Measurement and Spatial Correlations of Green Total Factor Productivities of Chinese Provinces

Abstract

The measurement of green total factor productivity (GTFP) helps to improve environmental evaluation and to supervise environmental protection. This article establishes a system of assessment indicators (AIS) for GTFP and computes the GTFPs of 30 provinces of China from 2000–2019, using the evidence-based measure (EBM) model. Then, the spatial correlation between provincial GTFPs was analyzed and the convergence between them was discussed with spatial panel data. The main results are as follows: China faces a regional difference in GTFP. In general, GTFP descends stepwise from east to west. The 30 Chinese provinces vary significantly in GTFP. The high GTFP provinces are concentrated in the east, and the low GTFP ones mainly exist in the west. According to Global Moran’s I, an indicator of spatial correlation, China’s GTFPs bear prominent features of spatial clustering. The spatial clustering of China’s GTFPs has a significant impact on GTFP convergence. If this spatial effect is considered in traditional convergence models, the GTFP convergence rate can be measured more correctly. The provincial GTFPs show a significant absolute beta convergence, the rate of which reached 0.943% in the research period. Among the various impactors of GTFP, industrial structure and technical innovation significantly enhance GTFP convergence; opening-up and urbanization level significantly suppress GTFP convergence; environmental governance does not significantly affect GTFP convergence. Unlike the previous studies, this paper includes the spatial effect in traditional convergence models to obtain spatial convergence models. The GTFP convergence measured by our spatial convergence models was slower than that measured by the traditional model, suggesting that the spatial effect plays a significant role in GTFP convergence. In addition, this paper proves that the GTFP gap between Chinese provinces has narrowed gradually. This absolute convergence trend of GTFPs provides the key basis for the catch-up effect of the green economy. To improve the convergence of China’s provincial GTFPs, it is important to fully consider the varied effects of factors such as industrial structure, technical innovation, opening-up, urbanization, and environmental governance, and to formulate green development policies according to local conditions.

1. Introduction

The past 40 years have seen China’s gross domestic product (GDP) expand at an average speed of 9.5% each year. Nevertheless, the fast growth of the economy consumes a huge sum of resources and energy, bringing serious resource and environmental problems. Statistics show that China consumed 23.18% of the world’s energy in 2017 [1]. The economic growth in China is increasingly constrained by the rising demand for energy. Meanwhile, China faces an urgent need to protect its eco-environment. The 2017 Global Environmental Performance Indicator (EPI) suggests that China ranked low (118th) among the 178 countries and regions being considered, with an EPI of only 43.00. It is imperative for the country to transform its traditional economic model, which consumes a large amount of energy and creates heavy output, and push forward green development [2]. To realize green development, China must vigorously improve its green total factor productivity (GTFP).

The traditional TFP assessment does not consider resource and environmental factors, which twists the true meaning of TFP [3]. To overcome this defect, more and more scholars are starting to include these factors in the traditional TFP and establish a framework of GTFP research. The existing studies on GTFP select different undesirable outputs for the system of assessment indicators (AIS) for GTFP. For example, Liu et al. [4] took chemical oxygen demand (COD) as well as sulfur dioxide (SO₂) as undesirable outputs, and computed China’s green TFPs in 1999 and 2012 through data envelopment analysis (DEA). With carbon dioxide as the undesirable output, Li and Lin [5] estimated the green productivities of 30 provinces of China in 1997–2010. Xie et al. [6] also selected carbon dioxide output as the undesirable output of GTFP and measured the GTFPs of 27 European Union members by the Global Malmquist–Luenberger (GML) indicator.

GTFP assessment is mainly achieved by two methods. One of them is stochastic frontier analysis (SFA). The other is DEA. The former method was adopted by Zhang et al. [7] to evaluate the green TFPs of 30 provinces of China in 1989–2008. The DEA is a flexible assessment tool, which needs no production function. Thanks to its flexibility, the DEA has gradually developed into the mainstream approach for GTFP measurement. On the regional level, Oh and Heshmati [8] used sequential DEA to evaluate the green TFPs of 26 nations and regions in 1970–2003 and to analyze the variation of the components of green TFP. Wang et al. [9] adopted the meta-frontier model of global production technology to measure the green productivities of 163 nations and regions in 1990–2017. On the industrial level, Zhu et al. [10] and Shi and Li [11] relied on DEA to measure the GTFPs of the quarrying industry and manufacturing industry in China, separately.

According to Tobler’s First Law of Geography, things between regions are intercorrelated. The correlation degree depends on the distance between the regions. The closer the regions, the stronger the correlation. The inverse is also true [12]. China is a large country. Different regions in China differ significantly in their level of economic development and resource endowments. It is an interesting topic whether China’s GTFPs have a significant spatial effect. Wang et al. [13] measured the Moran’s I value of China’s GTFPs from 2001 to 2016 and demonstrated that the spatial clustering effect of China’s GTFPs is on the rise. Overall, there are few studies on the spatial correlation between provincial GTFPs in China. This issue needs further explorations.

The above analysis shows that more and more researchers have turned their attention to GTFP. Nevertheless, there are two weaknesses of their research. Firstly, most researchers chose only one pollutant as the undesirable output. However, a single pollutant cannot fully reflect the environmental constraint [14]. Secondly, few of them have considered the convergence of GTFPs, which hinders the understanding of the dynamics of provincial GTFPs. To solve these weaknesses, this article considers solid, liquid, and air pollutants as undesirable outputs. The multiple pollutants can better demonstrate the environmental constraint than a single pollutant, making it a more accurate method to measure provincial GTFPs. Furthermore, spatial convergence models were adopted to investigate the convergence of GTFPs, shedding light on provincial GTFP variation across China.

2. Methodology

2.1. Evidence-Based Measure (EBM) Model

Before examining GTFP convergence, it is necessary to assess GTFPs accurately. In this research, the GTFP includes all sorts of environmental pollutants. DEA is a linear programming model representing the ratio of output to input. There are many types of DEA models. The early ones were mostly radial models, which cannot measure efficiency unless the outputs are maximized. Thus, they are not suitable for assessing efficiency containing environmental pollutants. If these pollutants are ignored in the efficiency assessment system, the measured efficiency may be biased [15]. To include undesirable outputs into the efficiency assessment system, Tone [16] proposed a non-radial, non-angular DEA called the slack-based measure (SBM), which is different from the traditional radial models. However, this model cannot realize the compatibility between radial inputs/outputs and non-radial ones. Therefore, Tsutsui and Tone [17] combined the merits of SBM with radial models into the EBM. This mixed distance model increases the accuracy of efficiency measurement, eliminating the defects of either radial or non-radial measurement.

Different methods have been adopted to measure GTFP. Chen and Golley [18] employed the directional distance function (DDF) to estimation the changing patterns of GTFP growth in 38 industrial sectors of China during 1980–2010. Later, Cárdenas Rodríguez et al. [19] extended the transformation function to measure multifactor productivity in OECD and G20 member states during 1990–2013. Xia and Xu [20] relied on the DDF to assess provincial GTFPs in China during 1997–2015. The above GTFP measurements show that: the DDF, as a radial DEA model, assumes that the inputs and outputs change proportionally, i.e., the inputs and outputs have a radial relationship. The transformation function also requires the inputs and outputs to change in the same direction. For the GTFP in this research, however, the inputs are closely associated with the undesirable outputs contained in the evaluation system; the two types of factors have a radial relationship. Meanwhile, the inputs are separable from the desirable outputs; these two types of factors have a non-radial relationship. When both radial and non-radial relationships exist between inputs and outputs, the DDF cannot work effectively. In this case, the EBM, a hybrid DEA model, can be introduced to tackle both types of relationships between inputs and outputs. Compared with the DDF, the EBM can improve the measuring accuracy of GTFP.

The EBM principle is as follows. Suppose it is necessary to measure the efficiency of a production system. In the system, each of the DMs need to receive certain production factors and produce certain outcomes. Let G denote the number of input production factors X; P and Q denote the number of desirable outputs Y and undesirable outputs Q, respectively. To facilitate model expression, the inputs are represented by a vector $X=(x_1,x_2,\dots ,x_n)\in R_{+}^G$, while the desirable and undesirable outputs are represented by $Y=(y_1,y_2,\dots ,y_n)\in R_{+}^P$ and $B=(b_1,b_2,\dots ,b_n)\in R_{+}^Q$, respectively. Thus, the possible production scenarios can be illustrated by a set $T=\left\{(x,y,b):xcanproduceyandb\right\}$. Let $DM{U}_j=(x_j,y_j,b_j)$ denote the j-th DM to be measured. Hence, the EBM model with undesirable outputs can be defined as:

$$\begin{array}{l}{\theta }^{*}=\min \frac{\gamma -{\phi }_x{\displaystyle \sum _{g=1}^G\frac{w_g^{-}{s}_g^{-}}{x_{gj}}}}{\epsilon +{\phi }_y{\displaystyle \sum _{p=1}^P\frac{w_p^{+}{s}_p^{+}}{y_{pj}}+{\phi }_b{\displaystyle \sum _{q=1}^Q\frac{w_q^{b-}{s}_q^{b-}}{b_{qj}}}}}\\ s_{.}{t}_{.}\gamma x_{gj}={\displaystyle \sum _{j=1}^n{x}_{gj}}{\lambda }_j+s_g^{-},g=1,\dots ,G\\ \epsilon y_{pj}={\displaystyle \sum _{j=1}^n{y}_{pj}}{\lambda }_j-s_p^{+},p=1,\dots ,P\\ \epsilon b_{qj}={\displaystyle \sum _{j=1}^n{b}_{qj}}{\lambda }_j+s_q^{b-},q=1,\dots ,Q\\ \lambda >0,s_g^{-},s_p^{+},s_q^{b-}\ge 0\end{array}$$

(1)

where θ* is the GTFP to be measured; $x_{gj}$, $y_{pj}$, and $b_{qj}$ are the g-th input, p-th desirable output, and q-th undesirable output of DM j, respectively; $w_g^{-}$, $w_p^{+}$, and $w_q^{b-}$ are the weight coefficients of $x_{gj}$, $y_{pj}$, and $b_{qj}$, respectively; $s_g^{-}$, $s_p^{+}$, and $s_p^{+}$ are the slack terms of inputs, desirable outputs, and undesirable outputs, respectively; ${\phi }_x$ is the core parameter involving both radial slackness ${\phi }_x$ and non-radial slackness $w_g^{-}$; ${\phi }_y$ and ${\phi }_y$ are the core parameters for desirable and undesirable outputs, respectively; λ is the weight coefficient of DM j.

2.2. GMI

The GTFP convergence depends on how significant the provincial GTFPs are correlated in space. If they are correlated in space, provincial GTFPs are not independent of each other in space, but spill over and diffuse across the space. The shorter the distance between two provinces, the more significant the spatial correlation between provincial GTFPs. In general, GMI indicates the spatial correlation between GTFPs. According to Moran [21], GMI can be defined as:

$$GlobalMoran’sI=\frac{n}{{\displaystyle \sum _{i=1}^n{(x_i-\overline{x})}^2}}\frac{{\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^n{W}_{ij}(x_i-\overline{x})(x_j-\overline{x})}}}{{\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^n{W}_{ij}}}}$$

(2)

where, n is the total number of Chinese provinces; x_i is the GTFP of province i; x_j is the GTFP of provinces j; $\overline{x}=({\displaystyle {\sum }_i{x}_i})/n$ is the average GTFP of Chinese provinces.

The value of GMI falls in the interval of [−1, 1]. If the indicator is within [−1, 0), and if it passes the test at a certain level of significance, the provinces have negative spatial correlations; if the indicator is within (0, 1] and if it passes the test at a certain level of significance, the provinces have positive spatial correlations. Only if the indicator equals zero are provinces not spatially correlated.

The parameter W_ij stands for a spatial weight matrix, which is added to the model. Considering the data availability and ease of computing, the spatial weight matrix is configured as an adjacency matrix composed of 1s and 0s:

$$W_{ij}=\{\begin{array}{l}1Regioniisadjacenttoregionj\\ 0Regioniisnotadjacenttoregionj\end{array}$$

(3)

Whether the computed GMI of GTFPs is authentic needs to be verified through a significance test. The expectation and variance must be computed to implement that test. The two parameters can be separately calculated by:

$$E_n(GlobalMoran’sI)=-\frac{1}{n-1}$$

(4)

$$Var(GlobalMoran’sI)=\frac{n^2{w}_1+n{w}_2+3w_0^2}{w_0^2(n^2-1)}-E_n^2(GlobalMoran’sI)$$

(5)

where $w_0={{\displaystyle \sum }}_{i=1}^n{{\displaystyle \sum }}_{j=1}^n{w}_{ij}$; $w_1=\frac{1}{2}{{\displaystyle \sum }}_{i=1}^n{{\displaystyle \sum }}_{j=1}^n{(w_{ij}+w_{ji})}^2$; $w_2={{\displaystyle \sum }}_{i=1}^n{\left(w_{i\cdot }+w_i\right)}^2$; $w_{i\cdot }$ is the sum of the values in row i of all spatial matrices; $w_{\cdot i}$ is the sum of the values in column i of all spatial matrices.

After the expectation and variance of GMI are obtained, the Z-score normal distribution equation is used to compute the Z-score, which verifies if the indicator passes the significance test. The Z-score normal distribution equation is as follows:

$$Z(d)=\frac{\left[GlobalMoran’sI-E(GlobalMoran’sI)\right]}{\sqrt{VAR(GlobalMoran’sI)}}$$

(6)

If the Z-score of GMI passes a certain numerical boundary, then the indicator is significant. Generally, there are three levels of significance: 10%, 5%, and 1%. The provinces have significant spatial correlations as long as the indicator passes the test at any level.

2.3. Spatial Convergence Models

In neoclassical economics, the convergence model was firstly applied to study the convergence or divergence of the incomes of various parts of the world. Later, this model gradually won recognition from academia and was extended from the economy to fields such as resources and the environment. Hence, this article relies on convergence models to analyze the convergence or divergence of GTFPs, providing an important basis for understanding the extract trend of GTFPs.

2.3.1. Spatial Absolute Beta Convergence (ABC) Models

The beta convergence model is the most common convergence model. By the presence/absence of control variables, beta convergence models are either absolute or conditional. Referring to Miller and Upadhyay [22], the ABC model for the convergence of provincial GTFPs can be simplified as:

$$gGTF{P}_{i,t}=\alpha +\beta Ln(GTF{P}_{i,t-1})+{\mu }_{i,t}$$

(7)

where $gGTF{P}_{i,t}=\Delta Ln(GTF{P}_{i,t})=Ln(GTF{P}_{i,t})-Ln(GTF{P}_{i,t-1})$ is the difference between the provincial GTFPs in two consecutive periods. The difference reflects the growth rate of GTFP in province i. $Ln(GTF{P}_{i,t})$ and $Ln(GTF{P}_{i,t-1})$ are the natural logarithms of province i in years t and t − 1, respectively. If β is smaller than zero and passes the test at the significance level of 10%, 5%, or 1%, then the provincial GTFPs tend to converge. In addition, α is a constant; ${\mu }_{i,t}$ is a random disturbance.

Equation (7) is the conventional ABC model. Based on common econometric methods, this model does not consider the possible spatial correlation between provinces. Therefore, the measured convergence rate may deviate from the actual rate. To solve the problem, this article draws on the relevant theories on spatial economy and combines the spatial econometric method with traditional convergence model. In this way, two spatial beta convergence models were obtained. One of them is the spatial autoregressive model (SAR). The other is the spatial error model (SEM). The SAR-based spatial ABC can be defined by [23]:

$$gGTF{P}_{i,t}=\alpha +\beta Ln(GTF{P}_{i,t-1})+\rho WLn(gGTF{P}_{i,t})+{\epsilon }_{i,t}\epsilon \text{~}N(0,{\sigma }_{}^2)$$

(8)

where ρ is the spatial autoregressive coefficient reflecting the scale of spatial effect; W is the spatial weight matrix coefficient, which would be introduced to the whole model; ε is a random error; N is normal distribution; σ is the standard deviation. The other symbols are of the same meaning as in Equation (7).

The spatial ABC based on SEM can be defined by [24]:

$$gGTF{P}_{i,t}=\alpha +\beta Ln(GTF{P}_{i,t-1})+{\epsilon }_{i,t}{\epsilon }_{i,t}=\lambda W+u,u\text{~}N(0,{\sigma }_{}^{2}I)$$

(9)

where λ is the spatial correlation parameter between regression residuals; u is a random disturbance; I is the identity matrix.

2.3.2. Spatial Conditional Beta Convergence (CBC) Models

When no control variable is considered, the ABC of GTFPs is a simple problem. In the real world, however, the dynamics of provincial GTFPs are inevitably disturbed by external factors. To improve practicality, the various factors affecting GTFP should be included in the ABC model as control variables, turning the model into a CBC model. It has been proven that GTFP depends heavily on industrial structure [25], technical innovation [26], opening-up [27], urbanization [28], and environmental governance [29]. Therefore, this article designates five control variables: industrial structure (IS), technical innovation (TI), opening-up (OU), urbanization (UL), and environmental governance (ER). Hence, the CBC model can be created for GTFPs:

$$gGTF{P}_{i,t}=\alpha +{\beta }_{1}Ln(GTF{P}_{i,t-1})+{\beta }_{2}I{S}_{i,t}+{\beta }_{3}T{I}_{i,t}+{\beta }_{4}O{U}_{i,t}+{\beta }_{5}U{L}_{i,t}+{\beta }_{6}E{R}_{i,t}+{\mu }_{i,t}$$

(10)

where $gGTF{P}_{i,t}$, $GTF{P}_{i,t}$ and $GTF{P}_{i,t-1}$ are of the same meaning as in Equation (7). The control variables in Model (10) are explained as follows: $I{S}_{i,t}$ is industrial structure, which is calculated as the secondary industry output of province i as a percentage of provincial GDP in year t; $T{I}_{i,t}$ is technical innovation, which is calculated as the natural logarithm of the number of patent applications of province i in year t; $O{U}_{i,t}$ is opening-up, which is calculated as the actual foreign direct investment (FDI) of province i as a percentage of provincial GDP in year t; $U{L}_{i,t}$ is urbanization level, which is calculated as the year-end urban population of province i as a percentage of provincial total population in year t; $E{R}_{i,t}$ is environmental governance, which is calculated as the ratio of the investment in industrial environmental pollution control to industrial added value of province i in year t.

Equation (10) is a CBC model based on traditional ordinary econometric models. To further improve the model’s estimation accuracy, this article sets up spatial CBC models based on SAR and SEM, respectively:

$$\begin{array}{ll}gGTF{P}_{i,t}& =\alpha +{\beta }_{1}Ln(GTF{P}_{i,t-1})+{\beta }_{2}I{S}_{i,t}+{\beta }_{3}T{I}_{i,t}+{\beta }_{4}O{U}_{i,t}+{\beta }_{5}U{L}_{i,t}\\ & +{\beta }_{6}E{R}_{i,t}+\rho W\ln (gGTF{P}_{i,t})+{\epsilon }_{i,t}\epsilon \text{~}N(0,{\sigma }_{}^2)\end{array}$$

(11)

$$\begin{array}{ll}gGTF{P}_{i,t}& =\alpha +{\beta }_{1}Ln(GTF{P}_{i,t-1})+{\beta }_{2}I{S}_{i,t}+{\beta }_{3}T{I}_{i,t}+{\beta }_{4}O{U}_{i,t}+{\beta }_{5}U{L}_{i,t}\\ & +{\beta }_{6}E{R}_{i,t}+{\epsilon }_{i,t}{\epsilon }_{i,t}=\lambda W+u,u\text{~}N(0,{\sigma }_{}^{2}I)\end{array}$$

(12)

Equations (11) and (12) are established by adding the control variables to Equations (8) and (9), respectively. Apart from these variables, the other symbols in the two formulas are the same as in Equations (8) and (9).

2.4. AIS

The GTFP in this article is an environmentally constrained TFP. It was established by incorporating environmental factors as constraints to the traditional TFP framework. Drawing on the research results of Lin and Chen [30] and Yu et al. [31], this article defines GTFP as a TFP constrained by resources and environment. Our AIS contains traditional inputs such as labor and capital, and two types of outputs: good outputs represented by the GDP, and bad outputs represented by different environmental pollutants.

As a TFP, the GTFP is controlled between 0 and 1. The GTFP value is positively correlated with its effectiveness. If GTFP = 1, the efficient frontier is reached, a sign of ideal GTFP.

Based on the definition of GTFP, this article sets up an AIS for GTFP, which comprises of inputs and outputs (

Table 1. GTFP AIS.

Type	Name	Meaning	Unit
Inputs	Labor	Number of year-end workers in each Chinese province within the research period.	10,000 persons
	Capital	Actual capital stock in each Chinese province within the research period. The nominal capital stock in each Chinese province in each year was estimated by per-petual inventory method: $K_{i,t}=I_{i,t}+\left(1-\delta \right)K_{i,t-1}{}_{}$ where $K_{i,t}$ is the capital stock of province i in year t; $I_{i,t}$ is the fixed capital formation of province i in year t; δ = 9.6% is capital depreciation rate. After solving the nominal capital stock in each province in each year, the result was deflated to real capital stock with 2000 as the base period, using the fixed asset price indicator.	100 million yuan
	Energy	Annual total energy consumption in each Chinese province in each year within the research period.	10,000 TCE
Outputs	GDP	Real annual GDP in each Chinese province within the research period, measured by a constant price with 2000 as the base period.	100 million yuan
	Industrial SO2 output	Annual industrial SO2 output in each Chinese province within the research period.	10,000 tons
	Industrial wastewater output,	Annual industrial wastewater output in each Chinese province within the research period.	10,000 tons
	Industrial solid waste pollutant output	Annual industrial solid waste output in each Chinese province within the research period.	10,000 tons

). The three inputs are energy, capital, and labor. Specifically, energy was described as the total energy consumption of each province. The nominal capital stock in each Chinese province in each year was estimated by perpetual inventory method. Since price has a major impact on capital, the nominal capital stock was deflated to real capital stock with 2000 as the base period with the aid of the fixed asset price indicator, in order to eliminate the price influence. Labor was calculated as the number of year-end workers in each province. Considering the necessity of capital accumulation, capital was calculated as capital stock.

Both desirable and undesirable outputs are included in the AIS. The desirable output is the annual GDP of each province. To eliminate the inflation effect, the nominal GDP was transformed into a constant price with 2000 as the base period, using the GDP indicator. The undesirable outputs refer to the various environmental pollutants emitted in each province during economic development. Currently, China mainly monitors three types of environmental pollutants, namely, air pollutants, water pollutants, and solid pollutants. Inspired by Liu et al. [4], this article measures the undesirable outputs by industrial SO₂ output, industrial wastewater output, and industrial solid waste output.

2.5. Data Sources

This article decided to study 30 provinces of China during 2000–2019. Four provinces were excluded, namely, Taiwan, Macao, Tibet, and Hong Kong, due to the incompleteness and inoperability of the data sources for the above indicators. The original data of these indicators are from China Statistical Yearbooks (2001–2020), the other statistical yearbooks of the country on environment, energy, and sci-tech in 2002–2020, as well as the provincial statistical yearbooks published in the same period. The missing data on a few variables were made up for by the moving average approach.

3. Results

3.1. Measured GTFPs

Starting with the GTFP AIS, the authors collected the original data of each indicator from various statistical yearbooks and preprocessed some indicator data. Next, the indicator data were inputted to MaxDEA and the GTFP of each Chinese province was measured by the EBM. The results are specified in

Table 2. GTFPs in China from 2000 to 2019.

Part	Province	2000	2005	2010	2019	Mean
East part	Beijing	1.0000	1.0000	1.0000	1.0000	1.0000
East part	Shanghai	1.0000	1.0000	1.0000	1.0000	0.9722
East part	Guangdong	1.0000	1.0000	1.0000	0.7628	0.9333
East part	Hainan	1.0000	1.0000	0.8584	0.5962	0.8391
East part	Zhejiang	0.9144	0.8383	0.8149	0.7528	0.8221
East part	Jiangsu	0.8704	0.8025	0.7937	0.6875	0.8051
East part	Fujian	1.0000	0.8150	0.7543	0.5702	0.7690
East part	Shandong	0.8813	0.8215	0.7407	0.5534	0.7556
East part	Hebei	0.8050	0.7910	0.7746	0.6247	0.7340
East part	Tianjin	1.0000	0.7719	0.6549	0.5579	0.7217
East part	Liaoning	0.8562	0.7827	0.7029	0.5896	0.7183
Middle part	Heilongjiang	0.9144	1.0000	0.8172	0.5894	0.8284
Middle part	Hubei	1.0000	0.8259	0.8367	0.6402	0.8153
Middle part	Hunan	0.8767	0.8276	0.8689	0.6713	0.8103
Middle part	Anhui	0.8497	0.8383	0.8465	0.7276	0.8016
Middle part	Jiangxi	0.8454	0.7656	0.7830	0.6548	0.7633
Middle part	Henan	0.8638	0.8356	0.7141	0.6393	0.7256
Middle part	Shanxi	0.7553	0.8131	0.7547	0.6913	0.7179
Middle part	Jilin	0.8370	0.8288	0.5732	0.5599	0.6872
West part	Gansu	0.7957	0.8285	0.8433	0.7294	0.7739
West part	Sichuan	0.7764	0.7534	0.7884	0.6794	0.7497
West part	Xinjiang	0.8966	0.7435	0.7769	0.5992	0.7275
West part	Yunnan	0.7803	0.8141	0.7858	0.6029	0.7257
West part	Guizhou	0.7200	0.7310	0.7632	0.5754	0.6976
West part	Guangxi	0.7939	0.7660	0.6572	0.5592	0.6736
West part	Shaanxi	0.7438	0.7168	0.6926	0.5894	0.6722
West part	Chongqing	0.7248	0.6645	0.6990	0.6052	0.6646
West part	Inner Mongolia	0.8243	0.7119	0.5475	0.5516	0.6398
West part	Qinghai	0.8139	0.6083	0.6036	0.5273	0.6236
West part	Ningxia	0.6198	0.5870	0.5926	0.5294	0.5796

Note: Not all data are provided due to the limited space.

. To highlight provincial variation, China was divided into eastern, middle, and western parts based on geographical location, abundance of resources, and development level.

In the eastern part, the provinces have a significant difference in GTFP. Specifically, Beijing optimized its GTFP in the research period; Shanghai, Guangdong, Hainan, Zhejiang, and Jiangsu achieved satisfactory GTFPs (average GTFP > 0.8); the other provinces saw their average GTFPs fall between 0.7 and 0.8. In the middle part, Heilongjiang, Hubei, Hunan, and Anhui realized relatively good GTFPs, while the other provinces had average GTFPs between 0.7–0.8, a signal of moderate performance. In the western part, Gansu, Sichuan, Xinjiang, and Yunnan performed generally average in GTFP, and the other provinces (e.g., Guizhou, Guangxi, Shaanxi, Chongqing, Inner Mongolia, Qinghai, and Ningxia) did not perform well (average GTFP < 0.7).

On the time evaluation of GTFPs, most provinces had a lower GTFP in 2019 than in 2000. Similar results were drawn by Song et al. [32], who measured the GTFPs of 11 provinces in the Yangtze River Economic Belt with the SBM, revealing that the GTFPs in most provinces declined with time. In this research, the GTFPs of most provinces dropped for the following reason. The measured data show that the undesirable outputs in most provinces, including industrial SO₂, industrial wastewater, and industrial solid waste, became increasingly redundant over time.

The above analysis shows that the GTFPs across China descend stepwise from east to west. This distribution pattern is closely associated with the three-step pattern of level of economic development and geography in the country. In addition, rich provinces have relatively high GTFPs and are concentrated in the east. Poor provinces have relatively low GTFPs and mainly exist in the middle and western parts. Overall, the GTFP level is closely intertwined with development level.

3.2. Spatial Correlation of GTFPs

Starting with the spatial adjacency matrix composed of 1s and 0s, the annual GTFPs of each province were inputted into GeoDa to derive the GMI for GTFPs during 2000–2019. The results in

Table 3. GMI for GTFPs in 2000–2019.

Year	GMI	E(I)	Mean	Z-Score
2000	0.3793 ***	−0.0345	−0.0251	3.3051
2001	0.3622 ***	−0.0345	−0.0391	3.2704
2002	0.3779 ***	−0.0345	−0.0359	3.3231
2003	0.3898 ***	−0.0345	−0.0392	3.4496
2004	0.4150 ***	−0.0345	−0.0352	3.5366
2005	0.2036 **	−0.0345	−0.0379	2.0281
2006	0.1402 *	−0.0345	−0.0348	1.4919
2007	0.1013 *	−0.0345	−0.0412	1.1627
2008	0.0241	−0.0345	−0.0332	0.4904
2009	0.1154 *	−0.0345	−0.0422	1.3001
2010	0.0792	−0.0345	−0.0366	0.9660
2011	0.0519	−0.0345	−0.0403	0.7366
2012	0.0502	−0.0345	−0.0373	0.6914
2013	0.0907 *	−0.0345	−0.0422	1.0830
2014	0.1211 *	−0.0345	−0.0398	1.3460
2015	0.1277 *	−0.0345	−0.0406	1.4826
2016	0.1852 **	−0.0345	−0.0405	1.9829
2017	0.1403 *	−0.0345	−0.0395	1.5213
2018	0.0329	−0.0345	−0.0420	0.6072
2019	0.0048	−0.0345	−0.0407	0.3391

Note: * is the significance level of 10%, ** is 5%, and *** is 1%.

show that, except for a few years, the GTFPs in China were positive in most years in the research period, all passing the test at the significance levels of 10%, 5%, or 1%. This fully demonstrates the significant positive spatial correlation between GTFPs and confirms the significant spatial clustering of China’s GTFPs. Thus, spatial correlation has a great impact on the dynamics of provincial GTFPs and must be considered in GTFP convergence analysis.

3.3. Results Analysis of Convergence Models

3.3.1. Stationary Test of Panel Data

The stationarity of the panel data is the premise for the empirical analysis of the model. Thus, this paper carries out the unit root test and the cointegration test on ABC and CBC, respectively. The relevant test results are given in

Table 4. Unit root test (ABC).

	Statistic	Z	p-Value
gTFP	0.0431	−28.4939	0.0000
LnTFPt−1	0.8361	−0.4902	0.3120
D(gTFP)	0.0303	−27.2756	0.0000
D(TFPt−1)	−0.4962	−44.9639	0.0000

,

Table 5. Unit root test (CBC).

	Statistic	Z	p-Value
gTFP	0.0431	−28.4939	0.0000
LnTFPt−1	0.8361	−0.4902	0.3120
IS	0.8802	1.0651	0.8566
TI	0.8415	−0.3018	0.3814
OU	0.6511	−7.0240	0.0000
UL	0.8566	0.2341	0.5926
ER	0.3028	−19.3231	0.0000
D(IS)	0.0303	−27.2756	0.0000
D(TFPt−1)	−0.4962	−44.9639	0.0000
D(IS)	0.1622	−22.8440	0.0000
D(TI)	−0.0317	−29.3561	0.0000
D(OU)	−0.2602	−37.0330	0.0000
D(UL)	−0.0480	−29.9059	0.0000
D(ER)	−0.4523	−43.4899	0.0000

and

Table 6. Cointegration test.

	ABC		CBC
	Statistic	p-Value	Statistic	p-Value
Modified Phillips-Perron t	4.8141	0.0000	9.2611	0.0000
Phillips–Perron t	3.0757	0.0011	3.8196	0.0001
Augmented Dickey-Fuller t	3.0201	0.0013	4.0801	0.0000

. Table 4 lists the unit root test results on the ABC. The results show that the original series of the dependent variable gTFP is stationary, while the original series of the independent variable LnTFP_t−1 is non-stationary. After first-order differencing, the first-order difference series of both gTFP and LnTFP_t−1 are stationary. Table 6 provides the cointegration results on the ABC, revealing the long-term cointegration relationship between gTFP and LnTFP_t−1. The above analysis shows that the panel data of the ABC are highly stationary, laying a good basis for the absolute convergence analysis of the model.

Table 5 presents the unit root test results on the ABC. The results show that the original series of the dependent variable gTFP and the independent variables OU and ES are stationary, while those of the independent variables LnTFP_t−1, IS, TI, and UL are not. After first-order differencing, the first-order difference series of all variables are stationary. Further, the cointegration test results in Table 6 suggest the long-term cointegration relationship between the seven variables, namely, gTFP, LnTFP_t−1, IS, TI, OU, UL, and ER. Like the ABC, the CBC can be applied to the subsequent empirical analysis.

3.3.2. Results on GTFP Convergence

Based on Equations (7) and (10), this article uses the common econometric method to estimate the traditional absolute and condition beta convergence models and tests the spatial correlation between residuals of the two models. The results (

Table 7. Results of ordinary panel data models.

Variable	ABC				CBC
	Non-FE	Space FE	Time FE	Bidirectional FE	Non-FE	Space FE	Time FE	Bidirectional FE
$Ln\left(GTF{P}_{t-1}\right)$	−0.0168 (−1.2673)	−0.0531 *** (−2.9537)	−0.0199 (−1.4585)	−0.1638 *** (−6.0362)	−0.0203 (−1.3446)	−0.1892 *** (−6.4466)	−0.0555 *** (−2.8384)	−0.1630 *** (−5.9352)
$\mathrm{IS}$					−0.0498 ** (−2.0977)	−0.0330 (−0.8810)	−0.0464 ** (−1.9116)	0.0467 (1.1180)
$\mathrm{TI}$					0.0006 (0.4379)	−0.0006 (−0.1510)	0.0038 *** (2.7979)	0.0083 **(2.1510)
$\mathrm{OU}$					−0.0076 (−0.0725)	−0.0518 (−0.3846)	−0.2153 *** (−2.4648)	−0.2032 * (−1.8136)
$\mathrm{UL}$					−0.0161 (−0.9101)	−0.2400 *** (−4.1912)	0.0235 * (1.5508)	−0.0640 (−1.1133)
$\mathrm{ER}$					−0.4072 (−0.7434)	−0.9822 * (−1.5453)	0.1058 (0.2288)	0.3814 (0.6860)
$\text{R-squared}$	0.0028	0.0151	0.0037	0.0602	0.0138	0.0712	0.0329	0.0745
$\text{Log-L}$	988.9025	1002.7661	1106.0303	1138.3715	992.0605	1025.6796	1114.4906	1142.7384
$\mathrm{DW}$	1.3213	1.2515	1.9608	1.9338	1.3474	1.3823	1.9938	1.9402
$\text{LM-lag}$	150.2932 ***	166.2020 ***	3.6139 **	4.7802 **	143.7033 ***	143.7983 ***	3.8628 **	6.2946 ***
$\text{Robust LM-lag}$	0.7751	11.9687 ***	1.4400	0.4893	18.3498 ***	14.9188 ***	2.6136 *	0.6392
$\text{LM-err}$	149.7214 ***	174.3504 ***	3.3930 *	5.5142 **	137.8126 ***	132.4887 ***	3.2954 *	7.1345 ***
$\text{Robust LM-err}$	0.2034	20.1172 ***	1.2191	1.2233	12.4590 ***	3.6092 **	2.0462	1.4791

Note: T-statistics are given in the parentheses; *, **, and *** stand for significance levels of 10%, 5%, and 1%, respectively; estimation and the spatial autocorrelation test were carried out using Matlab 7.11.

) cannot clearly demonstrate which of the four fixed effects (FE) models is superior or inferior. Therefore, Table 4 presents the results of models with different FE. These models were contrasted to display the effect of controlling FE on model effectiveness.

Judging by the results of ABC models, the non-FE model had the smallest coefficient of determination (R²) for goodness-of-fit among the four models. After adding the time effect and space effect, the R² of the bidirectional FE model was 0.0602, indicating that this model boasts the best fitness. According to the estimation results of CBC models, the R² (0.075) of the bidirectional FE model was the greatest among the four models. To sum up, the bidirectional FE model has the best fitness and the optimal overall quality, regardless of absolute or CBC models. In addition, the bidirectional FE model realized the largest log likelihood function value (Log-L) (1138.3715) among the four ABC models and the best Log-L (1142.7384) among the four CBC models. The above results show that the bidirectional FE model achieved the best performance among the above four econometric models. It obviously yielded the best estimation results.

The lower part of Table 4 gives the spatial correlation between the residuals of the ABC and CBC models, respectively. The spatial correlation between residuals can be judged by whether LM-lag and LM-err pass the significance test. According to the estimation of ABC models, the LM-lag and LM-err of the bidirectional FE model both passed the test at a significance level of 5%. Similarly, the estimation of CBC models shows that the LM-lag and LM-err of the bidirectional FE model both passed test at a significance level of 1%. The above results show a significant spatial correlation between the residuals of both convergence models. The empirical results may be biased if the convergence models are estimated by the ordinary least squares (OLS) method. Furthermore, whether for absolute or condition beta convergence models, the LM-err of bidirectional FE model was greater than LM-lag. Overall, the SEM was identified as the most suitable form of our spatial econometric model.

Since the residuals in both convergence models have significant spatial autocorrelation, this article re-estimates ABC and CBC models by the spatial econometric method, using Equations (8) and (9) and Equations (11) and (12), respectively. In this way, two basic forms, SAR and SEM, were obtained (

Table 8. Results of bidirectional FE model.

Variable	ABC		CBC
	SAR	SEM	SAR	SEM
$Ln\left(GTF{P}_{t-1}\right)$	−0.1622 *** (−6.0170)	−0.1641 *** (−6.0852)	−0.1602 *** (−5.9134)	−0.1611 *** (−5.9215)
IS			0.0607 * (1.4718)	0.0670 * (1.6356)
TI			0.0085 ** (2.2441)	0.0082 ** (2.1530)
OU			−0.2206 ** (−1.9946)	−0.2246 ** (−2.0135)
UL			−0.0694 (−1.2225)	−0.0829 * (−1.4344)
ER			0.4221 (0.7694)	0.3972 (0.7276)
W*dep.var.	−0.1200 *** (2.2065)		0.1440 *** (2.6813)
spat.aut.		0.1330 *** (2.4183)		0.1559 *** (2.8664)
R-squared	0.4167	0.4098	0.4281	0.4185
Log-L	1140.7612	1141.1494	1145.9032	1146.4582

Note: T-statistics are given in the parentheses; *, **, and *** stand for significance levels of 10%, 5%, and 1%, respectively.

). The results in Table 5 suggest that, for both absolute and condition beta convergence models, the spatial lag $W*dep.\mathrm{var}.$ of SAR and the spatial error $W*dep.\mathrm{var}.$ of SEM both passed the test at a significance level of 1%. Hence, it is correct to select the spatial econometric model. Unlike common models, the SAR and SEM had a very high R², as well as an excellent Log-L. That is, the spatial econometric model outperforms common data models. For both ABC and CBC models, the SEM achieved a larger Log-L than the SAR, indicating that the former has the stronger explanatory power. As a result, this article mainly interprets the econometric results of the explanatory variables in the SEM.

According to the estimation results of the spatial ABC model, the estimation coefficient of $Ln\left(GTF{P}_{t-1}\right)$ was strongly negative at 1%. Therefore, China’s GTFP exhibited an absolute convergence in the research period. Miller and Upadhyay [22] put forward a similar view: TFP reflects the convergence trend more clearly than the per-capita real GDP, suggesting that technical convergence is an important phenomenon. In addition, Miller and Upadhyay [22] found strong evidence for TFP convergence for low- and middle-income countries, and weak evidence for high-income countries. As a middle-income country, China is witnessing a strong convergence in GTFP. Thus, our research is strongly consistent with the work of Miller and Upadhyay [22].

The beta convergence was computed by $\left|\beta \right|=1-e^{-\omega T}$, where ω is the convergence rate and T is the length of GTFP samples. Thus, it can be derived that $\omega =-\frac{1}{T}\ln (1-\left|\beta \right|)$. By this formula, the absolute convergence rate of China’s GTFPs in the research period was 0.943%, contrary to that (0.942%) obtained by the common panel data model. Therefore, the GTFP convergence rate of China slows down a bit after the spatial effect is included in the common convergence model.

The spatial CBC models were extended from the spatial ABC models by adding the control variables. According to the SEM of the spatial CBC models, the estimation coefficient of $Ln\left(GTF{P}_{i,t-1}\right)$ was strongly negative at 1%. The convergence rate was calculated as 0.925% by the formula of beta convergence rate. Hence, China’s GTFPs have a quadrant of conditional convergence. Except for ER, all control variables, including IS, TI, OU, and UL, play a significant role in GTFP convergence.

The IS exerted a positive effect on GTFP convergence at 10%, suggesting that the GTFP convergence increases as the secondary industry output takes up a greater share in China’s GDP. Fan et al. [33] also found that IS upgrading can speed up economic development, and greatly boost energy efficiency. At present, China is advocating a new type of industrialization and is actively pursuing the green transformation of industrial development. In particular, the high-tech industry in China has boomed in recent years. The high-tech boom, coupled with the upgrading of heavy industrial equipment, has improved labor productivity and enhanced the greenness of the industry. This brings a positive influence on GTFP.

The estimation coefficient of TI was positive and passed the test at a significance level of 5%. Therefore, the growing number of patent applications promotes GTFP convergence. As stated by Chen and Golley [18], TI can significantly boost green productivity. It can be said that the rising power of provincial sci-tech innovation is becoming a major driver of energy conservation and emission reduction. The new production techniques brought by TI, especially advanced green production techniques, improve energy utilization rate and cut down the pollutant output of economic development.

The OU severely suppressed GTFP. If a province attracts a large amount of foreign investment, then it is difficult for the province to improve its GTFP. A possible reason is that the influence of the FDI on green development adheres to the hypothesis of pollution haven, rather than the pollution halo hypothesis. In the past four decades, China has attracted a huge quantity of foreign investment. Unfortunately, the environmental threshold was rather low for foreign capital in the early years. Some foreign enterprises entered the Chinese market, despite their low technological level and sub-standard pollution output. The entry of these enterprises adversely affects the green development of provinces of China. Lv et al. [34] discovered that FDI hinders China’s GTFP growth.

The UL had a negative effect on the GTFP at 10%. This is probably related to the extensive urbanization model in China, which consumes a large amount of materials and land. For quite a long period, urban sprawl in China has featured fast expansion in space and population and has been underpinned by heavy consumption of land and energy. This urbanization model not only causes hideous environmental problems such as the waste of land, air pollution, and water pollution, but also seriously challenges the environmental bearing capacity of urban resources.

The ER did not significantly affect GTFP convergence. This result is possibly associated with the low ER intensity of China. As stated by Barrett and Satterfield [35], governance is a key guarantee of effective environmental management and conservation. Drawing on the rich literature on governance, they summarized the four overall goals of ER: effectiveness, fairness, response, and robustness. They also discovered that effective, fair, sensitive, and robust ER relies on the joint efforts of governments, non-governmental organizations, private actors, local communities, and researchers. In China, the governmental departments are the leading actors of ER and pollution control investment is the main instrument of governmental ER. It is safe to say that pollution control investment represents the degree of ER by the government. The relevant data show that, in 2021, the investment in industrial pollution control accounted for merely 1.43% of China’s industrial added value.

4. Conclusions

GTFP measurement in the context of environmental factors can improve environmental evaluation and supervise environmental protection [36]. This paper mainly explores the spatial correlation and convergence of GTFPs. On the one hand, the spatial clustering of GTFPs was understood correctly, providing an important basis for accurate estimation by the spatial convergence model. On the other hand, the spatial effect was included in the ABC and CBC, producing spatial ABC and spatial CBC. By contrast, traditional convergence models never consider the spatial effect. Compared with the traditional convergence models, our spatial convergence models can accurately measure the long-term convergence rate of GTFPs and confirm the feasibility of this convergence as the path for the catch-up effect of the green economy.

This article sets up an AIS for GTFP containing undesirable outputs and adopts the EBM model to obtain the GTFPs in 30 provinces of China during 2000–2019. After measuring the Global Moran Index of provincial GTFPs, both absolute beta convergence and conditional beta convergence models were utilized to examine GTFP convergence. Below are the main findings:

(1)

During the research period, a significant provincial difference was found in China’s GTFPs. In the eastern part, Beijing, Shanghai, Guangdong, Hainan, Zhejiang, and Jiangsu achieved relatively satisfactory GTFPs, while the other provinces performed generally average. In the middle part, Heilongjiang, Hubei, Hunan, and Anhui realized relatively good GTFPs, but the other provinces had only average GTFPs. Most provinces in the western part did not perform well in terms of GTFP. In a large country such as China, the GTFP in each region is severely affected by the local level of economic development and resource endowments. Therefore, regional differences must be considered when China prepares policies for green development;

(2)

The Global Moran Index of GTFPs show that, in most years, the indicator was positive and passed the significance test. This demonstrates an apparent spatial clustering of provincial GTFPs. In particular, the GTFPs of adjacent provinces strongly imitate each other. The spatial correlation of China’s GTFPs affect the measurement of GTPF convergence. Traditional convergence models may have errors in measuring the convergence rate of China’s GTFPs. To improve the measuring accuracy, it is necessary to measure the rate with spatial convergence models, which contain the spatial effect;

(3)

China’s GTFPs exhibited an absolute convergence in the research period. After adding the spatial effect, the absolute beta convergence rate of China’s GTFPs measured by our spatial convergence model was slower than that measured by the traditional convergence models. Without considering other factors, the GTFPs between Chinese provinces were growing closer to each other. The absolute convergence trend of GTFPs provides key evidence of the catch-up effect of the green economy;

(4)

The conditional beta convergence rate of China’s GTFPs was slightly slower than the absolute beta convergence rate. GTFP convergence is significantly affected by industrial structure, technical innovation, opening-up, and urbanization. However, it is not influenced much by environmental governance. Overall, the GTFP convergence is affected differently by different factors. In practice, green policies should be formulated according to the varied effects of different factors and the local situation, in order to accelerate the long-term convergence of GTFPs.