**3. Materials and Methods**

### *3.1. Regional Overview*

The Yangtze River Economic Belt consists of the 11 provincial administrative units of Shanghai, Jiangsu, Zhejiang, Anhui, Jiangxi, Hubei, Hunan, Guizhou, Chongqing, Sichuan, and Yunnan (Figure 1) and covers an area of about 2.05 million km2, accounting for 21% of the country and more than 40% of the total population and economy [7]. It is one of the Chinese chemical industry agglomeration areas. In 2016, 11 provinces and cities in the Yangtze River Economic Belt achieved a total sales value of 8253.40 billion RMB, accounting for 43.46% of the total sales value in China. The sales output values of the chemical industry in downstream areas, middle reaches, and upstream area were 530.18 billion RMB, 1816.96 billion RMB, and 1134.663 billion RMB, accounting, respectively, for 27.91%, 9.57%, and 5.97% of that in China. The sales value of the chemical industry in Jiangsu province was the highest at 2954.89 billion RMB, about 15.56% of the whole country, while that in Yunnan province was the lowest at 139.00 billion RMB, accounting for 0.73% of that in the whole country [28].

**Figure 1.** Map of the Yangtze Economic Belt.

### *3.2. Methods*

3.2.1. Calculation of Grey Water Footprint of the Chemical Industry

Industrial wastewater is directly discharged into surface water. The main pollutants in industrial wastewater can be measured directly, such as chemical oxygen demand (COD) and ammonia nitrogen (NH<sup>+</sup> <sup>4</sup> -N) in chemical industry wastewater. Therefore, COD and NH<sup>+</sup> <sup>4</sup> -N are used as the main indicators to measure the grey water footprint of the chemical industry. The calculation formula is as follows [23]:

$$GWF\_{ind} = \max\left(GWF\_{\inf(COD)}, GWF\_{ind(NH\_4^+ - N)}\right)$$

$$GWF\_{ind(i)} = \frac{L\_{ind(i)}}{C\_{\max} - C\_{\text{nat}}} - W\_{cd}$$

$$GWF\_{rc\%} = \sum\_{i=1}^{n} GWF\_{ind(i)}$$

where *GWFind* (billion m3) is the grey water footprint of the chemical industry, *GWFind(i)* (billion m3) is the grey water footprint of the chemical industry with the standard of category *i* pollutants, *Wed* (billion m3) is the discharge amount of chemical industry wastewater, and *GWFreg* (billion m3) is the grey water footprint of the regional chemical industry. China's Standard Limits for Basic Items of Surface Water Environmental Quality Standard (GB 3838-2002) is used as the standard. In the standard, the water quality is required to meet the class III water quality index, and the concentration limits of COD and ammonia nitrogen (NH<sup>+</sup> <sup>4</sup> -N) in class III water are taken as the environmental concentration standards of COD and ammonia nitrogen (NH<sup>+</sup> <sup>4</sup> -N) in water.

#### 3.2.2. Measurement Model of Green Development Efficiency of the Chemical Industry

The SBM–undesirable model was proposed to measure the green development efficiency of the chemical industry. It is calculated as [34]: Supposing there are *n* individual *DMUs*, including input vector, expected output, and unexpected output, respectively, that are recorded as *<sup>x</sup>*, *<sup>x</sup>* ∈ *Rm*, *<sup>y</sup><sup>g</sup>* ∈ *Rs*1, and *<sup>y</sup><sup>b</sup>* ∈ *Rs*2. The matrix is defined as

$$X = \left[ \mathbf{x}\_1, \mathbf{x}\_2, \dots, \mathbf{x}\_n \right] \in R\_{\mathfrak{W} \times \mathfrak{W}}, \ Y^{\mathfrak{F}} = \left[ y\_1^{\mathfrak{F}}, y\_2^{\mathfrak{F}}, \dots, y\_n^{\mathfrak{F}} \right] \in R\_{\mathfrak{s} 1 \times n \nu}, \ Y^{\mathfrak{b}} = \left[ y\_1^{\mathfrak{b}}, y\_2^{\mathfrak{b}}, \dots, y\_n^{\mathfrak{b}} \right] \in R\_{\mathfrak{s} 2 \times n \nu}$$

According to the actual input and output, supposing *xi* > 0, *y g <sup>i</sup>* > 0, *<sup>y</sup><sup>b</sup> <sup>i</sup>* > 0, productive collection *P*, that is, *N* element input *X*. All combinations of expected and undesired outputs can be defined as

$$P = \left\{ (\mathfrak{x}, \mathfrak{y}^{\mathfrak{g}}, \mathfrak{y}^{\mathfrak{b}}) \, \Big| \, \mathfrak{x} \ge \mathbf{X}\lambda, \mathfrak{y}^{\mathfrak{g}} \ge \mathbf{Y}^{\mathfrak{b}}\lambda, \mathfrak{y}^{\mathfrak{b}} \ge \mathbf{Y}^{\mathfrak{b}}\lambda(\lambda \ge 0) \right\}.$$

Therefore, the SBM–undesirable model can be expressed as

$$p\* = \min \frac{1 - \frac{1}{m} \sum\_{i=1}^{\hat{I}} \frac{S\_i^-}{X\_{i0}^-}}{1 + \frac{1}{\sum\_{1} + S\_2} \left( \sum\_{r=1}^{S\_1} \frac{S\_r^\emptyset}{y\_{r0}^\emptyset} + \sum\_{r=1}^{S\_2} \frac{S\_r^\emptyset}{y\_{r0}^\emptyset} \right)}, \text{ s.t.} \begin{cases} X\_0 = X\lambda + S^-\\ y\_0^\emptyset = Y^\emptyset \lambda + S^\emptyset\\ y\_0^\emptyset = Y^\emptyset \lambda + S^\emptyset\\ S^- \ge 0, S^\emptyset \ge 0, S^\emptyset \ge 0, \lambda \ge 0 \end{cases}$$

Type: *S*− *<sup>i</sup>* , *<sup>S</sup><sup>g</sup> <sup>r</sup>* , and *S<sup>b</sup> <sup>r</sup>*, respectively, represent the first *i0* input redundancy, expected output deficiency, and expected output superscalar of each decision-making unit; *S*− *<sup>i</sup>* , *<sup>S</sup><sup>g</sup> r* , and *S<sup>b</sup> <sup>r</sup>*, respectively, denote their corresponding vectors; and λ is the weight vector. The optimal solution of the above formula is (λ\*, *S*−\*, *Sg*\*, *Sb*\*). *P*\* = 1 only when the bad output exists, that is, *S*−\* = 0, *Sg*\* = 0, *Sb*\* = 0 when *DMU0* is efficient.

#### 3.2.3. Dagum Gini Coefficient and Decomposition Method

By using the Dagum Gini coefficient method, this study analyzes the spatial differences and sources of green development efficiency of the chemical industry in the upper, middle, and lower reaches of the Yangtze River Economic Belt. According to the Gini coefficient and its subgroup decomposition method proposed by Dagum (1997), the definition of Gini coefficient G is as shown in Equation (1) [35]:

$$G = \frac{\sum\_{j=1}^{k} \sum\_{l=1}^{k} \sum\_{i=1}^{n\_j} \sum\_{r=1}^{n\_l} |y\_{ji} - y\_{lr}|}{2n^2 \overline{y}} \tag{1}$$

where *j* and *h* are subscripts for different regions; *i* and *r* are the indexes of provinces and cities, respectively; *n* is the total number of provinces and cities; *k* is the total number of regions; and *nj*(*nh*) and *j*(*h*) are the number of provinces and cities within a region. *yji(yhr)* is the green development efficiency of the chemical industry in *j(h)* regional provinces and cities *i(r)*, and *y* is the average value of green development efficiency of the chemical industry in all provinces and cities. On the overall Gini coefficient *G* by region, according to the average value of green development efficiency of the chemical industry in each region *k*, the region is sorted and then the Gini coefficient *G* is divided into three parts: intraregion (intra-group) difference pairs *G* contribution of *Gw*, interregional (inter-group) difference pairs *G* contribution of *Gnb*, and interregional (inter-group) ultra-variable density pairs *G* contribution of *Gt*. When the three meet, *G* = *Gw* + *Gnb* + *Gt*, in which the area *j* has a Gini coefficient of *Gjj* and intraregional differences *Gw*. The calculation formulas are Formulas (2) and (3), respectively; zones *j* and *h* have a Gini coefficient between *Gjh* and the regional net difference *Gnb*. The calculation formulas are Formulas (4) and (5), respectively. The calculation formula for the interregional super-variable density *Gt* is shown in Formula (6).

$$G\_{j\bar{j}} = \frac{\frac{1}{2\overline{y}\_{\bar{j}}} \sum\_{i=1}^{n\_{\bar{j}}} \sum\_{r=1}^{n\_{\bar{j}}} |y\_{j\bar{i}} - y\_{j\bar{r}}|}{n\_{\bar{j}}^2} \tag{2}$$

$$G\_{\rm w} = \sum\_{j=1}^{k} G\_{\vec{j}\vec{l}} P\_{\vec{j}} S\_{\vec{j}} \tag{3}$$

$$G\_{j\hbar} = \sum\_{i=1}^{n\_j} \sum\_{r=1}^{n\_h} \frac{|\mathcal{Y}\_{ji} - \mathcal{Y}\_{hr}|}{n\_j n\_h (\overline{\mathcal{Y}}\_j + \overline{\mathcal{Y}}\_h)} \tag{4}$$

$$G\_{nb} = \sum\_{j=2}^{k} \sum\_{h=1}^{j-1} G\_{jh} (p\_j s\_h + p\_h s\_j) D\_{jh} \tag{5}$$

$$G\_t = \sum\_{j=2}^k \sum\_{h=1}^{j-1} G\_{jh} (p\_j s\_h + p\_h s\_j)(1 - D\_{jh}) \tag{6}$$

In Equation (5), *pj* = *nj/n*, *sj* = *njyj* /*ny*, and *j* = 1, 2, 3. In Equation (7), *Djh* denotes region *j* and *h*. See Formula (7) for the relative influence of green development efficiency of the chemical industry. *djh* is the difference of the green development efficiency of the chemical industry between regions (see Equation (8)). *j*, *h* all *yji* − *yhr* > 0 is the mathematical expectation of the sample summation; *pjh* is the super-variable first-order moment, representing the region. *j*, *h* all *yhr* − *yji* > 0 is the mathematical expectation of the sample summation.

$$D\_{j\text{h}} = \frac{d\_{j\text{h}} - p\_{j\text{h}}}{d\_{j\text{h}} + p\_{j\text{h}}} \tag{7}$$

$$d\_{jh} = \int\_0^\infty dF\_j(y) \int\_0^y (y-x) dF\_h(x) \tag{8}$$

$$p\_{j\hbar} = \int\_0^\infty dF\_\hbar(y) \int\_0^y (y-x) dF\_\hbar(x) \tag{9}$$

where *Fj(Fh)* represents the area *j(h)C*, which is the cumulative distribution function of green development efficiency of the chemical industry.

#### 3.2.4. Convergence Model

To investigate the evolution trend of green development efficiency of the chemical industry in the whole Yangtze River Economic Belt and the upper, middle, and lower reaches, the convergence analysis is carried out, including σ Convergence and β Convergence.

σ Convergence refers to the trend where the deviation of green development efficiency of the chemical industry in different regions is decreasing over time. σ Convergence is measured by the coefficient of variation and can be calculated as [36]:

$$
\sigma = \frac{\sqrt{\sum\_{i}^{N\_{\boldsymbol{y}}} \left(F\_{\boldsymbol{y}} - \overline{F\_{\boldsymbol{y}}}\right)^{2} / N\_{\boldsymbol{y}}}}{\overline{F}\_{\boldsymbol{y}}}.
$$

where *j* indicates the number of areas (*j* = 1, 2, 3 ... ), *i* indicates the number of provinces and cities in the region (*i* = 1, 2, 3 ... ), *Nj* is the number of provinces and cities in each region, and *Fij* denotes that the region *j* exists *t* with an average value of green development efficiency of the chemical industry in the period.

The β convergence model is [36]:

$$\ln(\frac{F\_{\bar{i},t+1}}{F\_{\bar{i},t}}) = \varkappa + \beta F\_{\bar{i},t} + \mu\_i + \nu\_t + \varepsilon\_{\bar{i}t}$$

The left side of the model is the growth rate of green development efficiency of the chemical industry calculated by logarithmic difference, where μ*<sup>i</sup>* is a fixed effect, *vt* is a time-fixed effect, and ε*it* is a random error term.

In condition β, the convergence model is absolute β. A series of control variables is added to the convergence model. This study adds environmental regulation, industrial structure, technical level, and foreign investment intensity as control variables. The convergence model for condition β is

$$\ln(\frac{F\_{\bar{i},t+1}}{F\_{\bar{i},t}}) = \kappa + \beta F\_{\bar{i},t} + \delta X + \mu\_{\bar{i}} + \nu\_t + \varepsilon\_{\bar{t},t}$$

In the regression process, each variable is logarithmic. In this paper, a two-way fixed effect model is adopted to improve the coefficient. In the β accuracy of estimation, the robust error standard of clustering is adopted to the provincial and municipal levels. If β < 0 and is significant, the green development efficiency of the chemical industry in the Yangtze River Economic Belt converges, or it diverges. The rate of convergence *b* = −ln(1+ β)/*T*.

#### *3.3. Index Selection and Data Processing*

3.3.1. Measurement Index of Green Development Efficiency of the Chemical Industry

According to existing research results, combined with the classification and characteristics of the chemical industry, the evaluation index system of green development efficiency of the chemical industry is constructed from input and output. Manpower, capital, energy, and water for the chemical industry are selected as investment indexes. The sales output value of the chemical industry is selected as the expected output index and the grey water footprint of the chemical industry as the unexpected output index (Table 1).

**Table 1.** Evaluation index system of green development efficiency of the chemical industry.


Considering the availability of data of the chemical industry, the scope of the chemical industry is defined as five subsectors in the manufacturing industry by the *China Industrial Statistics Yearbook*: petroleum processing, coking and nuclear fuel processing; chemical raw materials and chemical products manufacturing; pharmaceutical manufacturing; chemical fiber manufacturing; and rubber and plastic products manufacturing. Relevant data come from the *China Industrial Statistics Yearbook*, *China Environmental Statistics Yearbook*, *China Statistical Yearbook*, and statistical yearbooks of various provinces and cities from 2003 to 2017. *China Industrial Statistical Yearbook*, *China Environmental Statistical Yearbook*, and *China Statistical Yearbook* are the most authoritative and important sources of data for conducting research on China's socioeconomic development, available in both paper and electronic versions, published annually by the National Bureau of Statistics of China, and can be accessed through a variety of official channels for direct access to relevant data. The details are as follows. The missing data are estimated by intermediate interpolation method. There are no direct statistical data of total industrial water consumption and wastewater discharge in the statistical yearbook, so we apply the data of industrial wastewater and pollutant discharge in wastewater for each subsector in China to estimate the data of pollutant discharge in industrial wastewater for each subsector in each province [37]. Energy data of the chemical industry are estimated by reference [38]. For the net fixed capital and industrial sales output value of the chemical industry, the fixed assets investment price index of corresponding provinces and cities and the ex-factory price index of industrial producers are used for price reduction, which is reduced to the level of 2000.

#### 3.3.2. Variables Affecting the Efficiency of Green Development of the Chemical Industry

Using environmental regulations, industrial structure, foreign investment intensity and technological progress as control variables, this paper studied their influence on the green development efficiency of the chemical industry in the Yangtze River Economic Belt. Among them, the total amount of environmental governance for environmental regulation represents the proportion of GDP. Science and technology investment is represented by the proportion of science and technology expenditure in fiscal expenditure, which is representative of the investment amount of foreign-funded enterprises at the end of the year. The proportion of the secondary industry in GDP represents the industrial structure.

#### **4. Results**

#### *4.1. Evolution Characteristics of Grey Water Footprint of the Chemical Industry in the Yangtze River Economic Belt*

The grey water footprint of the chemical industry in the Yangtze River Economic Belt declined from 2002 to 2016 with a trend of fluctuation. It decreased from 16.03 billion m3 in 2002 to 12.03 billion m<sup>3</sup> in 2008 and then increased to 14.43 billion m<sup>3</sup> in 2016. In 2008, due to the impact of the financial crisis, the operation of chemical enterprises was impacted, the production capacity decreased, and the total grey water footprint was at its lowest point. After the financial crisis, thanks to the support of relevant national policies, chemical enterprises gradually eliminated the crisis, the output of the chemical industry gradually recovered, and the discharge of wastewater in the chemical industry increased, leading to an increase in the total grey water footprint of the chemical industry.

The grey water footprint of the chemical industry in Jiangsu, Zhejiang, Hubei, Hunan, Sichuan, and Yunnan provinces is relatively high. These provinces are the main concentration provinces of the chemical industry in the Economic Belt, with large-scale enterprises that have high amounts of wastewater discharge. The chemical industry in Shanghai has the lowest wastewater footprint. On the one hand, Shanghai has accelerated the adjustment of its industrial structure, the proportion of the chemical industry in the national economy has decreased, and the overall scale of the chemical industry has shrunk. In 2016, the sales value of its chemical industry only accounted for 2.67% of that in China. On the other hand, the chemical industry in Shanghai is gradually transforming and upgrading to the direction of a high-end, green, and low-carbon chemical industry. Shanghai has carried out the construction of a "Green Industrial zone" earlier in China, and its environmental and economic indicators of 10,000 CNY of output value led the national level of the same industry. The grey water footprint of the chemical industry in Guizhou is relatively low, mainly because of the small scale of the chemical industry. In 2016, the sales value of the chemical industry in Guizhou only accounted for 0.83% of the national total (Figure 2).

#### *4.2. Spatial and Temporal Evolution of Green Development Efficiency of the Chemical Industry in Yangtze River Economic Belt*

From 2002 to 2016, the green development efficiency of the chemical industry in the Yangtze River Economic Belt showed an overall development and evolution trend of first decreasing and then increasing, with an average of 0.5163, only reaching the optimal level of 51.63% (Table 2). This trend showed that the overall level of green development efficiency of the chemical industry is not high and still has great growth potential. Note that the green development efficiency of the chemical industry showed a downward trend from 2002 to 2005, which may be due to the reversal of China's economic model in the later stage of its 11th Five-Year Plan. Moreover, the chemical industry turned back to the development model of high consumption, high pollution emission, and low efficiency. The average green development efficiency of the chemical industry in the Yangtze River Economic Belt increased significantly during 2012 and 2016, which is the reason that provinces and cities

in the Economic Belt accelerated the green development, transformation, and upgrading of the chemical industry and achieved remarkable results after the 18th National Congress.

**Figure 2.** Grey water footprint of the chemical industry in Yangtze River Economic Belt.

**Table 2.** Green development efficiency of the chemical industry in the Yangtze River Economic Belt from 2002 to 2016.


From the upstream, midstream, and downstream areas, the average green development efficiency from 2002 to 2016 of the chemical industry in the downstream area was 0.8343, which was in a high-level development state with a small overall change range. The average green efficiencies of the chemical industry in the midstream and upstream areas were 0.4156 and 0.2739, respectively, which are relatively low and generally show an evolutionary trend of first declining and then rising (Table 2).

In terms of provinces and cities, the green development efficiency of the chemical industry in Shanghai, Zhejiang, and Jiangsu has been maintained at the optimal state of 1.00 (except when it was at 0.79 in 2005), while that in Hunan province also reached the optimal state of 1.00 from 2012 to 2016. The green development efficiency of the chemical industry in Anhui, Hubei, Chongqing, Sichuan, Guizhou, and Yunnan provinces increased to varying degrees, showing a development trend of first decreasing and then increasing. However, there is still a large gap in the green development efficiency of the chemical industry between these provinces and the Shanghai, Zhejiang, and Jiangsu provinces (Figure 3).

**Figure 3.** The average green development efficiency of the chemical industry from 2002 to 2016.

#### *4.3. Regional Difference Analysis of Green Development Efficiency of the Chemical Industry in the Yangtze River Economic Belt*

To further reveal the regional differences and sources of green development efficiency of the chemical industry in the Yangtze River Economic Belt, Dagum Gini coefficient and its decomposition method were used to calculate and decompose its relative level.

#### 4.3.1. Overall Regional Differences

From 2002 to 2016, the average regional difference of green development efficiency of the chemical industry in the Yangtze River Economic Belt was 0.3080, showing a development trend of first expanding and then narrowing. The maximum and minimum regional differences of green development efficiency of the chemical industry appeared in 2007 and 2016 at 0.3347 and 0.2577, respectively. From 2007 to 2010, the green development efficiency of the chemical industry fluctuated greatly, due mainly to the impact of the financial crisis and the inconsistent degree of recovery of such efficiency in various provinces and cities. From 2012 to 2016, the regional differences in green development efficiency of the chemical industry narrowed, mainly because since the 18th National Congress of the Communist Party of China, the middle and upper reaches with low green development efficiency of the chemical industry have strengthened the treatment of the chemical industry, improved its resource and energy utilization efficiency, reduced waste water discharge, and improved the green development efficiency, thereby reducing the regional differences in green development efficiency of the chemical industry.

#### 4.3.2. Intraregional Differences

On the whole, the regional difference of green development efficiency of the chemical industry in downstream areas is the largest, with an average of 0.1472. The second is the middle reaches, with an average of 0.1043. The upstream area is the smallest, with an average of 0.0873. From the evolution trend, from 2002 to 2012, the regional difference of green development efficiency of the chemical industry in the middle and lower reaches showed an upward trend in fluctuation. From 2012 to 2016, it showed a downward trend. From 2002 to 2016, the green development efficiency of the chemical industry in the upstream region showed an upward trend in fluctuation, indicating that the regional differences are expanding. Note that, although the regional differences of green development efficiency of the chemical industry in the upstream region is the smallest, they are expanding. Hence, it is necessary to strengthen the regulation of regional difference of green development efficiency of the chemical industry in the upstream region. Although there are great regional differences in the green development efficiency of the chemical industry in the middle reaches and downstream areas, these have narrowed significantly since 2012.

#### 4.3.3. Differences between Regions

From the mean value of green development efficiency of the chemical industry among the three regions, the regional difference between the downstream and upstream areas is the largest at 0.5081, between the lower and middle reaches is 0.3805, and between the middle reaches and the upper reaches is the smallest at 0.1872. From the changing trend, the regional difference between the middle and upper reaches tends to expand, whereas those between downstream and upstream and between downstream and midstream tend to narrow (Figure 4).

**Figure 4.** Regional differences in green development performance of the chemical industry in the Yangtze River Economic Belt.

#### 4.3.4. Source of Difference

From the perspective of difference sources, the contribution of inter-group differences is the largest with an average value of 0.2545, which is higher than that of regional differences with an average value of 0.0453, and the contribution of over variable density with an average value of 0.0082. The evolution trend of inter-group differences is similar to that of overall regional differences, and the contribution rate of the average value of inter-group differences is as high as 78.94%. This percentage showed that the difference between groups is the main factor affecting the overall regional difference of green development efficiency of the chemical industry in the Yangtze River Economic Belt. The contribution rates of intra-group difference and hypervariable density were 14.05% and 2.54%, respectively, which have relatively small contributions to the overall regional difference (Table 3).
