The division k input i resource for D M U j in period t is: x i j k t ∈ R + i = 1 , K , m k ; j = 1 , K , n ; K = 1 , … K , K ; t = 1 , K , T . The division K output i resource for D M U j in period t is: y r j k t ∈ R + r = 1 , K , r k ; j = 1 , K , n ; K = 1 , … K , K ; t = 1 , K , T . If some of the outputs are undesirable, we treat them as division k inputs.

The link between D M U j intermediate products from division k to division h in period t is Z j k h t t ∈ R + j = 1 , K , n ; l = 1 ; k ; L h k ; t = 1 ; K ; T , where L h k is the number of items in connections from k to h; L i n k i n k is the number of “as input” links from division k; and L i n o u t k is the number of “as output” links from division k.

The carryover of D M U j from period t to period t+1 at division k is Z j k l t , t + 1 ∈ R + j = 1 , K , n ; l = 1 , K , L k ; k = 1 , K , K ; t = 1 , K , T − 1 , where L k is the total number of items in the division k carryover, and n g o o d k and n b a d k , respectively, are the number of desirables (good) and undesirables (bad) for each division k.

The overall efficiency is evaluated using the following program: θ o * = min ∑ t = 1 T W t ∑ k = 1 K W k 1 − 1 m k + l i n k i n k + n b a d k ∑ i = 1 m k S i o k t − x i o k t + ∑ k l = 1 n b a d k S o k l b a d t , t + 1 Z o k l b a d t , t + 1 + ∑ k , h l = 1 L i n k i n k S o k , h l i n t Z o k , h l i n t ∑ t = 1 T W t ∑ k = 1 K W k 1 + 1 r k + l i n k o u t k + n g o o d k ∑ i = 1 r k S i o k t + y i o k t + ∑ k l = 1 n g o o d k S o k l g o o d t , t + 1 Z o k l g o o d t , t + 1 + ∑ k , h l = 1 L i n k o u t k S o k , h l o u t t Z o k , h l o u t t (1) In Formula (1), θ o * represents the overall efficiency value. When θ o * = 1 , it means that the decision making unit is relatively effiective. When θ o * < 1 , it means that the decision making unit is invalid; With ∑ t = 1 T W t = 1 , ∑ k = 1 K W k = 1 , W t ≥ 0 ∀ t , W k ≥ 0 ∀ k , where W t t = 1 , K , T is the weight to period t, and W k k = 1 , K , K is the weight to division k.

The constraints are as follows: x o k t = X k t λ k t + S k o t − k = 1 , K , K ; t = 1 , K , T y o k t = Y k t λ k t − S k o t + k = 1 , K , K ; t = 1 , K , T e λ k t = 1 k = 1 , K , K ; t = 1 , K , T λ k t ≫ 0 , S k o t + ≫ 0 , S k o t − ≫ 0 ∀ k , ∀ t Z k h f r e e t λ h t = Z k h f r e e t λ k t ∀ k , h f r e e , ∀ t w h e r e   Z k h f r e e t = Z k h f r e e t , K , Z n k h f r e e t ∈ R L k h f r e e × n Z o k l f r e e t , t + 1 = ∑ j = 1 n Z j k l f r e e t , t + 1 λ j k t + S o k l f r e e t , t + 1 ; k l = 1 , k , n f r e e k ; k = 1 , K , K ; t = 1 , K , T (2) where X k t = X 1 k t , K , X n k t ∈ R m k × n × T an Y k t = y 1 k t , K , y n k t ∈ R r k × n × T are input and output matrices, and S k o t − and S k o t + are input/output slacks, respectively.

The term (period) efficiency is defined by: τ o t * = min ∑ k = 1 K W k 1 − 1 m k + l i n k i n k + n b a d k ∑ i = 1 m k S i o k t − x i o k t + ∑ k , h = 1 l i n k i n k S o k , h l i n t Z o k , h l i n t + ∑ k l = 1 n b a d k S o k l b a d t , t + 1 Z o k l b a d t , t + 1 ∑ k = 1 K W k 1 + 1 r k + l i n k o u t k + n g o o d k ∑ i = 1 r k S i o k t + y i o k t + ∑ k , h l = 1 l i n u o t k S o k , h l o u t t Z o k , h l o u t t + ∑ k l = 1 n g o o d k S o k l g o o d t , t + 1 Z o k l g o o d t , t + 1 t = 1 , K , T (3) In Formula (3), τ o t * represents the term (period) efficiency value. When τ o t * = 1 , it means that the decision making unit is relatively effiective. When τ o t * < 1 , it means that the decision making unit is invalid.

Divisional efficiency is defined by: δ o k * = ∑ t = 1 T W k 1 − 1 m k + l i n k i n k + n b a d k ∑ i = 1 m k S i o k t − x i o k t + ∑ k , h = 1 l i n k i n k S o k , h l i n t Z o k , h l i n t + ∑ k l = 1 n b a d k S o k l b a d t , t + 1 Z o k l b a d t , t + 1 ∑ t = 1 T W t 1 + 1 r k + l i n k o u t k + n g o o d k ∑ i = 1 r k S i o k t + y i o k t + ∑ k , h l = 1 l i n u o t k S o k , h l o u t t Z o k , h l o u t t + ∑ k l = 1 n g o o d k S o k l g o o d t , t + 1 Z o k l g o o d t , t + 1 k = 1 , K , K (4) In Formula (4), δ o k * represents the divisional efficiency value. When δ o k * = 1 , it means that the decision making unit is relatively effiective. When δ o k * < 1 , it means that the decision making unit is invalid.

Term (period)-divisional efficiency is defined by: ρ o k t * = 1 − 1 m k + l i n k i n k + n b a d k ∑ i = 1 m k S i o k t − x i o k t + ∑ k , h = 1 l i n k i n k S o k , h l i n t Z o k , h l i n t + ∑ k l = 1 n b a d k S o k l b a d t , t + 1 Z o k l b a d t , t + 1 1 + 1 r k + l i n k o u t k + n g o o d k ∑ i = 1 r k S i o k t + y i o k t + ∑ k , h l = 1 l i n u o t k S o k , h l o u t t Z o k , h l o u t t + ∑ k l = 1 n g o o d k S o k l g o o d t , t + 1 Z o k l g o o d t , t + 1 k = 1 , K , K ; t = 1 , K , T (5) In Formula (5), ρ o k t * represents the term (period)-divisional value. When ρ o k t * = 1 , it means that the decision making unit is relatively effiective. When ρ o k t * < 1 , it means that the decision making unit is invalid.

Furthermore, we used Hu’s (Hu and Wang, 2006) approach to assess the undesirable output efficiency: P M 2.5   e f f i c i e n c y : T a r g e t   U n d e s i r a b l e   P M 2.5   i n p u t i , t A c t u a l   U n d e s i r a b l e   P M 2.5   i n p u t i , t (6) S O 2   e f f i c i e n c y : T a r g e t   U n d e s i r a b l e   S O 2   i n p u t i , t A c t u a l   U n d e s i r a b l e   S O 2   i n p u t i , t (7) N O x   e f f i c i e n c y : T a r g e t   U n d e s i r a b l e   N O x   i n p u t i , t A c t u a l   U n d e s i r a b l e   N O x   i n p u t i , t (8) I m p r o v e m e n t   r a t i o   o f   v a r i a b l e = 1 − e f f i c i e n c y   o f   v a r i a b l e (9)

In the above equations, i represents area and t represents time. When the target air pollutant input is equal to the actual input level, air pollutant control efficiency is equal to 1, indicating overall high efficiency; on the other hand, when the target air pollutant input is lower than the actual input level, air pollutant control efficiency is lower than 1, indicating overall inefficiency.

This study evaluates 30 provinces in China (including autonomous regions and municipalities directly under the central government), excluding Hong Kong, Macao, Tibet, and Taiwan. These are omitted because the majority of the data is missing. We divide the provinces into regions based on geographical differences: eastern, central, and western (Figure 1). The eastern region includes Beijing, Tianjin, Hebei, Shanghai, Hainan, and other provinces; the central area is composed of Shanxi, Jilin, Heilongjiang, Anhui, Jiangxi, Henan, and other provinces; and the western area is made up of Inner Mongolia, Chongqing, Guangxi, and other provinces. In addition, the “China Population and Employment Statistical Yearbook,” the “China Health and Health Yearbook,” and the “China Statistical Yearbook” provide data on Chinese economic and social development from 2015 to 2020. The “China Environmental Protection Bureau Annual Report” and the “China Environmental Statistics Yearbook” provide data on Chinese air pollutants.

Economic development stage variables:

Regarding input indicators, with reference to previous studies (Li et al., 2019a; Li et al., 2019b; He et al., 2020; Li et al., 2020), we chose to use labor and energy consumption as input indicators. However, this paper cannot include fixed assets as input indicators due to limitations in data availability. Regarding output indicators, we selected the Gross Domestic Product (GDP) as the output indicator (Sueyoshi et al., 2021).

Link economic development stage and healthy production stage variables:

The links PM2.5, SO₂, and NO_x are from (Zhang et al., 2018a; Lin et al., 2021). The carry-over variable for multiple periods is government health expenditures, referring to (Zhang et al., 2022).

Health production stage variables:

Regarding input indicators, this paper restricts health inputs to those that act directly on health (i.e., inputs in healthcare). In line with the relevant literature (Kawaguchi et al., 2014; Flokou et al., 2017; Top et al., 2020), we selected the number of health technicians per 1,000 population and the number of beds per 1,000 population as input indicators. Regarding output indicators, it is clear from the literature (Evans et al., 2000; Afonso and Aubyn, 2005; Spinks and Hollingsworth, 2009; Rajaratnam et al., 2010; Rutherford et al., 2010) that the main output indicators of population health status are: average life expectancy, disability-adjusted life expectancy, maternal mortality, and infant mortality, among others. Due to the lag in the release of Chinese health statistics, there are many gaps in current data on average life expectancy and disability-adjusted life expectancy, which do not reflect the sustained level of healthy production. Thus, this paper selects the maternal mortality rate and perinatal mortality rate as output indicators. However, since the levels of maternal mortality and perinatal mortality do not represent whether the trend of health output efficiency is positive or not, this indicator of health output is in inverse form (i.e., a higher value of the indicator represents a lower level of health output; Hadad et al., 2013). Consequently, we borrowed from (Sayem et al., 2019) to take the inverse of the indicator and transform it into maternal survival rate and perinatal survival rate.

Based on the above analysis, Figure 2 depicts the framework of the DNSBM model’s intertemporal efficiency measures and variables.

We estimated the economic development efficiency of 30 provinces from 2015 to 2020 using the DNSBM model, including labor and energy consumption as input indicators and GDP as an output indicator. The results (Table 1; Figure 4A) show that Beijing, Shanghai, and Jiangsu had the highest average efficiency of economic development; provinces such as Tianjin, Zhejiang, and Fujian had an average efficiency of economic development of around 0.9, which was significantly higher than that of other provinces. Provinces such as Ningxia, Qinghai, Anhui, and Hubei had an economic development efficiency of 0.4–0.8. Xinjiang had the lowest average economic development efficiency of 0.34, followed by Gansu at 0.391, showing that the region requires further improvement.

There are also important regional differences. In the east (Figure 4B), the efficiency of economic development in Beijing, Shanghai, Jiangsu, and Guangdong was always equal to 1, suggesting that economic resources in these provinces are adequately employed. Hainan’s efficiency was equal to 1 in all previous periods, but declined significantly to around 0.5 in 2020, showing that the high efficiency of economic resource usage in the first 5 years did not continue. Hebei’s trend of changing economic development efficiency is similar to Liaoning’s, where efficiency has declined for 6 years, with Liaoning reaching a low of 0.286 in 2020. Tianjin’s and Shandong’s economic development efficiency values were equal to 1 in 2015–2018 but dropped to around 0.7 in 2019–2020. In the central region (Figure 4C), Jiangxi had the highest economic development efficiency, with a stable efficiency value of 1 in 2015–2019, but it dropped sharply to about 0.4 in 2020. Hunan had the greatest swing, with an economic development efficiency of 1 in 2016–2018 that fell to 0.495 in 2020. Jilin’s and Heilongjiang’s economic development efficiency values steadily declined over the last 6 years and are projected to decrease to around 0.25 by 2020. In the western region (Figure 4D), during the study period, the economic development efficiency of Yunnan reached 1. Except for Guangxi, Chongqing, Sichuan, and Shaanxi, most remaining provinces were below 0.6 in 2015–2020. For example, Xinjiang was below 0.4 in four out of 6 years studied. Gansu’s efficiency was below 0.4 in three of the last 6 years, and it fell to a minimum of 0.217 in 2020.

We estimated the health production efficiency of 30 provinces from 2015 to 2020 by applying the DNSBM model, using health technicians per 1,000 population and beds per 1,000 population as input indicators and maternal survival rate and perinatal survival rate as output indicators. The study results (Table 2; Figure 5A) show that only Beijing, Shanghai, Guangdong, and Jiangxi had an average efficiency of 1 in health production. This demonstrates that the healthcare services provided in these places are of outstanding quality and that the health production scale effect may be fulfilled. In contrast, health production efficiency in other provinces is generally poor; in different years, some provinces were severely inefficient, falling below 0.3. This indicates the region’s failure to integrate economic development with healthy production and the need for significant improvements.

There are also important regional differences. In the eastern region (Figure 5B), health production efficiency was generally higher in the east than in the midwest. The fact that some provinces’ health production efficiency was comparable to or even lower than that of the midwest should be emphasized. For example, Liaoning’s health production efficiency has been consistent, at roughly 0.4 during the last 6 years. The health production in Hainan and Tianjin remained equal to 1 in the early period, but exhibited a slight fall in 2019–2020. Zhejiang is the most volatile province, with healthy production efficiency remaining around 0.6 in 2015–2016 but rising to 1 in 2020. In the central region (Figure 5C), Jiangxi has the most efficient health production. Shanxi, Heilongjiang, and Jilin have low health production efficiency, which remained between 0.4 and 0.5 for the past 6 years. In Henan, health production efficiency decreased over the first 5 years but peaked at 0.741 in 2020. In the western region (Figure 5D), Yunnan had the highest health production efficiency, reaching over 0.6; Xinjiang had the lowest value of 0.235. The efficiency of the remaining provinces, such as Inner Mongolia, Gansu, and Qinghai, was below 0.4. Ningxia was the most volatile, with healthy production efficiency falling below 0.4 in 2015–2018, but reaching a peak of around 0.7 in 2019–2020.

We additionally estimated the overall efficiency of the 30 provinces for the period 2015–2020 using the DNSBM model. Table 3 and Figure 6 display the calculated outcomes.

The findings reveal significant variation in the overall efficiency of the provinces. For example, the last 6 years have seen overall efficiency equal to 1 in Beijing, Shanghai, and Guangdong; these provinces have the highest resource utilization efficiency in the study. Zhejiang’s overall efficiency was less than 1 in 2015–2019 but rose to 1 in 2020; Jiangxi’s and Hainan’s overall efficiency values were 1 in 2015–2019 but fell to around 0.74 in 2020. Tianjin, Jiangsu, Yunnan, and Shandong performed well in terms of overall efficiency among the inefficient provinces; with the highest efficiency of less than 0.32 during the past 6 years, Xinjiang has the lowest performance. The efficiency of Liaoning, Jilin, and Guangxi was between 0.5 and 0.7, while that of Shanxi, Heilongjiang, Inner Mongolia, Guizhou, Qinghai, and Ningxia was around 0.4. As a result, these provinces must focus on overall efficiency improvement.

Over time, different trends in overall efficiency emerged among the provinces. For example, the overall efficiency of four provinces—Zhejiang, Fujian, Yunnan, and Ningxia—consistently climbed. Among them, Zhejiang experienced the largest increase, from 0.794 in 2015 to 1 in 2020, followed by Ningxia, from 0.388 in 2015 to 0.595 in 2020. Yet, the overall efficiency of the remaining 26 provinces decreased. Among them, Jiangxi and Liaoning had the largest decline, from 1 to 0.668, respectively, in 2015 to 0.732 and 0.4 in 2020. According to these results, we discovered that there are more provinces with falling efficiency values than with growing efficiency values. This demonstrates that most provinces must perform better in terms of economic development and health production.

As shown in Figure 7A, economic development efficiency is the most crucial component of China’s total efficiency performance, followed by health production efficiency. Figure 7B displays some trends in the data. Over the period 2015–2020, the decline in the efficiency of economic development led to a drop in overall efficiency, while the rise in the efficiency of health production was the main contributor to mitigating the decline in overall efficiency. Specifically, economic development efficiency exhibited negative growth in all years except 2017–2018. In contrast, health productivity efficiency showed positive growth in all years except 2016–2017 and 2018–2019, which showed negative growth.

The Kruskal–Wallis test was used to analyze the efficiency differences across the eastern, central, and western regions, and the p-values were compared with the confidence level, α , which was set at 0.01, 0.05, and 0.10. Table 4 provides detailed test results. Most of the p-values in the various phases from 2015 to 2020 are less than 0.05, and the validation findings are very significant, showing substantial variation in efficiency across the east, central, and west. Specifically, regarding overall efficiency (Figure 8A), the eastern region began from a relatively high base, and it extended its advantage over the central and western regions during the study period. This indicates that the east outperformed the west and central regions regarding economic development and health production. It is well known that unbalanced regional development has become a growing concern in China. However, the Chinese government has tried to promote the development of the central and western regions by introducing preferential policies and investing significant resources to solve this problem. Still, our calculations indicate that the midwest has continued to lag in terms of efficiency levels. These gaps have widened in recent years and may continue to do so in the future. Furthermore, economic development efficiency (Figure 8B) decreased in all three regions. The east began with a relatively high standard among the three regions, suggesting that it performed more efficiently, using its economic output for economic development. According to the findings, the eastern region had better economic development efficiency in 2020, an advantage that appears to be expanding in the years ahead. Despite the fluctuating downward trend in health production efficiency in the three significant regions around 2017 (Figure 8C), it still improved at the end of the observation period compared to 2015. Finally, the eastern region’s health production efficiency is higher than the national average; as evidence of the “central collapse” phenomenon, the values for the central and western areas are lower than the national average.

This study also evaluated the air pollution control capacity of 30 Chinese provinces using the DNSBM model for 2015–2020. The results reveal that China’s average PM2.5, SO₂, and NO_x control efficiency are 0.786, 0.710, and 0.718, respectively; these are relatively low and have considerable room for improvement. Specifically, regarding PM2.5 (Figure 9A), 13 provinces have a governance efficiency higher than 0.9, accounting for 43.3% of the total. The provinces with the lowest efficiency are Shanxi, Xinjiang, Gansu, and Ningxia, with governance efficiencies below 0.5. Regarding SO₂ (Figure 9B), ten provinces have a governance efficiency higher than 0.9, accounting for 33.3% of the total. The eight provinces with the lowest efficiency are Shanxi, Inner Mongolia, Gansu, Liaoning, Chongqing, Guizhou, Xinjiang, and Ningxia, with governance efficiencies below 0.5. Turning to NO_x (Figure 9C), ten provinces have a governance efficiency higher than 0.9, accounting for 33.3% of the total. The eight provinces with the lowest efficiency are Hebei, Shanxi, Inner Mongolia, Heilongjiang, Anhui, Liaoning, Xinjiang, and Ningxia, all with governance efficiencies below 0.5.

Considering these dramatic regional differences, China’s potential to reduce air pollution is enormous. If these inefficient provinces are given the management capacity and cutting-edge technology possessed by the more efficient provinces, they should be able to achieve this goal. In addition, as shown in Table 5, most of the p-values for air pollutants from 2015 to 2020 are less than 0.05, and the validation findings are very significant, showing substantial variation in the air pollution control efficiency across the eastern, central, and western provinces. Figure 9 makes it clear that all of the high-efficiency provinces are in the developed eastern region. Five of the eight provinces that are inefficient are located in the west, while three are located in the center of the country. It is evident that regional economic development is positively connected with air pollution control. Thus, economic growth could be essential in improving the effectiveness of regional air pollution control in China.

Next, we applied the DNSBM model for each inefficient province to capture their air pollution reduction targets. However, when we examined the data we discovered that these provinces are struggling to meet the DNSBM model-calculated targets because of their significant differences from the efficient provinces regarding economic development, management capability, and technological level. As a result, the DNSBM model’s air pollution reduction targets in this study are considered long-term goals, as they are not achievable in the short term for inefficient provinces. To further demonstrate the point, Table 6 shows the actual and target values for each province in China and the improvement in PM2.5 concentrations, SO₂ emissions, and NO_x emissions.

As seen in Table 6, Beijing, Shanghai, Jiangsu, Jiangxi, Guangdong, and Yunnan have zero air pollution reduction targets and are benchmarks for other inefficient Chinese provinces. For low-efficiency provinces to achieve high efficiency (e.g., Hubei, with PM2.5, SO₂, and NO_x control efficiencies of 0.694, 0.830, and 0.860, respectively), their PM2.5 concentrations should be reduced from 39.16 ug/m³ to 27.18 ug/m³ (30.59% improvement), SO₂ emissions from 212,946.50 tons to 176,847.42 tons (16.95% improvement), and NO_x emissions from 420,771.00 tons to 361,894.87 tons (13.99% improvement). Meanwhile, Hunan, with PM2.5, SO₂, and NO_x control efficiency values of 0.843, 0.695, and 0.894, respectively, should reduce PM2.5 concentrations from 36.17 ug/m³ to 30.48 ug/m³ (15.74% improvement), SO₂ emissions from 283,944.33 tons to 197,406.04 tons (30.48% improvement), and NO_x emissions from 414,936 tons to 371,080.54 tons (10.57% improvement). For these two higher-ranked provinces, these air pollution reduction goals are immediately realizable. Nevertheless, we also discovered that it is difficult to meet the targets for some less efficient regions in a single step or within a short period of time. For example, Xinjiang’s PM2.5, SO₂, and NO_x control efficiencies are 0.394, 0.301, and 0.334, respectively, and it must reduce these values by 60.55%, 69.87%, and 66.61%, respectively. Thus, for these inefficient provinces, these goals cannot be achieved overnight or even within a short time, and should be considered long-term goals.