Spatial Effects of Digital Economy Development on Carbon Emissions: Empirical Evidence from the Provincial Level in China

doi:10.21203/rs.3.rs-3234064/v1

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Spatial Effects of Digital Economy Development on Carbon Emissions: Empirical Evidence from the Provincial Level in China

https://doi.org/10.21203/rs.3.rs-3234064/v1

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The digital economy presents unprecedented opportunities to address the current dilemma between economic growth and environmental protection. Based on panel data from China's provinces during 2013–2021, this study employs spatial econometric models to empirically analyze the spatial effects of digital economy development on carbon emissions, and discusses the underlying mechanisms. The findings indicate that the advancement of the digital economy not only contributes to reducing local carbon emissions, but also exhibits spatial spillover effects on neighboring regions. The development of the digital economy indirectly achieves emission reduction through facilitating industrial restructuring, promoting technological advancements, and enhancing energy efficiency. These factors drive the spatial overflow of carbon emissions due to the digital economy's influence. Consequently, this study also provides policy implications for achieving economic low-carbon development in China and other emerging economies.

JEL Classification : Q56 ; C520 ; C34 ; O3 ; O4

Digital Economy

Carbon Dioxide Emissions

Emission Reduction Effect

Spatial Spillover Effects

Panel Data

Spatial Econometric Modeling

Climate change, characterized by global warming, poses a significant threat to human life, and reducing carbon emissions has become a crucial global concern. The 27th Conference of the Parties to the United Nations Framework Convention on Climate Change (COP27) calls for urgent action from the international community to reduce greenhouse gas emissions, build resilience, and adapt to the inevitable impacts of climate change. In 2022, global energy-related carbon dioxide emissions exceeded 36.8 billion tons, with China contributing 12.1 billion tons, accounting for 32.88% of global emissions (IEA, CO2 emissions in 2022). As the world's largest carbon-emitting economy, how China responds to carbon reduction is of vital importance in mitigating global climate change(Gao et al., 2021). Additionally, as the largest developing country, China's experience in carbon reduction can provide valuable insights for sustainable development in other developing nations(Wei et al., 2023). In response, the Chinese government has set dual targets to achieve "carbon peaking" by 2030 and "carbon neutrality" by 2060(Qin et al., 2022). However, the main challenge in achieving these goals lies in balancing the reduction of carbon emissions while sustaining economic well-being, and striking a balance between economic growth and emission reduction appears to be an arduous task(Jianda Wang, Kangyin Dong, Xiucheng Dong, et al., 2022; Yang et al., 2020). Fortunately, with the widespread application of digital technologies, production and consumption patterns are undergoing transformation, and innovative trade models, labor-force allocation, and technological advancements are reshaping the landscape(Saia, 2023). The emerging digital economy seems to provide opportunities for addressing the current dilemma of economic sustainability and environmental protection(Z. Li and Wang, 2022; Yi et al., 2022).

It is worth noting that many scholars have discussed the relationship between the digital economy and carbon emissions. As the digital economy integrates with production activities, digital technologies are penetrating and emerging in various sectors(Chen et al., 2022; Jetter et al., 2009), and the industrial and service sectors and even the agricultural sector are facing digital transformation in terms of redistribution of factors of production, improvement of production efficiency and optimization of business methods(Jianda Wang, Kangyin Dong, Yezhou Sha, et al., 2022; Yi et al., 2022). The digital economy's rapid expansion has driven industrial upgrading and transformation(Y. Li et al., 2021; Paschou et al., 2020), optimizing industrial structures and laying the foundation for comprehensive green production and effective greenhouse gas control(Hu et al., 2022; Xu et al., 2022). Scholars have recognized the significant potential of digital technologies in reducing energy consumption and improving energy efficiency, such as enhancing resource availability and energy monitoring and management during economic expansion(Haldar and Sethi, 2022; Lange et al., 2020; Zhang et al., 2023). Moreover, the digital economy has accelerated the dissemination of green information technology and innovations in energy utilization(Zheng and Wang, 2021), lowering the cost of clean energy and expediting energy transition(Wang et al., 2023; Williams, 2011). The digital economy has demonstrated multiple advantages in optimizing resource allocation and efficiency(Song et al., 2022; Jun Wang et al., 2022), which can effectively reduce fossil fuel consumption, curbing carbon emissions, and driving economies towards carbon neutrality.

In summary, when studying the relationship between economic development and decarbonization, digital economy development is a crucial factor to consider, as it offers a promising pathway to achieve carbon reduction while promoting economic growth. Although scholars have addressed the role of the digital economy in carbon reduction, most of them have only focused on its local impact, paying insufficient attention to the spatial effects in achieving carbon reduction and promoting green development. This may result in an inaccurate understanding of the true relationship and weaken the overall emission reduction effect. Therefore, this study focuses on the following questions: (1) Does the development of the digital economy have a carbon reduction effect, and if so, does it exhibit spatial spillover effects? (2) The pathways of emission reduction are particularly critical, so what is the pathway for digital economy spatial carbon reduction? Addressing these questions will help accurately grasp and utilize the opportunities presented by the rapid development of the digital economy, providing valuable references for coordinated regional development and collaborative governance of carbon emissions.

The marginal contributions of this study include three aspects. Firstly, it provides a summary and analysis of the characteristics of carbon emissions and the development of the digital economy in China, serving as a practical basis for the theoretical analysis of their relationship. Secondly, it takes a spatial-temporal perspective and employs spatial econometric models to analyze the spatial effects of the digital economy and carbon emissions. This not only offers guidance for the coordinated development of the digital economy and carbon emissions control among different regions in China, but also provides valuable insights for other emerging economies in implementing "digital decarbonization", promoting cross-border cooperation on carbon reduction internationally, and establishing a three-dimensional prevention and control system worldwide. Finally, the study analyzes the mechanism of the spatial carbon reduction effects of the digital economy, which is essential for formulating more targeted digital decarbonization plans and maximizing the "digital dividend" in carbon reduction actions. The organization of the remaining parts of this paper is as follows. Section 2 introduces the research methods, Section 3 presents the current situation analysis, Sections 4 and 5 discuss empirical analysis, and Section 6 provides the conclusions and policy implications of the research.

2.1. Calculation of Carbon Emissions

Taking into account the guidelines provided by the United Nations Intergovernmental Panel on Climate Change (IPCC), this paper follows the methodology used by Shan(Shan et al., 2020) and utilizes the mass balance to calculate the carbon dioxide emissions resulting from energy consumption, household consumption, and exhaust emissions processes in each province of China. Carbon emissions (CE) are divided into energy-related emissions (CE_e) and process-related emissions (CE_m). Energy-related emissions are the conversions during fossil fuel combustion, while process-related emissions result from industrial raw material conversion. The specific calculation formulas are as follows.

$$C{E_t}=C{E_e}_{t}+C{E_{mt}}$$

$$C{E_{et}}=\sum\limits_{{i=1}}^{{17}} {C{O_{2,it}}=} \sum\limits_{{i=1}}^{8} {A{D_{it}} \times } NV{C_i} \times C{C_i} \times O$$

$$C{E_{mt}}=C{A_t} \times E{F_t}$$

Where t represents the period, i represents 17 types of fossil fuels, AD_it denotes the combustion volume of fossil fuel i in period t, NVC_i represents the heat value per physical unit produced by the combustion of fossil fuel i, CC_i represents the carbon content of fossil fuel i, and O is the oxidation ratio during combustion. CA_t represents cement production[1], and Ef_t represents the emission coefficient.

2.2. Measurement of Digital Economy Development Level

Currently, there is no consensus on the definition of the digital economy's development in the academic community. Various indicators and measurement methods have been used, but single indicators often fail to reflect the comprehensive development of the digital economy. In this study, we refer to the "China Digital Economy Development White Paper" and related research to construct a measurement system for the development level of the digital economy from four dimensions: digital industrialization, industrial digitalization, digital governance, and data valorization (as shown in Table 1). Then we use principal component analysis to calculate the digital economy development index for each province in China. The calculation process is as follows.

Let the index system have a total of m indicators, denoted by${x_1},{x_2}, \cdots ,{x_m}$, where $X=({x_1},{x_2}, \cdots ,{x_m})'$ is the set of random variables that constitute the random vector.

Due to significant differences in the scale and dimension of basic indicators, it is necessary to standardize them to ensure the accuracy of the composite index. The standardization process is as follows.

$$x_{j}^{ * }=\frac{{{x_j} - \hbox{min} {x_j}}}{{\hbox{max} {x_j} - \hbox{min} {x_j}}}~~,j=1,2, \cdots ,m$$

Where${x_j}$,$\hbox{min} {x_j}$and$\hbox{max} {x_j}$are the observed value, minimum value, and maximum value of indicator j, and $x_{j}^{ * }$ is the dimensionless result of indicator j. For convenience, the dimensionless data table is still denoted as X.

Calculate the covariance matrix S and correlation matrix R of the original data X.

$$S=\frac{1}{{n - 1}}\sum\limits_{{i=1}}^{n} {\left( {{X_k} - \overline {{{X_{}}}} } \right)} {\left( {{X_k} - \overline {{{X_{}}}} } \right)^\prime }={\left( {{s_{ij}}} \right)_{m \times m}}$$

$$R={\left( {{r_{ij}}} \right)_{m \times m}},{r_{ij}}=\frac{{{s_{ij}}}}{{\sqrt {{s_{ii}}{s_{jj}}} }}$$

Where $\overline {X} =(\overline {{{x_1}}} ,\overline {{{x_2}}} , \cdots ,\overline {{{x_m}}} )',\overline {{{x_i}}} =\frac{1}{n}\sum\limits_{{k=1}}^{n} {{x_{ki}}} ,i=1,2, \cdots ,m,{s_{ij}}=\frac{1}{{n - 1}}\sum\limits_{{k=1}}^{n} {({x_{ki}} - \overline {{{x_i}}} } )({x_{ki}} - \overline {{{x_j}}} )$, n is the number of samples.

Suppose the eigenvalues of the correlation matrix R are $\lambda ({\lambda _1} \geqslant {\lambda _2} \geqslant \cdots \geqslant {\lambda _m} \geqslant 0)$, and the corresponding standard orthogonal eigenvectors are ${e_1},{e_2}, \cdots ,{e_m}$. Then, the i-th sample principal component can be represented as ${F_i}=\sum\limits_{{i=1}}^{m} {{e_i}X}$, and the contribution rate of the i-th sample principal component is ${{{w_i}={\lambda _i}} \mathord{\left/ {\vphantom {{{w_i}={\lambda _i}} m}} \right. \kern-0pt} m}$.

Set the $\sum\limits_{{i=1}}^{k} {{{{\lambda _i}} \mathord{\left/ {\vphantom {{{\lambda _i}} m}} \right. \kern-0pt} m}}$ (cumulative contribution rate) to exceed 85% and the eigenvalue to be more than 1 as criteria to determine the number of principal components, denoted as k. Finally, calculate the comprehensive evaluation value of the digital economy development level.

$$~{Y_{}}=\mathop \sum \limits_{{i=1}}^{k} {w_i}{F_i}$$

Table 1

Evaluation index system of the digital economy development
indicator	Measurement methods
Digital Industrialization
Number of workers in relevant enterprises	Average number of workers employed by enterprises in the communications equipment, computer and electronic equipment manufacturing industry (people)
Per capita software business income	Software Business income/Resident Population (RMB/people)
Practitioners in related industries	Number of Employed Persons in Information Transmission, Computer Services and Software Industry (10,000 people)
Per capita telecommunication business volume	Telecommunication business volume/permanent population (RMB/people)
Industrial Digitalization
E-commerce transactions per capita	Electronic commerce transaction volume / Resident Population (RMB/people)
Industrial digitalization application	Number of companies using information management
Degree of financial digitization	Peking University Digital Financial Inclusion Index first-level index (Guo et al., 2020)
Digital Governance
Government Attention	Frequency of digital economy keywords mentioned in the government work reports (times)
Breadth of Digital Finance Coverage	Peking University Digital Financial Inclusion Index first-level index
Fixed Asset Investment	Investment in Fixed Assets in Information Transmission, Computer Services and Software Industry (100 million RMB)
Data Valorization
Depth of Digital Finance Usage	Peking University Digital Financial Inclusion Index first-level index
Internet data usage	Share of PC views (%)

2.3 Spatial Correlation Analysis

Moran's I is a commonly used method for measuring spatial autocorrelation, which includes both global Moran's I and local Moran's I.

Global Moran's I is used for global correlation analysis to examine the overall aggregation of the entire spatial sequence. The calculation formula is as follows.

$$I=\frac{{\sum\nolimits_{{i=1}}^{n} {\sum\nolimits_{{j=1}}^{n} {{w_{ij}}({x_i} - \overline {x} )({x_j} - \overline {x} )} } }}{{{S^2}\sum\nolimits_{{i=1}}^{n} {\sum\nolimits_{{j=1}}^{n} {{w_{ij}}} } }}$$

Where ${S^2}=\frac{{\sum\nolimits_{{i=1}}^{n} {{{({x_i} - \overline {x} )}^2}} }}{n}$ represents the sample variance. ${w_{ij}}$is the spatial weight matrix of element (i, j), which used to measure the distance between region i and region j. $\sum\nolimits_{{i=1}}^{n} {\sum\nolimits_{{j=1}}^{n} {{w_{ij}}} }$ is the sum of all spatial weights. The standardized Moran's I obeys an asymptotic standard normal distribution, allowing the use of critical values from the standard normal distribution to test whether the sample exhibits spatial autocorrelation.

Local Moran's I is used for local correlation analysis and reflects the spatial clustering around a specific region i. The calculation formula is as follows.

$${I_i}=\frac{{({x_i} - \overline {x} )}}{{{S^2}}}\sum\nolimits_{{i=1}}^{n} {{w_{ij}}({x_j} - \overline {x} )}$$

Generally, Moran's scatter plot is used to visually describe local spatial correlation. The scatter plot consists of four quadrants: the first quadrant is high-high (H-H) clustering, representing regions with high values and their neighboring areas with high values; the second quadrant is low-high (L-H) clustering, representing regions with low values and their neighboring areas with high values; the third quadrant is low-low (L-L) clustering, representing regions with low values and their neighboring areas with low values; the fourth quadrant is high-low (H-L) clustering, representing regions with high values and their neighboring areas with low values. Quadrants in the first and third represent positive spatial correlation, while quadrants in the second and fourth represent negative spatial correlation.

2.4 Spatial Panel Model

Classical econometric models generally assume the independence of regions, but variables often exhibit spatial correlation due to various factors. Common modeling methods for spatial effects in panel data include the Spatial Autoregressive Model (SAR), Spatial Error Model (SEM), and Spatial Durbin Model (SDM), and the specific forms of the three models are as follows.

$${Y_{it}}={\lambda _1}W{Y_{it}}+{\alpha _1}{X_{it}}+{\alpha _k}{Z_{it}}+{\mu _i}+{\varepsilon _{it}}$$

$${Y_{it}}={\alpha _1}{X_{it}}+{\alpha _k}{Z_{it}}+{\mu _i}+{u_{it}},{u_{it}}=\rho W{u_{it}}+{\varepsilon _{it}}$$

$${Y_{it}}={\lambda _1}W{Y_{it}}+{\lambda _2}W{X_{it}}+{\lambda _k}W{Z_{it}}+{\alpha _1}{X_{it}}+{\alpha _k}{Z_{it}}+{\mu _i}+{\varepsilon _{it}}$$

Where W is the spatial weight matrix, ${X_{it}}$ is the explanatory variable, ${Z_{it}}$is the control variable, ${\mu _i}$ is the individual effect, ${\varepsilon _{it}}$ is the random disturbance term, ${u_{it}}$ is the disturbance term with spatial dependence, ${\lambda _1}$ is the spatial autoregressive coefficient, $\rho$ is the spatial error coefficient, ${\alpha _1}$and ${\alpha _k}$ are the estimators for explanatory variables and control variables. $W{X_{it}}$ indicates the effect of the independent variable from neighboring areas, ${\lambda _2}$ is the coefficient corresponding to the effect. $W{Z_{it}}$denotes the effect of control variables from neighboring regions, and ${\lambda _k}$is their corresponding coefficients.

2.5 Variable Selection and Definition

China's digital economy has developed rapidly since 2010. However, some indicator data has a starting year of 2012 or 2013. In order to ensure data continuity, the sample period is set from 2013 to 2021. Due to missing data for Tibet, Hong Kong, Macau, and Taiwan, and considering data completeness, these regions are excluded from the study, hence the research focuses on the 30 provinces and autonomous regions of China. To summarize, this article uses panel data from 30 Chinese provinces for the period 2013 to 2021. Individual missing values are filled using interpolation and exponential smoothing methods. The data mainly come from China Statistical Yearbooks, provincial Statistical Yearbooks, the Wind database, and the CEADs database.

The dependent variable is the regional carbon emission level. Considering the significant differences in population sizes among regions, we measure regional carbon emission level using per capita carbon emissions to minimize the estimation bias caused by emissions from residents' living and consumption. The core explanatory variable is the level of digital economy development, measured by the calculated digital economy development index of each region. To accurately evaluate the impact of the digital economy on carbon emissions and reduce the estimation bias caused by omitted variables, we use economic development level, regional marketization, urbanization, and openness to foreign investment as control variables. To further determine the pathways through which digital economy development affects carbon emissions, based on the previous analysis, we consider industrial structure, technological advancement, and energy efficiency as mediating variables. The detailed descriptions of each variable are presented in Table 2.

Table 2

Variable Descriptions
Symbol	Variable meaning	Measurement methods
implicit variable
percarbon	carbon emissions per capita	carbon emissions/regional resident population (ton/10,000 people)
independent variable
digital	level of digital economy development	digital Economy Index calculated under the Principal component Analysis methodology
Control variables
FDI	degree of openness to foreign investment	actual utilised FDI / Regional real GDP
market	degree of marketization	Fan Gang Market-oriented Index(Fan et al., 2011)
Pop	Population size	logarithmic value of the size of the resident population
urban	level of urbanization	urban population/total population
perGDP	level of economic development	Regional real GDP per capita is logarithmic
Mediation variables
struc	advancement of industrial structure	proportion of value added of tertiary sector to value added of secondary sector
tech	technological progress	logarithmic value of the number of patents granted by 10,000 people in the region
eff	energy total factor efficiency	using capital, labor and energy as input indicators, and regional real GDP as output indicators, calculated using the super-efficient SBM model

3.1. Spatial and Temporal Analysis of Carbon Emissions

3.1.1 Temporal Evolution Trend of Carbon Emissions

Figure 1 depicts the average changes in carbon emissions, per capita carbon emissions, and carbon emission intensity across 30 provinces in China from 2013 to 2021. In absolute terms, carbon emissions show a gradual increase over time. In relative terms, per capita carbon emissions exhibit a slow upward trend with minimal growth, significantly lower than the growth rate of carbon emissions. However, carbon emission intensity demonstrates a clear decreasing trend year by year. Overall, while China's average carbon emissions continue to rise, achieving the goal of peak carbon emissions and controlling greenhouse gas emissions requires more effort. Nevertheless, the declining trend in per capita carbon emissions and carbon emission intensity indicates a notable improvement in carbon emission efficiency, reflecting some initial positive outcomes in greenhouse gas control.

3.1.2 Spatial Evolution Trend of Carbon Emissions

To visually present the overall level, distribution evolution, extension, and planning trends of carbon emissions across provinces in China, we further use three-dimensional dynamic kernel density estimation to plot the per capita carbon emissions and carbon emission intensity of the 30 provinces, as shown in Fig. 2. Observing Fig. 2, the following significant characteristics of China's provincial carbon emissions emerge. Firstly, regarding the distribution position, the centroids of all variables exhibit a clear left-skewed pattern, indicating that China's provinces have achieved certain success in low-carbon development, with the overall carbon emission level on a downward trajectory. Secondly, concerning the primary peak distribution, the height of the main peak of per capita carbon emissions shows a slight increase, while the main peak of carbon emission intensity experiences a notable increase with a narrower width, which indicates a declining trend in the disparity of carbon emissions among regions. Moreover, the number of peaks in the kernel density curves for each variable is consistent, with a single peak and relatively gentle shape, suggesting that China's provincial carbon emission level does not display a pronounced polarization feature. Lastly, regarding the distribution extension, the kernel density curves of all variables have evident right-tailed characteristics, indicating the presence of certain provinces with significantly higher carbon emission levels than others. In summary, China's provincial carbon emissions continue to decline, the disparity in carbon emission levels among provinces is gradually narrowing, and there is no clear polarization feature, although some provinces exhibit higher emission levels.

3.1.3 Spatial Correlation Analysis of Carbon Emissions

The kernel density analysis shows significant spatial differences in carbon emissions among China's provinces. To further examine whether there is spatial correlation between provinces, this study conducts both global and local spatial correlation analyses on carbon emission levels.

The global correlation analysis assesses the overall spatial clustering of carbon emissions among China's provinces. Based on the geographical adjacency weight matrix, we calculate the global Moran's Index of per capita carbon emissions to estimate the spatial correlation of carbon emissions. The results are presented in Table 3. It can be observed that the Moran's Index for per capita carbon emissions during the sample period is positive and mostly statistically significant, indicating a significant positive spatial autocorrelation in China's provincial carbon emissions, reflecting a strong spatial clustering phenomenon.

Table 3

Global Moran's Index of Carbon Emission Levels and Digital Economy Development Levels in China from 2013 to 2021
	2013	2014	2015	2016	2017	2018	2019	2020	2021
percarbon	0.2996^*** (3.056)	0.2901^*** (2.985)	0.2929^*** (2.989)	0.3045^*** (3.057)	0.2896^*** (2.909)	0.277^*** (2.818)	0.2882^*** (2.889)	0.2961^*** (2.942)	0.2995^*** (2.964)
digital	0.0424 (0.6458)	0.0222 (0.4852)	-0.0122 (0.1889)	0.0202 (0.461)	-0.0395 (-0.0427)	0.1081 (1.2118)	0.199^** (1.9835)	0.2289^** (2.2613)	0.2879^*** (2.668)
Note: The values in parentheses represent Z statistics; , , ** indicate significance at the 15%, 10%, and 5% levels, respectively.

The local correlation analysis examines the spatial clustering of carbon emissions around each province. Figure 3 displays the scatter plots of local Moran's Index for per capita carbon emissions in 2013 and 2021. It can be observed that most provinces are located in the first and third quadrants, indicating positive spatial correlation in per capita carbon emissions. This corresponds to the results of the global Moran's Index test, showing that the majority of provinces exhibit a trend of positive spatial clustering. Specifically, "H-H" clustering is evident in provinces such as Shaanxi, Liaoning, Inner Mongolia, Shanxi, Ningxia, Heilongjiang, and Shanxi, while "L-L" clustering includes provinces with larger numbers, such as Beijing, Shanghai, Zhejiang, Jiangsu, Chongqing, Sichuan, Fujian, and Guangdong. "L-H" clustering is represented by provinces like Henan, Gansu, and Hebei, while "H-L" clustering is mainly seen in Xinjiang and Shandong.

3.2. Spatial and Temporal Characteristics of Digital Economy Development

3.2.1 Spatial and Temporal Evolution of Digital Economy Development

Based on the established index system and selected methods, the Digital Economy Development Index of the 30 provinces in China from 2013 to 2021 was calculated. Three cross-sectional data points from 2013, 2017, and 2021 were selected and ranked for display, as shown in Fig. 4. The color gradient from yellow to red represents the gradual increase in the level of digital economy development.

In terms of timing, the digital economy development level in each province of China shows an overall upward trend. In terms of sub-years, the digital economy development index ranges from 0.129 to 0.305 among provinces in 2013, with Beijing, Jiangsu, Shanghai, and Guangdong having relatively higher digital economy development indices, of which Guangdong was the highest at 0.472. In 2017, the level of digital economy development increased across provinces, showing a pattern of differentiation. The eastern coastal regions experienced faster growth, becoming the forefront of China's digital economy development, while the central and western regions exhibited slower growth, especially the northeastern provinces showing generally slow progress. By 2021, the level of digital economy development in each province had further improved, with the overall mean increasing from 0.238 in 2013 to 0.678 in 2021, and regional disparities had been effectively mitigated.

Spatially, the digital economy development among Chinese provinces exhibits a distinct pattern of the first-developed areas driving the later-developed areas. From the left to the right in Fig. 4, the spatial distribution of digital economy development in Chinese provinces shows a diffusion pattern centered around Beijing in the northern coastal region, Jiangsu in the southern coastal region, and Guangdong in the eastern coastal region. This indicates a spatial pattern of decreasing digital economy development from the center to the periphery, reflecting the driving effect of central provinces and suggesting the possible presence of spatial spillover effects in digital economy development among provinces.

3.2.2 Spatial Correlation of Digital Economy Development

To study the spatial correlation effects of digital economy development, both global and local Moran's I indices were calculated for the digital economy development index. The results are presented in Table 3 and Fig. 5. As time progresses, the global Moran's I index for the digital economy gradually increases, reaching its peak at 0.2879 in 2021, with a similar trend of increasing significance level, indicating a growing spatial clustering of digital economy development among Chinese provinces and demonstrating significant spatial positive correlation. Further calculations of the local Moran's I index for digital economy development reveal relatively weaker local clustering compared to per capita carbon emissions. Nonetheless, the provinces falling into the first and third quadrants are more prominent. Specifically, "H-H" clustering is represented by Shanghai, Jiangsu, Zhejiang, Shandong, Fujian and Tianjin; "L-L" clustering includes provinces such as Jilin, Gansu, Liaoning, Inner Mongolia, Shanxi, Ningxia, Guizhou, Heilongjiang, Yunnan and Shanxi. "L-H" clustering is represented by Hebei and Guangxi, while "H-L" clustering is mainly seen in Sichuan, Chongqing, Guangdong, and Beijing.

3.3 Correlation Analysis between Digital Economy and Carbon Emissions

By comparing the clustering characteristics of the digital economy development index ("H-H" clustering) and per capita carbon emissions ("L-L" clustering), it is evident that there is a high degree of similarity between the regions with advanced digital economy development and low per capita carbon emissions. Combined with the analysis in the introduction, the close correlation between digital economy development and carbon emissions is reasonably suspected. Figure 6 provides an intuitive description of the relationship between the digital economy and carbon emissions. From Fig. 6, it is evident that, without considering the influence of other variables, there is a negative correlation between digital economy development and per capita carbon emissions in that higher digital economy development in a region tends to be associated with lower per capita carbon emissions. However, further research is required to rigorously demonstrate whether promoting digital economy development contributes to emission reduction, how this mechanism operates, and whether it exhibits spatial spillover effects. In the subsequent sections, econometric methods will be employed to explore the relationship more rigorously.

4.1. Variable Testing

Panel data includes both time and cross-sectional dimensions. If the time series is non-stationary, it may lead to biased estimates, invalid t-tests, and the occurrence of "spurious regression." To avoid these situations, we conducted unit root tests on the sample data to determine whether the data process is stationary. In order to ensure strong stationarity and scientificity of the test results, we used three methods of the LLC test, Fisher test, and Hadri LM test. The results are shown in Table 4. According to the results of the three tests, all variables rejected the null hypothesis of "existing a unit root", indicating that the panel data is stationary.

Table 4

Results of Panel Unit Root Test
Variables	LLC	Fisher				Hadri LM
Variables	Adjusted t*	p	z	L*	Pm	z
percarbon	-2.9472^***	67.706	-0.9938^*	-1.1122^*	0.7035	11.1457^***
digital	-7.3116^***	101.5147^***	-3.9451^***	-3.7991^***	3.7898^***	9.4556^***
FDI	-4.1506^***	153.5059^***	-7.0464^***	-7.2478^***	8.5359^***	7.5663^***
market	0.798	169.5662^***	-5.498^***	-6.8346^***	10.002^***	11.8633^***
popu	-7.7887^***	135.5436^***	-5.544^***	-5.6672^***	6.8962^***	13.5279^***
urban	-25.4921^***	166.2562^***	-7.3506^***	-7.7569^***	9.6998^***	13.3747^***
perGDP	3.0609	113.7238^***	-5.297^***	-5.0324^***	4.9043^***	11.0370^***
struc	-5.3547^***	153.2615^***	-7.2236^***	-7.1585^***	8.5136^***	7.9419^***
tech	7.7656	28.2868	5.1178	5.2089	-2.8950	12.1308^***
eff	-11.9231^***	199.451^***	-9.6713^***	-9.9123^***	12.7301^***	2.9405^***
Note: , and ** represent rejection of the null hypothesis at the 15%, 10%, and 5% significance levels, respectively.

4.2. Model Testing

To ensure the effectiveness and reliability of the empirical analysis, it is necessary to identify the model's form and model effects. The test results are presented in Table 5. Firstly, the results of the global and local Moran's I in previous sections indicate the presence of strong spatial correlation in the key variables. Combined with the results of the LM test (see Table 5(1), (2)), we can infer that both the LMlag and LMerr statistics are significant, indicating the existence of spatial lag and spatial error characteristics in the regression equation, thus confirming the rationality of selecting a spatial panel model. Secondly, the panel model can be categorized into random effects and fixed effects models. The Hausman test statistics (Table 5(3)) strongly reject the null hypothesis, suggesting that the fixed effects model is superior to the random effects model. Finally, the fixed effects can be spatial fixed, time fixed, or spatiotemporal fixed effects. The LR test results (Table 5(4), (5)) strongly reject the null hypothesis that spatial fixed or time fixed effects are superior to spatiotemporal fixed effects, indicating that the appropriate spatial econometric model for testing and analysis is a spatiotemporal fixed effects model.

Table 5

Model Effects and Model Selection Tests
	Inspection method	Null hypothesis	Statistic	p-value
(1)	LM-spatialerror	no spatial error	25.934	0.000
(2)	LM-spatiallag	no spatial lag	42.555	0.000
(3)	Hausman test	difference in coefficients not systematic	46.57	0.000
(4)	LR-ind	ind nested in both	16.08	0.098
(5)	LR-time	time nested in both	932.61	0.000
(6)	Wald-spatiallag	sdm can degenerate to sar	41.72	0.000
(7)	Wald-spatialerror	sdmCan degenerate to sem	41.18	0.000
(8)	LR-spatiallag	sar nested in sdm	38.98	0.000
(9)	LR-spatialerror	sem nested in sdm	40.08	0.000

4.3. Spatial spillover effect analysis

Table 6 presents the regression results of SAR, SEM, and SDM models with the adjacency weight matrix. The estimated coefficients of the core explanatory variable "digital" are all negative and highly statistically significant, indicating that the development of the digital economy can reduce per capita carbon emissions, demonstrating a significant emission reduction effect. The spatial autoregressive coefficient (ρ) and spatial error coefficient (λ₁) of per capita carbon emissions are significantly positive, indicating the presence of significant spatial dependence in carbon emissions among provinces. Local carbon emissions will spill over to neighboring regions, leading to an increase in carbon emissions in these neighboring regions. Among the control variables, both the degree of marketization and the level of urbanization have significant emission reduction effects. Economic development also plays a role in mitigating carbon emissions to some extent, but its effect is not statistically significant. Population size and the actual use of foreign capital have a positive effect on carbon emissions, but the effect of actual use of foreign capital is not significant.

Table 6

Regression Estimation Results of the Spatial Carbon Emission Reduction Effect of Digital Economy Development
Variables	SAR	SEM	SDM
digital	-17.84126^***(-6.26)	-17.49119^***(-6)	-18.00346^***(-6.47)
market	-0.5550509^**(-1.93)	-0.6711339^***(-2.28)	-0.7148275^***(-2.43)
FDI	3.035964(0.21)	-0.7218082(-0.05)	3.01738(0.21)
popu	23.68519^***(4.49)	26.12201^***(4.32)	31.90378^***(5.57)
urban	-0.2951011^***(-3.17)	-0.3287552^***(-3.35)	-0.4009071^***(-4.18)
perGDP	-1.247255(-0.98)	-0.8365865(-0.62)	0.5491237(0.41)
${\lambda _1}$	0.2096651^***(2.73)		0.170514^***(2.06)
$\rho$		0.2540591^***(2.54)
sigma2_e	2.130734^***(11.57)	2.128031^***(11.49)	1.851499^***(11.58)
time fixed	yes	yes	yes
spatial fixed	yes	yes	yes
Note: , , and ** indicate significance at the 15%, 10%, and 5% levels, respectively, and in () are Z statistics. The same below.

For spatial econometric models, the marginal effects of explanatory variables on the dependent variable need to be assessed in terms of direct effects, indirect effects, and total effects. As spatial econometric models capture complex dependency structures among sample units, changes in the explanatory variable not only affect local unit but also potentially affect units of other regions. The local change is referred to as the direct effect, and the other regions’ alteration is called the indirect effect. The sum of the two effects is the total effect. Table 7 provides the effect decomposition results based on the SDM and SAR models with spatiotemporal fixed effects. Regarding the core explanatory variable "digital," the results in Table 7 show that the direct effect is significantly negative, indicating that an increase in the level of regional digital economy development will decrease per capita carbon emissions. As for the indirect effect, both SDM and SAR models yield negative coefficients for the "digital" variable, with the SAR model's estimate being highly statistically significant. Therefore, based on the SAR model's estimation, the development of the digital economy has a significant inhibitory effect on per capita carbon emissions of nearby areas through indirect effects. If the level of digital economy development in other regions increases by 1%, it will reduce per capita carbon emissions in the local region by more than 4.645%. The total effect of the "digital" variable in both the SDM and SAR models is also significantly negative, further confirming the emission reduction effect of digital economy development.

Table 7

Spatial Carbon Emission Reduction Effect Decomposition of Digital Economy Development
Variables	SDM			SAR
Variables	Direct effects	Indirect effects	Total effects	Direct effects	Indirect effects	Total effects
digital	-17.97505^*** (-6.24)	-2.517879 (-0.36)	-20.49293^*** (-2.63)	-17.96377^*** (-6.12)	-4.645675^*** (-2.16)	-22.6094^*** (-5.66)
market	-0.658033^*** (-2.36)	1.91424^*** (2.41)	1.256206^** (1.54)	-0.5753678^** (-2.04)	-0.1496957^* (-1.41)	-0.72506^*** (-1.98)
FDI	7.676105 (0.53)	85.09512^*** (2.19)	92.77123^*** (1.98)	4.537415 (0.32)	1.208592 (0.3)	5.746007 (0.32)
popu	30.36383^*** (5.45)	-38.88914^*** (-2.64)	-8.525312 (-0.54)	23.91269^*** (4.5)	6.406541^*** (1.8)	30.31923^*** (3.81)
urban	-0.389101^*** (-4.11)	0.3551723^** (1.44)	-0.0339294 (-0.13)	-0.3000229^*** (-3.16)	-0.0793336^** (-1.68)	-0.37935^*** (-2.94)
perGDP	0.4124585 (0.31)	-4.613593^* (-1.62)	-4.201135 (-1.3)	-1.24123 (-0.98)	-0.3134632 (-0.82)	-1.554693 (-0.97)
time fixed	yes	yes	yes	yes	yes	yes
spatial fixed	yes	yes	yes	yes	yes	yes

4.4. Robustness Test and Endogeneity Correct

4.4.1 Robustness Test

Among the SAR, SEM, and SDM models, which one is more compatible with the sample data? To determine this, we conducted Wald test and LR test, and the relevant test results are provided in Table 5(6) to (9). The Wald test results strongly reject the hypothesis that the SDM model degenerates into the SAR or SEM model. The LR test results are consistent with the Wald test results, indicating that estimating the SDM model is superior to the SAR or SEM model, and the SDM model is more compatible with the sample data. Therefore, the robustness analysis will focus on the SDM model.

To further verify the spatial carbon emission reduction effect of digital economy development, we conducted three robustness tests. First, we replaced the adjacency weight matrix with the geographic distance spatial weight matrix and re-estimated the SDM. Second, the SDM is re-estimated by replacing the adjacency spatial weight matrix with the economic distance spatial weight matrix. Third, considering the disparity in population size among regions, while we used per capita carbon emissions to measure regional carbon emission levels in the previous analysis, the level of economic development also exhibits significant differences among regions. Therefore, in this case, we replaced per capita carbon emissions with carbon emission intensity[2] and re-estimated the SDM. The test results are shown in Table 8. It can be observed that the negative relationship between the digital economy and carbon emissions remains robust. The direct effects, indirect effects, and total effects of the "digital" variable are predominantly negative and highly statistically significant in most cases, which are broadly consistent with the results in Table 6 and Table 7, validating the spatial carbon emission reduction effect of digital economy development.

Table 8

Robustness and Endogeneity Testing Results
Variables	Robustness test
Variables	geographic distance weight matrix(1)	economic distance weight matrix(2)	replace the explanatory variable(3)	GS2SLS	first stage of 2SLS		second stage of 2SLS
digital	-21.0842^*** (-6.95)	-18.69413^*** (-6.87)	-1.610459^*** (-3.99)	-10.8182^*** (-3.28)		-134.9253^*** (-2.41)
IV					0.015014^*** (2.49)
direct effect	-21.0246^*** (-6.68)	-18.75334^*** (-6.69)	-1.564299^*** (-3.7)
indirect effect	4.233557 (0.41)	-7.01816 (-0.7)	-0.6597804 (-0.85)
total effect	-16.79109^* (-1.44)	-25.7715^*** (-2.45)	-2.22408^*** (-2.82)
control variables	yes	yes	yes	yes	yes	yes
Kleibergen-Paap rk LM						4.619^***
Shea's partial F						6.18741^***

4.4.2 Endogeneity Correct

Although the negative relationship between the digital economy and carbon emissions has been preliminarily verified, there might be a reverse effect where carbon emissions also affect the development of the digital economy. Additionally, there could be measurement errors and omitted variables, leading to endogeneity issues in the estimation model. To address this, we selected instrumental variables (IV) for the endogenous digital economy, which is the interaction term between the number of fixed telephone lines per 100 people in 1984 and the number of national internet users in the previous year during the sample period. On the one hand, as an important historical telecommunication infrastructure, the usage of fixed telephone lines in 1984 could influence advanced digital economy development from technical levels and usage habits, satisfying the relevance condition of instrumental variables. On the other hand, the fixed telephone data from 1984 would not directly affect current regional carbon emissions. Instead, it affects regional carbon emissions through modern digital technology application and innovation, satisfying the exogeneity condition of instrumental variables. Furthermore, since the fixed telephone data from 1984 is cross-sectional data, it cannot be directly analyzed with panel data. Therefore, we used the lagged internet users multiplied by the number of fixed telephone lines to construct the interaction term, granting the instrumental variable time-varying properties. We used GS2SLS and 2SLS to correct for endogeneity, and the estimation results are shown in the columns (4), (5) and (6) of Table 8.

The results show that the LM statistic is significant, rejecting the null hypothesis of insufficient instrument relevance, indicating that the exogeneity condition of the instrumental variable is satisfied. In the column (5), the estimated coefficient of the IV is significantly positive, and the F statistic is significant, rejecting the null hypothesis that the first-stage regression coefficient of the instrumental variable is zero, confirming the relevance condition of the instrumental variable, indicating that the instrumental variable selection is appropriate. Under both GS2SLS and 2SLS estimation methods, the regression coefficient of "digital" remains significantly negative, indicating that the previous conclusions are robust even after considering endogeneity issues.

After establishing the basic relationship between the digital economy and carbon emissions, it is necessary to further clarify the spatial emission reduction paths of digital economy development. Based on the analysis of relevant research in the introduction, the specific roles of industrial structure, technological progress, and energy efficiency in the emission reduction process of digital economy development will be examined. In the following analysis, the author employs the classical three-step regression method based on the SDM to conduct a mediation analysis.

5.1. Model Design

In the first step, the dependent variable is regressed on the explanatory variable to verify whether the digital economy significantly affects carbon emissions, as already confirmed in the previous analysis.

In the second step, the explanatory variable is regressed on the mediator variable to verify whether the explanatory variable significantly affects the mediator variable. The model is formulated as follows.

$${M_{it}}={\lambda _1}W{M_{it}}+{\lambda _2}Wdigita{l_{it}}+{\lambda _k}W{Z_{it}}+{\alpha _1}digita{l_{it}}+{\alpha _k}{Z_{it}}+{\mu _i}+{\varepsilon _{it}}$$

Where ${M_{it}}$ is the set of mediator variables. If the coefficient ${\alpha _1}$ is significant, it indicates that the explanatory variable significantly affects the mediator variable, supporting the existence of a mediating effect; otherwise, the mediating effect is not established.

In the third step, the dependent variable is regressed on the explanatory variable and the mediator variable to verify whether the mediator variable significantly affects the dependent variable. The model is formulated as follows.

$$percarbo{n_{it}}={\lambda _1}Wpercarbo{n_{it}}+{\lambda _2}Wdigita{l_{it}}+{\lambda _3}W{M_{it}}+{\lambda _k}W{Z_{it}}+{\alpha _1}digita{l_{it}}+{\alpha _2}{M_{it}}+{\alpha _k}{Z_{it}}+{\mu _i}+{\varepsilon _{it}}$$

If both ${\alpha _1}$ and ${\alpha _2}$ are significant, it indicates that the mediating effect exists, and the mediator variable is a partial mediator, suggesting the presence of other paths. If ${\alpha _2}$ is significant but ${\alpha _1}$ is not, it indicates that the mediating effect exists, and the mediator variable is a complete mediator, indicating that there is only one path. If ${\alpha _2}$ is not significant, the mediating effect is not established.

5.2. Empirical Test

Table 9 presents the results of the mediation effect test. Columns (1), (3), and (5) correspond to the mediation effect test in Eq. (13), while columns (2), (3), and (4) correspond to the mediation effect test in Eq. (14). Based on the results in columns (1), (3), and (5) of Table 9, it can be observed that after introducing the mediator variable as the dependent variable, the estimated coefficient of the explanatory variable "digital" is significantly positive, indicating that the explanatory variable has a significant promoting effect on the mediator variable. This suggests that the development of the digital economy can promote the advancement of industrial structure, technological progress, and energy efficiency. The results in columns (2), (3), and (4) show that after introducing the mediator variable as the explanatory variable, the estimated coefficients of "digital", "struc", "tech", and "eff" are all negative and mostly statistically significant. This indicates that industrial structure, technological progress, and energy efficiency play indirect effects in the mediation process of the digital economy, contributing to reducing local carbon emissions. Additionally, both the coefficients of the explanatory variable and the mediator variable pass the significance test, indicating that all three mediator variables are partial mediators.

Table 9

Mediation Effect Analysis Results
Variables	Industrial Structure		Technological Progress		Energy Efficiency
Variables	struc(1)	percarbon(2)	tech(3)	percarbon(4)	eff(5)	percarbon(6)
digital	0.9759502^*** (4.53)	-13.1864^*** (-4.95)	34.02918^*** (5.58)	-16.91433^*** (-5.76)	0.5795483^*** (2.43)	-16.85532^*** (-5.99)
struc		-4.509833^*** (-6.13)
tech				-0.037238* (-1.35)
eff						-0.9537353* (-1.36)
$\rho$	0.0417361 (0.51)	0.000352 (0)	0.1097266^* (1.39)	0.173031^*** (2.09)	-0.0443305^*** (-0.52)	0.1838605^*** (2.23)
sigma2_e	0.01119^*** (11.61)	1.580277^*** (11.62)	8.933651^*** (11.61)	1.837328^*** (11.58)	0.0136893^*** (11.62)	1.81926 (11.57)
control variables	Yes	Yes	Yes	Yes	Yes	Yes

As a key driver of technological advancements and industrial transformations, the development of the digital economy provides opportunities for low-carbon transformation and energy-saving emission reduction. In this article, we first summarized the spatiotemporal characteristics of carbon emissions and digital economy development in China and explored their negative correlation, which may become an important practical issue for promoting the green development of China's digital economy industry and achieving dual carbon goals. Furthermore, based on panel data from 30 provinces in China during 2013–2021 and using spatial panel econometric models, we investigated the spatial effects of digital economy development on carbon emissions and analyzed the spatial emission reduction mechanism of digital economy development through the pathways of industrial structure, technological progress, and energy efficiency. The main conclusions are as follows.

(1) During the study period, Chinese provincial carbon emissions showed an overall downward trend over time, with a gradual reduction in regional disparities. In the spatial dimension, significant positive spatial autocorrelation was observed. There was a negative correlation between Chinese digital economy development and carbon emissions.

(2) Digital economy development has a restraining effect on carbon emissions. Empirical analysis results show that digital economy development can reduce per capita carbon emissions and has a significant emission reduction effect, which remains robust after conducting robustness tests such as replacing spatial weight matrices and dependent variables, and correcting for endogeneity using instrumental variables. This validates the reliability of the emission reduction effect of digital economy development.

(3) Digital economy development's emission reduction effect exhibits significant spatial spillover. The development of the digital economy not only promotes local carbon emission reductions but also exerts a suppression effect on carbon emissions in neighboring areas, leading to reductions in carbon emissions in both the local and adjacent regions.

(4) The digital economy can indirectly affect carbon emissions through three pathways: industrial structure, technological progress, and energy efficiency. The pathway analysis results demonstrate that the local emission reduction effect of digital economy development is mainly achieved through various pathways, including promoting industrial structure upgrading, driving regional technological progress, and improving energy efficiency.

Currently, not only in China but also in many developing economies, there are challenges in economic development and environmental protection. The empirical results obtained in this study provide direction for formulating emission reduction action plans in China and other similar developing economies. Firstly, digital transformation provides an important opportunity for economic low-carbon transformation and energy-saving emission reduction. Accelerating digital economy development and promoting the penetration of digital technology into traditional industries, especially high-energy-consuming and high-pollution industries, are crucial to achieve cleaner production and green development. Secondly, under the context of strong spatial dependence between the digital economy and carbon emissions, the connection between regional economic development and environmental governance needs to be further strengthened. On one hand, inter-regional digital economy development connections should be enhanced through measures such as industry support and policy subsidies to facilitate effective integration among digital economy enterprises, thereby constructing a balanced development, orderly market, and goal-consistent digital economy industrial system. On the other hand, inter-regional joint prevention and control mechanisms should be established, including mutual coordination of cross-regional pollution control actions and coordinated environmental policy design. Lastly, based on the spatial emission reduction pathways achieved through digital economy development, it is essential to enhance the inducing effect of digital economy development on industrial upgrading and promote the deep integration of intelligent, digital, and networked modern services with traditional industries. Moreover, fostering the benign spillover effects of digital economy development on technological progress, promoting the digital transformation of energy, and fully leveraging the positive emission reduction effect of digital economy through its quality improvement are crucial to achieving the carbon peak and carbon neutrality targets.

Although this research provides meaningful policy implications for sustainable economic development, it has some limitations. The study did not consider the regional heterogeneity of the emission reduction effect of the digital economy. Moreover, this research took a macro perspective to analyze the impact of digital economy development on carbon emissions, without discussing the micro mechanisms of the effects, which is a significant focus of our future research.

Ethical Approval and Consent to Participate

We declare that we have no human participants, human data, or human issues.

Consent to Publish

Not applicable

Author Contributions

Material preparation, data collection and analysis, and draft of the manuscript of this research were performed by Yajing Li.

Funding

This research was supported by the National Social Science Fund of China (Grant numbers: 21BJY086).

Competing Interests

The authors have no relevant financial or non-financial interests to disclose.

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Only cement production is included because it accounts for 70% of process-related emissions in China.
carbon emission intensity is measured by the ratio of regional carbon emissions to regional GDP.

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Spatial Effects of Digital Economy Development on Carbon Emissions: Empirical Evidence from the Provincial Level in China

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Abstract

Figures

1. Introduction

2. Methodology and Data

2.1. Calculation of Carbon Emissions

2.2. Measurement of Digital Economy Development Level

2.3 Spatial Correlation Analysis

2.4 Spatial Panel Model

2.5 Variable Selection and Definition

3. Status Analysis

3.1. Spatial and Temporal Analysis of Carbon Emissions

3.1.1 Temporal Evolution Trend of Carbon Emissions

3.1.2 Spatial Evolution Trend of Carbon Emissions

3.1.3 Spatial Correlation Analysis of Carbon Emissions

3.2. Spatial and Temporal Characteristics of Digital Economy Development

3.2.1 Spatial and Temporal Evolution of Digital Economy Development

3.2.2 Spatial Correlation of Digital Economy Development

3.3 Correlation Analysis between Digital Economy and Carbon Emissions

4. Empirical Analysis

4.1. Variable Testing

4.2. Model Testing

4.3. Spatial spillover effect analysis

4.4. Robustness Test and Endogeneity Correct

4.4.1 Robustness Test

4.4.2 Endogeneity Correct

5. Further Discussion

5.1. Model Design

5.2. Empirical Test

6. Conclusion and Implication

Declarations

References

Footnotes

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