighted by the divisional weight W k and further by the period weight W t , and result in the overall-efficiency θ * 0 . This objective function is a generalization of the slacks-based measure (SBM) developed in Tone and Tsutsui [80]. In the Equation (8), the overall efficiency is uniquely determined. However, the period efficiency may not be uniquely determined, so we use priority principle scheme to solve the non-uniqueness problem (Tone and Tsutsui [80]).

(b) Period and division efficiencies:
Period and division efficiencies are as follows.

Input and Output Efficiencies
We follow Hu and Wang's [87] total-factor energy efficiency index to overcome any possible bias in the traditional energy efficiency indicator. There are seven key features of this present study:

Input and Output Efficiencies
We follow Hu and Wang's [87] total-factor energy efficiency index to overcome any possible bias in the traditional energy efficiency indicator. There are seven key features of this present study: Energy consumed efficiency, CO 2 efficiency, SO 2 efficiency, NO x efficiency, Health expenditure efficiency, Phthisis efficiency, and Death rate efficiency. In our study, "i" represents area and "t" represents time. The seven efficiency models are defined as follows.
Energy consumed efficiency = Target Energy consumed Undesirable output (i, t) Actual Energy consumed Undesirable output (i, t) Death rate efficiency = Target Death rate output (i, t) Actual Death rate output (i, t) If the target Energy consumed and Health expenditure inputs equal the actual input, then the Energy consumed and health expenditure efficiencies equal 1, indicating overall efficiency. If the target Energy consumed and Health expenditure inputs are less than the actual input, then the Energy consumed and health expenditure efficiencies are less than 1, indicating overall inefficiency. If the target phthisis, death rate, CO 2 , SO 2 , and NO 2 undesirable outputs equal the actual undesirable outputs, then phthisis, death rate, CO 2 , SO 2 and NO 2 efficiencies equal 1, indicating overall efficiency. If the target phthisis, death rate, CO 2 , SO 2 , and NO 2 undesirable outputs are less than the actual undesirable outputs, then the phthisis, death rate, CO 2 , SO 2 and NO 2 efficiencies are less than 1, indicating overall inefficiency. From the above, we are able to obtain the overall efficiency, period efficiency, division efficiency, and division period efficiency for the 30 provinces for 2013-2016.

Data Sources and Description
This study uses panel data for economic and social developments from 2013 to 2016 in the 30 provinces. The data sources are [1], China Population and Employment Statistics Yearbook [88], China Health and Family Planning Statistical Yearbook [89], and China Energy Statistics Yearbook [90]. The 30 provinces have large differences in natural resources, total population, industrial structure, pollutant discharge, and governance.
The input and output variables are shown in Table 1. The inputs are labor and energy consumption, referring to [35,87,91]. The desirable output GDP refers to Wang et al. [92] and Li et al. [91]. For fixed assets as carry-over, we refer to Chang et al. [93]. The links Air, CO 2 , NO x , and SO 2 are from Li et al. [94]. Input health expenditure, desirable output Birth rate, and undesirables Phthisis and Death rate come from Zhang [95]. The variables we employ are explained as follows.    From the phthisis indicator, there is a downward trend in the average of each year, and there is an upward trend in the maximum value of each year. The increase in 2015 is higher than that in other years. The minimum value drops slowly, but then increases in 2016. Table 2 shows the overall efficiency scores of provinces from 2013 to 2016. Those with an overall efficiency score of 1 for all four years include Beijing, Tianjin, Shanghai, Hainan, Qinghai, and Ningxia. The efficiency score of Xinjiang in 2013 is higher than 0.8, but the efficiency score for the next three years is 1. There is room for improvement in the overall efficiency scores for each of the From the phthisis indicator, there is a downward trend in the average of each year, and there is an upward trend in the maximum value of each year. The increase in 2015 is higher than that in other years. The minimum value drops slowly, but then increases in 2016. Table 2 shows the overall efficiency scores of provinces from 2013 to 2016. Those with an overall efficiency score of 1 for all four years include Beijing, Tianjin, Shanghai, Hainan, Qinghai, and Ningxia. The efficiency score of Xinjiang in 2013 is higher than 0.8, but the efficiency score for the next three years is 1. There is room for improvement in the overall efficiency scores for each of the other provinces.

Total Efficiency Scores for Each Year
Provinces with an efficiency score above 0.5 include Jiangsu, Fujian, Shandong, and Guangdong. The efficiency scores of Fujian and Shandong are all lower than 0.6 in 2013, but then rise above 0.8 in the next three years, showing great efficiency improvement. The scores of Hebei, Shanxi, Inner Mongolia, Liaoning, Jilin, Heilongjiang, Zhejiang, Anhui, Jiangxi, Henan, Hubei, Hunan, Guangxi, Chongqing, Sichuan, Guizhou, Yunnan, Shaanxi, and Gansu are all below 0.5. There is room for improvement in the overall efficiency of these provinces.
The division of east, central, and west in the following table is based on the China Yearbook of Health Statistics. Eleven provinces in the eastern region include Beijing, Tianjin, Hebei, Liaoning, Shanghai, Jiangsu, Zhejiang, Fujian, Shandong, Guangdong, Hainan. Eight provinces in the central region include Heilongjiang, Jilin, Shanxi, Anhui, Jiangxi, Henan, Hubei, and Hunan. Twelve provinces in the western region include Inner Mongolia, Guangxi, Chongqing, Sichuan, Guizhou, Yunnan, Tibet, Shaanxi, Gansu, Qinghai, Ningxia, and Xinjiang. The eastern region has the highest average efficiency, followed by the western region, and the lowest is in the central region. The average efficiency of the eastern region is about 0.7. The efficiencies of Beijing, Tianjin, Shanghai, Fujian, Shandong, and Hainan are mostly higher than the regional average efficiency and show less room for improvement. Hebei, Liaoning, Jiangsu, Zhejiang and Guangdong's efficiency values in most years are below the regional average, and there is room for improvement. The average efficiency of the western region is less than 0.6. Qinghai, Ningxia, and Xinjiang's efficiency values are 1. Most western provinces have efficiency values fluctuating around 0.4, and Sichuan has the lowest efficiency value. The average efficiency of the central region is below 0.4. Jiangxi has the highest efficiency. The lowest efficiency is in Heilongjiang at around 0.2, giving it large room for improvement. Table 3 shows   Table 4 and Figure 4 illustrate the two-stage efficiency scores for the 30 provinces from 2013 to 2016. Most provinces have better overall efficiency scores in the first stage than in the second stage.

Annual Efficiency Analysis at Each Stage
From the first stage, Beijing, Tianjin, Shanghai, Hainan, Qinghai, and Ningxia have an efficiency score of 1 for all four years. Xinjiang's efficiency score in 2013 is higher than 0.7 and is 1 in the last three years. Those with an efficiency below 1 and above 0.5 are Inner Mongolia, Liaoning, Jilin, Jiangsu, Zhejiang, Anhui, Fujian, Jiangxi, Shandong, Hubei, Hunan, Guangdong, Chongqing, and Shaanxi. Hebei, Shanxi, Heilongjiang, Henan, Guangxi, Yunnan, Gansu, Sichuan, and Guizhou are all lower than 0.5.
The eastern region has the highest average efficiency value in the first stage, followed by the western region, and the central region has the lowest average efficiency value. Beijing, Tianjin, Shanghai, and Hainan are higher than the eastern region's average efficiency value, while Hebei, Hebei, and Liaoning are significantly lower than the eastern region's average efficiency value. Shandong rises from below 0.6 in 2013 to nearly 0.9 in 2016. The average efficiency of the first stage in the western region is about 0.6. Efficiencies in Qinghai, Ningxia, and Xinjiang in most years are 1. The efficiency values of the other western provinces are all below 0.6, with Sichuan and Guizhou having the lowest efficiency values. The average efficiency of the first stage in the central region is around 0.5. Jiangxi has the highest efficiency value at above 0.6. The lowest efficiency in the central region is Shanxi at below 0.4, giving it much room for improvement.
From the second-stage health treatment efficiency score, the gap between the provinces is large. The provinces with a second-stage efficiency score of 1 include Beijing, Tianjin, Shanghai, Hainan, Qinghai, Ningxia, and Xinjiang. In 2013, the efficiency values of Fujian and Shandong are slightly higher than 0.4, but in the following three years they are 1. The provinces with efficiency values higher than 0.3 but less than 1 in each year are Guangxi, Guizhou, and Gansu. Jiangxi, Inner Mongolia, Jiangsu, and Guangdong are around 0.3. Hebei, Shanxi, Liaoning, Jilin, Heilongjiang, Zhejiang, Anhui, Henan, Hubei, Hunan, Chongqing, Sichuan, Yunnan, and Shaanxi all score below 0.3. The efficiency value of the second stage is much lower than the first stage in most provinces. The eastern region has the highest average efficiency in the second stage, and the lowest is the central region.    Most provinces' first-stage production efficiency has increased. Moreover, the efficiency value remains at a high level. However, the vast majority of provinces in the second stage have declining values. The health stage is thus inefficient and has much room for improvement.   Most provinces' first-stage production efficiency has increased. Moreover, the efficiency value remains at a high level. However, the vast majority of provinces in the second stage have declining values. The health stage is thus inefficient and has much room for improvement. Table 5 shows correlation tests, where from 2013 to 2016 the average efficiency of the first stage is between 0.6301 and 0.6589. The average efficiency of the second stage ranges from 0.4246 to 0.4887. The average efficiency value of the first stage is higher than the average efficiency value of the second stage. From 2013 to 2016, the correlation coefficient between the different year in first stage ranges from 0.9421 to 1.000, and the correlation coefficient between the different year in the second stage ranges from 0.9099 to 1.000. The correlation between the different year in first stage is high, but they are all highly correlated. The correlation between the efficiency value of the first stage and the second stage ranges from 0.7552 to 0.8192 and is also highly correlated.  Table 6 shows the efficiency scores of energy consumption, CO 2 , SO 2 , and NO x as input and output indicators for each province from 2013 to 2016.
From the energy consumption efficiency scores, we can see the gap between the provinces is large. The efficiency scores of Beijing, Tianjin, Shanghai, Hainan, Qinghai, and Ningxia are all 1 in the four years. The efficiency values of Fujian, Shandong, and Xinjiang in 2013 are above 0.8 and are all 1 in the other three years. Jilin, Jiangsu, Zhejiang, Anhui, Jiangxi, Henan, Hubei, Hunan, Guangdong, Guangxi, Chongqing, Yunnan, Shaanxi, and Gansu have efficiency scores below 1 and above 0.5. The provinces with energy consumption efficiency below 0.5 include Hebei, Shanxi, Inner Mongolia, Liaoning, Heilongjiang, Sichuan, and Guizhou. In provinces with efficiency below 1, the provinces with an increasing trend are Jilin, Zhejiang, Henan, Hubei, Hunan, and Sichuan. The provinces with a decreasing trend are Hebei, Shanxi, Inner Mongolia, Liaoning, Anhui, Jiangxi, Guangxi, Guangdong, Chongqing, Guizhou, Yunnan, and Shaanxi.
The eastern region has the best performance in energy consumption efficiency, with an average efficiency above 0.8. The lowest efficiency is in the central region at an average annual efficiency of about 0.6. Energy efficiency in most provinces is less than 0.5. Among them, Hebei and Liaoning belong to the eastern region, Shanxi and Heilongjiang belong to the central region, and Inner Mongolia, Sichuan, and Guizhou belong to the western region. There is much room for improvement in energy efficiency in these provinces.
From the CO 2 efficiency score, the provinces with efficiency values of 1 in each year are Beijing, Tianjin, Shanghai, Hainan, Qinghai, Ningxia, and Xinjiang. Fujian and Shandong have efficiencies higher than 0.5 in 2013 and then at 1 in the next three years. The provinces with efficiency values less than 1 but greater than 0.5 are Jiangxi, Zhejiang, Hunan, Guangdong, Chongqing, Yunnan, and Gansu. Jiangxi, Zhejiang, Hunan, Guangdong, Chongqing, Yunnan, Gansu, Hebei, Shanxi, Inner Mongolia, Liaoning, Jilin, Heilongjiang, Jiangsu, Anhui, Henan, Hubei, Guangxi, Sichuan, Guizhou, and Shaanxi have efficiency values below 0.5.
The eastern region has the best CO 2 efficiency performance with an average efficiency close to 0.8. The lowest average efficiency is in the central region, with an average annual efficiency at only about 0.6. Most provinces in the eastern region perform well, but Liaoning and Hebei have the lowest CO 2 efficiency. Most provinces in the central region have poor CO 2 efficiency. Jiangxi has the highest efficiency value at only about 0.6. Shanxi has the lowest efficiency value at around 0.2 in each year. Qinghai, Ningxia, and Xinjiang in the western region perform well. The lowest CO 2 efficiency is in Inner Mongolia and Guizhou, which is around 0.3, and there is much room for improvement.
From the SO 2 efficiency score, the provinces with efficiency values of 1 or nearly 1 in each year are Beijing, Tianjin, Shanghai, Hainan, Qinghai, Ningxia, Xinjiang, Fujian, and Guangdong. Shandong's efficiency value in 2013 is only 0.4, but then hits 1 in the next 3 years. Provinces with an efficiency value less than 1 but greater than 0. The eastern region has the best NO x efficiency performance, and the average efficiency is close to 0.8. The lowest average efficiency is in the central region, and the average annual efficiency is less than 0.4. Most provinces in the eastern region have better efficiency, but Hebei, Liaoning, Jiangsu, Zhejiang, and Guangdong are below the average efficiency value. In the central region, Jiangxi has the highest efficiency value with efficiency less than 0.6, and Heilongjiang has the lowest efficiency value at only 0.2. The average NO x efficiency in the western region is about 0.6. Inner Mongolia has the worst efficiency performance with an efficiency value of only about 0.2 and has much room for improvement.
The provinces with higher energy consumption efficiency also have higher efficiency values of CO 2 , SO 2 , and NO x . Increasing energy consumption efficiency can reduce emissions of atmospheric pollutants. Table 7 shows correlation tests, from 2013 to 2016, where the average Com efficiency value is 0.7037 to 0.7352, the average CO 2 efficiency value is 0.5884 to 0.6384, the average SO 2 efficiency value is 0.5113 to 0.6304, and the average NO 2 efficiency value is 0.5613 to 0.6222. From 2013 to 2016, the Com correlation coefficient is 0.9648 to 1.000, the CO 2 correlation coefficient is 0.9230 to 1.000, the SO 2 correlation coefficient is 0.8724 to 1.000, and the NO 2 correlation coefficient is 0.9012 to 1.000. The correlations between Com and CO 2 , SO 2 , and NO 2 are above 0.8, and the correlations between CO 2 and SO 2 and NO 2 are also above 0.8. From the above results we see that the more energy consumption there is, the more air pollution arises from CO 2 , SO 2 , and NO 2 .  Table 8 shows the efficiency scores of health expenditure, death rate, and phthisis input and output indicators for each province from 2013 to 2016.
From the health expenditure score, those with efficiency scores of 1 for four years include Beijing, Tianjin, Shanghai, Hainan, Qinghai, Ningxia, and Xinjiang. In For the death rate, those with efficiency score of 1 include Beijing, Tianjin, Shanghai, Hainan, Qinghai, Ningxia, and Xinjiang. Fujian's 2013 efficiency value is above 0.8, and for the other three years it is 1. Those with efficiency values above 0.6 include Hebei, Shanxi, Zhejiang, Anhui, Jiangxi, Henan, Hubei, Hunan, Guangxi, Chongqing, Sichuan, Guizhou, Yunnan, Shaanxi, and Gansu. The efficiency value of Inner Mongolia is slightly higher than 0.6 in the first two years, but fell below 0.6 in the next two years. Jiangsu's efficiency value in 2013 dropped from 0.8 to less than 0.6 in the next three years. The provinces with efficiency values below 0.6 are only Liaoning, Jilin, and Heilongjiang.
There is not much difference in the death rate among regions. The death rate efficiency of most provinces in the eastern region performs well, but the death rate efficiencies of Liaoning and Jiangsu are relatively low. There is not much difference in the efficiency of the death rate among the provinces in the central region. Anhui, Jiangxi, and Hunan have the highest efficiency, and Jilin and Heilongjiang have the lowest efficiency. The efficiency values of the provinces in the western region exhibit less difference. Qinghai, Ningxia, and Xinjiang have an efficiency value of 1, while Inner Mongolia, Chongqing, and Sichuan have relatively low efficiency values around 0.6.
In the 20 provinces with efficiency below 1, most provinces show a downward worsening trend. Hebei, Heilongjiang, and Jiangsu present the most distinct declining trend. Those with an upward trend are Jiangxi, Guangxi, Chongqing, and Guizhou.
For phthisis, those with an efficiency score of 1 for four years include Beijing, Tianjin, Shanghai, Fujian, Shandong, Hainan, Gansu, Qinghai, Ningxia, and Xinjiang. The efficiency values of Anhui, Jiangxi, Yunnan, and Shaanxi are all 1 in the first three years, but decline in 2016. The efficiency value of Guangdong in the first two years is about 0.6 and in the last two years is 1. For the first two years, Hebei has an efficiency value of 1, but in the next two years it fell to above 0.8. Those provinces with efficiency values below 1 and greater than 0.7 are Hebei, Shanxi, Jiangsu, Zhejiang, Inner Mongolia, Henan, Hubei, Hunan, Guangxi, Chongqing, and Sichuan. Provinces with efficiency values below 0.7 are Liaoning, Jilin, Heilongjiang, and Guizhou. Most provinces show high efficiency at controlling phthisis.
The average efficiency of phthisis in the western region is leading the other two regions in the first three years, while the average efficiency of phthisis in the eastern region is leading in the fourth year. The worst performance in the eastern region is Liaoning. In the eastern region, the efficiency of phthisis in Guangdong increases, while Hebei, Liaoning, Jiangsu, and Zhejiang show a downward trend. The lowest efficiency of phthisis in the central region is in Jilin and Heilongjiang. Except for the increase in efficiency in Hubei, the efficiency in other central provinces declines. Most provinces in the western region have higher phthisis efficiency, and Guizhou has the lowest efficiency value at about 0.6. Except for Chongqing having a rising efficiency, most other western provinces show a downward trend in efficiency. From the above analysis, we see that although the efficiency of phthisis governance in many provinces is at a high level, the efficiency declines in many provinces. Table 9 shows correlation tests, whereby from 2013 to 2016 the average health efficiency value is 0.4448 to 0.5117, the average death rate efficiency is 0.7811 to 0.8029, and the average efficiency of phthisis is 0.8223 to 0.9297. For 2013 to 2016, the health correlation coefficient is 0.9051 to 1.000, the death correlation coefficient is 0.9364 to 1.000, and the phthisis correlation coefficient is 0.6862 to 1.000. The correlation between health expenditure and death is higher than between phthisis, indicating that health expenditure has a positive relationship with lower mortality. Health expenditure, death, and phthisis are all highly correlated. Table 10 summarizes the efficiency of health treatment stages in various regions, which can help us compare the efficiency characteristics of variables in different places.

Conclusions
This study uses the Modified Undesirable Dynamic Two Stage DEA model to assess productivity and health management efficiencies in 30 provinces of China from 2013 to 2016. Variables include labor, fixed assets, energy consumption, GDP, CO 2 , SO 2 , NO x , health expenditure, birth rate, death rate, and tuberculosis incidence. The following conclusions are drawn from the findings here.
(1) From the average, maximum, and minimum values, we see that labor, fixed assets, and energy consumption inputs and GDP output in the production stage are rising from 2013 to 2016. Atmospheric pollutants SO 2 and NO x show a downward trend, with the most distinct declining trend in 2016. From the analysis of the health governance stage, the amount of health expenditure is also increasing year by year, but the changes in birth rate, death rate, and tuberculosis incidence are not large.
(2) The overall efficiencies of Beijing, Tianjin, Shanghai, Hainan, Qinghai, and Ningxia hit 1 for all years. Xinjiang's efficiency score in 2013 is higher than 0.8 and then moves to 1 in the next three years. In provinces with overall efficiency value below 1, the efficiency values of 19 provinces are all below 0.5. From a regional comparison, the highest average overall efficiency is in the eastern region, second is the western region, and the lowest is the central region. The average overall efficiency in the eastern region is about 0.7, while the average overall efficiency in the western region is only about 0.4.
(3) From the first stage, Beijing, Tianjin, Shanghai, Hainan, Qinghai, and Ningxia all have a production efficiency score of 1 for four consecutive years. Xinjiang's efficiency score in 2013 is higher than 0.7, and its total efficiency is 1 in the last three years. The annual efficiency values of Hebei, Shanxi, Heilongjiang, Henan, Guangxi, Yunnan, Gansu, Sichuan, and Guizhou are below 0.5. From a regional comparison, the highest average efficiency of the first stage is in the eastern region, second is the western region, and lowest is the central region. The average efficiency in the eastern region is about 0.8, and the average efficiency in the central region is around 0.5.
(4) The efficiencies in the second stage for most provinces are much lower than those in the first stage. The provinces with an efficiency score of 1 in the second stage include Beijing, Tianjin, Shanghai, Hainan, Qinghai, Ningxia, and Xinjiang. In 2013, the efficiency values of Fujian and Shandong are slightly higher than 0.4 and then turn to 1 in the following three years. Provinces with an efficiency value higher than 0.3 but lower than 1 are Guangxi, Guizhou, and Gansu. In the first three years of Jiangxi, its efficiency value is higher than 0.3, but then fell below 0.3 in 2016. The efficiency values of the other 17 provinces are below 0.3. The second stage clearly has room for efficiency improvement. From a regional comparison, the average efficiency of the second stage of the eastern region is the highest, and the lowest is the central region. The efficiency values of the provinces in the region exhibit large differences.
(5) The two-stage efficiency values of Beijing, Tianjin, Shanghai, Hainan, Qinghai, Ningxia, and Xinjiang are equal to or close to 1. The second-stage efficiency values of Fujian and Shandong are higher than their first-stage efficiency values. In most other provinces, their second-stage efficiency values are much lower than the first stage. The efficiency values in the production stages of Jiangsu, Zhejiang, and Guangdong are higher than 0.7, but the efficiency values for most years of the health treatment stage are low at between 0.1 and 0.3.
(6) Among the provinces with annual efficiency values below 1, most of them have a downward trend in energy consumption, CO 2 , and NO x efficiency values in the four years. However, their SO 2 efficiency values are on the rise, and the growth rates of SO 2 efficiency in Liaoning, Jilin, Heilongjiang, Zhejiang, Anhui, Henan, Hubei, Hunan, Sichuan, and Shaanxi are much higher than in previous years. In the provinces with higher energy consumption efficiency, the efficiencies of CO 2 , SO 2 , and NO x are also high. The eastern region has the highest average efficiency of these variables, while the central region has the worst efficiency performance.
(7) Among the provinces with health expenditure efficiencies below 1, the efficiency values of most provinces are around 0.3, with trending declines in the next three years. From a regional comparison, the eastern region has the highest average health expenditure efficiency with an average efficiency around 0.6, and the central region has the lowest average efficiency with an average efficiency of less than 0.3.
(8) For the death rate, most provinces have higher efficiency values. Beijing, Tianjin, Shanghai, Shandong, Guangdong, Hainan, Qinghai, Ningxia, and Xinjiang have efficiency scores of 1 in four years. The efficiencies of Hebei, Heilongjiang, and Jiangsu are declining, while the efficiencies of Jiangxi, Guangxi, Chongqing, and Guizhou are increasing. With economic development and the improvement of people's living standards, most provinces have achieved a higher level of death management efficiency. From a regional comparison, the average death rate efficiency in the eastern region is slightly better, and there is not much difference between regions.
(9) For phthisis, those with efficiency scores of 1 for four years include Beijing, Tianjin, Shanghai, Fujian, Shandong, Hainan, Gansu, Qinghai, Ningxia, and Xinjiang. Those with efficiencies around 0.5 are Liaoning, Jilin, Heilongjiang, and Guizhou. Most provinces exhibit high efficiency in the control of tuberculosis infections. From a regional comparison, the average efficiency of phthisis in the western region is slightly ahead in the first three years, and the eastern region is slightly ahead in the fourth year. Many provinces show a downward trend in phthisis efficiency.

Policy Suggestion
(1) Increasing the efficiency of energy consumption can effectively reduce emissions of greenhouse gases and atmospheric pollutants such as sulfur dioxide and nitrogen oxides. There are many measures to improve energy consumption efficiency, such as continuing to eliminate high energy consumption, improving the low efficiency of backward production capacity, strengthening publicity to raise public awareness of energy conservation and environmental protection, advocating green lifestyles represented by green behavior, and developing clean energy with less environmental pollution.
(2) From the rapid improvement of sulfur dioxide emission efficiency in most provinces, it can be seen that technology applications such as desulfurization and sulfur reduction in the production process advocated by the government in recent years have achieved great results. The government should promote broader practical applications of environmental protection technologies through administrative purchases, tax incentives, media publicity, and other means to improve the emission efficiency of atmospheric pollutants such as greenhouse gases and nitrogen oxides.
(3) There are two reasons for the inefficiency of health expenditures. First, more money is spent on disease treatment than on prevention, and the government is helping to increase the efficiency of health expenditures through advocacy and disease prevention. Second, the emission of pollutants and the deterioration of the environment make health problems very serious. Therefore, the government has adopted measures such as health promotion, disease prevention, and environmental pollution control measures to help improve the efficiency of health spending.
(4) In Liaoning, Jilin, Heilongjiang, and other provinces, CO 2 , NO x , health expenditure, mortality, and phthisis are relatively inefficient. The government needs to adjust these areas' industrial structure, environmental pollution rectification, disease prevention, and disease treatment. Funding: This study was supported by the philosophy and social science research project of higher education institutions of the Jiangsu Provincial Department of Education, and the mixed teaching mode of private higher vocational accounting training courses, number 2018SJA1500.