Spatial Interdependence, Spillover Effects and Moderating Mechanisms of the Digital Economy on Carbon Productivity: Empirical Analysis Based on Spatial Econometric Models

Abstract

In the context of China’s “dual carbon” strategy, carbon productivity serves as a central in dicator for coordinating economic development with carbon emissions. While the digital economy reshapes spatial economic configurations and affects regional carbon productivity, its spatial interdependence and spillover effects remain insufficiently explored. Our study constructs composite indicators to measure both digital economy development and carbon productivity, examining 30 Chinese provinces from 2011 to 2022 using the super-efficiency SBM model and exploratory spatial data analysis. Spatial regression is applied to assess the spatial influences of the digital economy and the moderating role of industrial structure transforming. Results reveal that: (1) China’s carbon productivity has improved overall but with notable regional disparities; (2) a U-shaped linkage between digital development and carbon productivity is confirmed, with early-stage suppression and later environmental benefits; (3) industrial rationalization and upgrading significantly enhance this relationship, though structural frictions remain obstacles.

1. Introduction

Global climate change has become a complex and pressing set of challenges, posing profound risks to ecology ical security and the foundations of sustainable development. Latest figures published by the International Energy Agency [1] show that energy-related carbon dioxide emissions reached a record-breaking 37.8 billion tons in 2024. This unprecedented figure not only sets a historical peak but also vividly highlights the immense pressure that human activities continue to exert on the global climate system [2]. Transitioning away from the traditional high-carbon development paradigm and fostering a profound transformation of economic and social systems toward green, low-carbon growth has become the viable pathway to safeguard our shared planet and ensure sustainable development [3].

As the world’s leading emitter of carbon dioxide [1], China faces dual and interrelated challenges: transitioning from high-speed to high-quality economic growth while meeting environmental objectives. The “dual carbon” goals—carbon peaking by 2030 and neutrality by 2060—demonstrate China’s firm commitment to global climate governance and its adaptation to industrial and technological shifts [4]. Achieving these targets requires enhancing carbon productivity, advancing low-carbon industries, effective utilization of rapidly evolving digital technologies. These efforts are admittedly essential for reshaping national and regional sustainability trajectories while enhancing industrial competitiveness in a digital era.

Existing research has extensively demonstrated digital economy’s contributions to technological innovation, industrial upgrading, and economic transformation [5,6,7]. However, the impact of digital economy on carbon productivity remains insufficiently explored. While some research hilight the digital economy’s potential to enhance carbon productivity through high levels of innovation [8], strong cross-sectoral penetration [9], and extensive coverage [10]. Other scholars warn the potential risks, noting that technological and environmental integration frictions at the current stage of development may induce the “Jevons’ paradox,” where efficiency gains paradoxically stimulate higher overall consumption, thereby undermining improvements in carbon productivity [11,12]. Moreover, important questions remain regarding the spatio-temporal evolution patterns of digital economy and carbon productivity, along with the presence of spatial effects in their interaction mechanisms.

Our study aims to conduct innovative research on relevant issues from three perspectives: theoretical, methodological, and policy application. Theoretically, the research expands the perspective from “direct impact” to “spatial correlation,” systematically analyzing the cross-regional effects of digital economy on carbon productivity through industrial structure transforming, thereby deepening the intrinsic connection between the digital economy and low-carbon transition. Methodologically, the study abandons traditional static panel models and comprehensively employs exploratory spatial data analysis, spatial Durbin model, and moderation effect tests to reveal the evolution patterns of China’s carbon productivity in both temporal and spatial dimensions, identifying its stable spatial dependence and heterogeneous patterns. Furthermore, our paper innovatively introduces the Markov chain methods to predict the dynamic trends of future carbon productivity, effectively addressing the limitations of existing studies that are often confined to cross-sectional or short-term panel data, thereby enhancing the forward-looking nature and policy reference value of the conclusions. In terms of application, the findings of the research not only provide new empirical evidence for coordinated emission reduction but also offer theoretical foundations and methodological support for designing differentiated and coordinated environmental governance policies, which holds significant implications for promoting high-quality economic development in China and achieving the “dual carbon” goals.

2. Literature Review

2.1. The Concept and Measurement of Carbon Productivity

Kaya and Yokobori (1997) [13] were the first to introduce the concept of carbon productivity, defining it as the ratio of regional GDP to carbon emissions within a defined period, thereby indicating the economic efficiency of carbon usage. Since its inception, the concept has attracted significant academic attention. The McKinsey Report on The Carbon Productivity Challenge (MGI, 2008) [14] identified carbon productivity as a critical tool for balancing economic expansion and carbon emissions., emphasizing that substantial improvements in carbon productivity must accompany economic expansion to achieve sustainable development.

As research on carbon productivity has evolved, related concepts and methodologies have been continuously refined. To better account for environmental performance, researchers have adapted the traditional total factor productivity framework by integrating carbon output into the analysis [15,16]. By integrating the environmental consequences of energy consumption and carbon emissions with traditional inputs (labor, capital, and energy), this approach facilitates a more robust assessment of a region’s green and low-carbon development level.

A variety of methodologies has been employed to analyze and measure carbon productivity. As recalled by Bai et al. (2019) [17], the Malmquist Productivity Index (MPI) [18] has been extensively employed to assess total factor carbon productivity with its decomposition into efficiency change (catching up to the best practice) and technological change (shifts in the production frontier), providing insights into the key factors that drive carbon productivity growth. Wei et al. (2025) [19] proposed using the Malmquist-Leuenberger index to measure carbon productivity, which extends the MPI by incorporating environmental undesirable outputs through a non-parametric directional distance function. Additionally, the Stochastic Frontier Analysis model [20] has emerged as important tools for evaluating carbon productivity. Researchers indicate that SFA quantifies the maximum potential output attainable at a given level of carbon input by estimating a parametric production frontier that incorporates carbon emissions and decomposing the deviation from this frontier into two components: managerial inefficiency and random noise, providing a robust statistical measure of carbon efficiency [21,22]. Recent studies have also increasingly focused on the evolutionary trends, determinants, and mechanisms behind carbon productivity growth, as well as its heterogeneity across industries and regions. In brief, a consensus in the literature suggests that while carbon productivity has demonstrated a steady upward trend in many regions, significant disparities persist across different sectors and geographic areas [23,24]. To achieve the twin objectives of economic growth and improved carbon productivity, scholars have identified the necessity of policy support [25,26], industrial structure optimization [27,28], technological innovation [19], and efficient resource allocation [29].

2.2. The Impact of Digital Economy on Low-Carbon Development

Existing studies on the relationship between the digital economy and carbon emission can be recalled with 3 points of view:

(1) The Synergy Between the Digital Economy and Low-Carbon Development.

Extensive research has well-established a positive correlation between the development of the digital economy and the achievement of carbon reduction goals, primarily through technological advancements and structural transformation. However, some studies highlight the potential adverse effects of the “Jevons’ paradox”, where inefficiency gains driven by digital technologies are offset by increased consumption, ultimately reducing carbon productivity. On one hand, the rapid expansion of digital infrastructure has led to a significant rise in global energy demand, thereby exacerbating carbon emissions [17]. On the other hand, research suggests that in resource-intensive regions, a non-linear, U-shaped relationship is observed between the level of digital transformation and carbon productivity [30]. In the early phase of digital transformation, the introduction of new technologies and industrial adjustments increases resource and energy consumption, temporarily hindering carbon productivity improvements [24,31]. Furthermore, the impact of the digital economy on carbon productivity exhibits significant regional heterogeneity, which can be attributed to disparities in economic development levels, energy resource endowments, and technological innovation capabilities [32,33].

(2) Regional and Industry-Level Analyses.

Yao et al. (2022) [33] emphasized that China’s digital economy enhances carbon productivity in eastern provinces, urban clusters, areas not reliant on natural resources. While other scholars have explored the impact of technological innovation on carbon productivity within particular sectors, such as China’s industrial sector [6], manufacturing [21], Australia’s construction industry [34], and the global meat export industry [35].

(3) Mechanisms and Pathways of Influence.

Meng and Niu (2012) [36] proposed that the digital economy influences carbon productivity is mediated by two key channels: promoting technological advancement and optimizing industrial structures. Furthermore, these authors observed that such influences exhibit distinct spatial heterogeneity and spillover effects. Zhao et al. (2022) [24] validated that the positive influence of the digital economy on carbon productivity is channeled through three key pathways: advancements in technology, reductions in energy intensity, and gains in urban productivity. Other studies have explored more specific mechanisms, such as the effects of digital finance and digital service trade on regional carbon productivity [37,38].

3. Theoretical Analysis and Research Hypotheses

3.1. The Spatial Impact of Digital Economy Development on Carbon Productivity

It has been mentioned that digital economy accelerates the flow of production factors, overcomes traditional spatial and temporal limitations due to its decentralized, mobile, and shared nature, as well as its strong externalities [39]. Scholars have explored the various pathways by which the advancement of the digital economy influences carbon productivity, including policy implementation, technological innovation, industrial chain optimization, and energy utilization.

Moyer and Hughes (2012) [40] highlighted that the digital economy is capable of transforming traditional resource-intensive growth models, mitigates dependence on natural resources, reduces environmental pollution, and promotes energy conservation and low-carbon development. Han et al. (2022) [41] argued that the role of the digital economy in driving total factor carbon productivity growth is constrained by technology accumulation, and the driving effect is non-linear considering the moderating effect of technological accumulation. However, the spatial mechanisms through which the digital economy influences carbon productivity are not well understood, with empirical evidence in particular remaining limited.

Our study posits that the digital economy, powered by technologies such as big data and AI, drives the spatial clustering of green sectors like renewable energy and smart manufacturing [42], which is instrumental in accelerating the transition of local industries to a low-carbon paradigm. Moreover, the digital economy enhances the spatial allocation efficiency of production factors such as labor, capital, and technology [43], achieving green emission reduction effects by minimizing resource mismatches and waste. Additionally, the deployment of integrated data platforms enables governments and enterprises to identify pollution sources, track carbon footprints, and implement targeted interventions, thereby improving environmental governance efficiency and boosting carbon productivity. Based on the above, our study proposes the following hypothesis:

Hypothesis 1:

Digital economy development has a significant positive spatial impact on carbon productivity.

New economic geography theory posits that the spatial clustering of economic activities facilitates knowledge diffusion, resource sharing, and improved factor matching, thereby enhancing productivity in surrounding regions. As regional economic interconnections deepen and environmental concerns gain increasing attention, researchers are now increasingly exploring the geographic variations in how the digital economy impacts carbon productivity.

Our study aims to verify the spatial spillover effects between the digital economy and carbon productivity, which can be realized through the following mechanisms: First, the advancement of the digital economy is accompanied by significant knowledge spillovers and technological diffusion [10]. When a region achieves significant progress in the digital economy, its green technological innovations, advanced management practices, and heightened environmental awareness can spill over to neighboring or related regions through channels such as industrial linkages, talent mobility, and information networks.

In addition, the agglomeration dynamics of the digital economy stimulate local green industrial development while simultaneously creating positive demonstration effects for surrounding regions. This may further integrate neighboring regions into low-carbon industrial clusters, thereby enhancing their carbon productivity [27]. Drawing upon these findings, our study proposes the second hypothesis:

Hypothesis 2:

Digital economy development has spatial spillover effects on carbon productivity.

3.2. The Moderating Effect of Industrial Structure Transformation and Upgrading

Achieving carbon reduction hinges on leveraging both technological innovation and industrial upgrading has become a widely recognized and accepted strategy. In recent years, a broad consensus has emerged that achieving significant carbon reduction hinges on leveraging both technological innovation and industrial upgrading. Existing literature suggests that industrial structure upgrading exerts complex and dynamic influences on the relationship between the digital economy and carbon productivity.

On one hand, the application and diffusion of digital technologies can effectively reduce carbon emissions by increasing R&D investment, adjusting industrial structures, and optimizing resource allocation [25,44]. These mechanisms contribute to optimizing energy consumption patterns and promoting cleaner and more efficient industrial practices. Conversely, a debate persists regarding the effect of industrial structural transformation on carbon productivity is not universally positive and may even have adverse effects in certain contexts. For instance, Feng and Wu (2022) [45] states while industrial structural optimization suppresses national carbon emissions, industrial structural rationalization does not exhibit significant effects. Similarly, Li et al. (2019) [46] highlighted the carbon reduction effects of manufacturing structural transformation vary across stages of industrialization. The positive impact of a rising industrial share on emission reductions can be undermined by issues like persistent resource dependency or frictions in the processes of structural optimization and industrial upgrading. Furthermore, multiple studies emphasize the significant spatial heterogeneity in the carbon reduction effects driven by digital technology development and industrial structural adjustment [47,48].

Building on these insights, the present research investigates the moderating role of industrial structure transformation from two key dimensions: industrial structure rationalization and industrial structure advancement. Both dimensions capture both the internal efficiency and external evolution of the industrial system, allowing for a more nuanced understanding of how structural transformation interacts with digital economy development to affect carbon productivity. Accordingly, we propose the following hypothesis:

Hypothesis 3:

Industrial structure transformation and upgrading play a moderating role in the relationship between digital economy development and carbon productivity.

4. Models, Variables, and Data

4.1. Exploratory Spatial Data Analysis (ESDA)

ESDA involves a set of spatial statistical methods designed to visualize and analyze the spatial distribution characteristics of data [49]. By detecting patterns of spatial clustering and spatial dependence, ESDA provides an understanding of spatial interaction mechanisms underlying the regional distribution patterns and dynamic transition trends of carbon productivity across Chinese provinces during the observation period. Furthermore, ESDA helps to determine whether significant spatial clustering effects exist in the distribution of carbon productivity [50].

4.1.1. Kernel Density Estimation

As a non-parametric approach, Kernel Density Estimation (KDE) constructs an estimate of a variable’s probability density function based on a chosen kernel function [51]. Unlike parametric approaches, KDE does not assume a specific functional form, which allows it to flexibly capture the underlying spatial probability distribution of sample data. The primary advantage of KDE lies in its ability to clearly reveal n the dependence, while maintaining high robustness and adaptability to data with complex distributions. The estimation method is expressed as shown in Equation (1), where n represents the number of observed samples, h denotes the bandwidth of the function, x₁, x₂, …… x_i are independently distributed observed samples, and K (x) is the kernel function (in our study, the Gaussian kernel density function is selected, as shown in Equation (2):

$$f(x)={\displaystyle \frac{1}{nh}}{\displaystyle \sum _{i=1}^{n}K\left(\frac{x-x_i}{h}\right)}$$

(1)

$$K(x)={\displaystyle \frac{1}{\sqrt{2\pi }}}\exp (-{\displaystyle \frac{x^2}{2}})$$

(2)

4.1.2. Spatial Markov Matrix Approach

The traditional Markov matrix approach serves as a tool for analyzing stochastic systems that operate with discrete time steps and states [52]. By discretizing data into m categories and constructing a m order transition probability matrix, the model explores the probability of a random variable transitioning from one state at time t to another state at time t + 1. Specifically, the probability of a random variable x transitioning from state i at time t to state j at time t + 1 is expressed as:

$$P_{ij}(x_t=i\left|x_{t+1}=j\right.)=N_{ij}/N_i$$

(3)

In the formula, N_ij represents the frequency of transitions from state i to state j during the observation period, and N_i denotes the total frequency of state i. The transition probability P_ij depends on the previous state. If the current state is the same as the previous state, it is considered stable. An upward transition indicates an improvement in state, while a downward transition reflects a decline. Additionally, state changes may involve transitions that skip adjacent categories.

The Spatial Markov matrix incorporates spatial concepts by combining spatial lags with the traditional Markov matrix, accounting for the influence of different spatial regions on the Markov transition matrix. Specifically, the traditional m -order matrix is decomposed into m separate m*m matrices, where the spatial lag values are calculated as the spatially weighted average of the attributes within the spatial domain. The specific calculation method is as follows:

$$P_{ij,t+1}(m)=P_{ij,t}(m)\cdot W_{ij}\cdot M$$

(4)

In the formula, P_ij,t(m) represents the probability of a spatial state transitioning from i to j under the condition of spatial lag matrix. W_ij denotes a spatial lag matrix, which is defined as an adjacency matrix—taking a value of 1 if two regions are adjacent [nearest neighbors] and 0 otherwise. M represents the m-order transition matrix.

4.1.3. Global Spatial Autocorrelation Analysis

The Global Moran’s I index (as recalled in Equation (5)) is primarily used to test whether an indicator exhibits spatial correlation:

$$Moran’s I={\displaystyle \frac{n{\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^n{W}_{ij}\left(Y_i-\overline{Y}\right)\left(Y_j-\overline{Y}\right)}}}{{\displaystyle \sum _{i=1}^n\left(Y_i-\overline{Y}\right){\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^n{W}_{ij}}}}}}$$

(5)

where W_ij denotes the spatial weight matrix. To comprehensively evaluate the spatial and economic impacts of digital economy on carbon productivity, we incorporated the spatial weight matrix W which is constructed by integrating geographic distance and economic development levels. Specifically, this matrix is calculated based on the inverse of the standardized per capita GDP differences and the inverse of geographic distances between provinces during the 2011–2022 period. Y_i represents the observed value of individual i, and n denotes the total number of individuals. The value of Moran’s I ranges between (−1, 1). A positive Moran’s I value indicates a strong positive spatial correlation of the indicator, while a negative Moran’s I value suggests a significant negative spatial correlation.

4.2. Spatial Regression Model

To explore the impact of varying levels of digital economy development on carbon productivity and the potential spatial effects on both local and neighboring regions, our study employs spatial econometric models. In our study, the Spatial Durbin Model is initially adopted (as in Equation (6)), where TFCP_it represents the “total factor carbon productivity” level of region i in year t (Wan et al., 2023), and DED_it denotes the level of digital economy development. To account for potential non-linear effects of digital economy development, a DED²_it is included [53,54].

$$\begin{array}{l}TFC{P}_{it}={\alpha }_0+{\alpha }_{1}DE{D}_{it}+{\alpha }_{2}DE{D}_{it}^2+{\alpha }_3{X}_{it}+{\rho }_0{\displaystyle \sum _{j=1}^{n}WTFC{P}_{jt}+}\\ {\rho }_1{\displaystyle \sum _{j=1}^{n}WDE{D}_{jt}+{\rho }_2{\displaystyle \sum _{j=1}^{n}WDE{D}_{jt}^2+}}{\rho }_3{\displaystyle \sum _{j=1}^{n}W{X}_{jt}+}{u}_t+{\lambda }_i+{\epsilon }_{it}\end{array}$$

(6)

X_it represents control variables influencing carbon productivity, while α_1–3 are the coefficients of the carbon productivity from the nearest neighboring regions, and ρ_1–3 represent the spatial spillover effects of explanatory variables from neighboring regions on the local region; W denotes the spatial weight matrix; u_t, λ_i, ε_it denote time effects, individual effects, and random error terms, respectively. When ρ_1–3 = 0, it indicates that local carbon productivity is influenced by the spatial lag effects; thereby the model becomes a Spatial Autoregressive Model, as in Equation (7):

$$TFC{P}_{it}={\alpha }_0+{\alpha }_{1}DE{D}_{it}+{\alpha }_{2}DE{D}_{it}^2+{\alpha }_3{X}_{it}+{\rho }_0{\displaystyle \sum _{j=1}^{n}WTFC{P}_{jt}+{\epsilon }_{it}}$$

(7)

Conversely, if the error term of local carbon productivity is influenced by changes in the independent variables of neighboring areas, the model is equivalent to a Spatial Error Model, as in Equation (8).

$$TFC{P}_{it}={\alpha }_0+{\alpha }_{1}DE{D}_{it}+{\alpha }_{2}DE{D}_{it}^2+{\alpha }_3{X}_{it}+{\mu }_i+{\lambda }_t+v_{it},v_{it}=\gamma W{v}_t+{\epsilon }_{it}$$

(8)

To comprehensively evaluate the spatial and economic impacts of digital economy on carbon productivity, we incorporated a spatial weight matrix W which is constructed by integrating geographic distance and economic development levels. Specifically, this matrix is calculated based on the inverse of the standardized per capita GDP differences and the inverse of geographic distances between provinces during the 2011–2022 period. γ represents the spatial autocorrelation coefficient and Wv_t stands for the spatial lag of the error term.

4.3. Variable Settings and Data Sources

4.3.1. Dependent Variable

The dependent variable in our study is the total factor carbon productivity (TFCP). TFCP focuses on the economic benefits generated per unit of carbon emission [13,17,55]. While this method is simple and easy to measure, it has limitations such as narrow evaluation criteria and the neglect of other important influencing factors. Recent studies have increasingly adopted a total-factor approach to measure carbon productivity. This method incorporates economic and energy-related factors closely associated with carbon emissions and treats carbon emissions as an undesirable output, providing a more comprehensive assessment of carbon productivity. This approach offers a more comprehensive and policy-relevant measure by accounting for substitution effects between factors and the opportunity cost of emissions reduction.

Drawing on the work of relevant scholars, our study employs an undesirable-output super-efficiency Slacks-Based Measure (SBM) model to calculate total factor carbon productivity of China. The SBM model incorporates non-radial features to directly handle input and output slacks, thus providing a more accurate and comprehensive efficiency evaluation [56]. Moreover, our model incorporates carbon emissions into the production framework as an undesirable output to effectively capture the trade-off between economic growth and environmental performance. The approach has been widely adopted for measuring green total-factor productivity in environmental efficiency studies [44,57]. The specific calculation method is as follows:

$$\begin{array}{l}\min \theta ={\displaystyle \frac{1+\frac{1}{m}{\displaystyle \sum _{i=1}^m{s}_i^{-}}/x_{ik}}{1-\frac{1}{s}{\displaystyle \sum _{r=1}^s{s}_r^{+}}/y_{rk}}}\\ s.t.\left\{\begin{array}{l}{\displaystyle \sum _{j=1,j\ne k}{x}_{ij}{\lambda }_j-s_i^{-}\le x_{ik}(i=1,2,\cdots ,m)}\\ {\displaystyle \sum _{j=1,j\ne k}{y}_{rj}{\lambda }_j+s_r^{+}\ge y_{rk}(i=1,2,\cdots ,m)}\\ {\lambda }_j\ge 0,j=1,2,\cdots ,n(j\ne k),s_i^{-}\ge 0,s_r^{+}\ge 0\end{array}\right.\end{array}$$

(9)

In this formula, θ denotes the target efficiency value, with x and y representing input and output variables, respectively. And s_i⁻ and s_r⁺ represent the slack variables of output and input, respectively. The input indicators in our study include labor input, capital input, and energy input. The desirable outputs are represented by regional GDP (billion yuan) and local general public budget revenue (billion yuan), reflecting the level of regional economic development and fiscal revenue growth. All relevant indicators are deflated to the base year 2000. The undesirable output is measured using regional carbon dioxide emissions data, calculated based on the carbon content and CO₂ emission factors for various fuel types provided by the Intergovernmental Panel on Climate Change (IPCC, 2019) (as shown in Equation (10)):

$$C{O}_2={\displaystyle {\sum }_{i=1}^{14}C{O}_{2,i}={\displaystyle {\sum }_{i=1}^{14}{E}_i}\cdot NC{V}_i\cdot C{C}_i}\cdot CO{F}_i\cdot (44/12)$$

(10)

In this formula, CO₂ represents the estimated carbon dioxide emissions; subscript i represents each of the 14 common energy types.; E_i represents the combustion consumption of each energy type; NCV_i is the average net calorific value of each energy type; CC_i is the carbon content of each energy type; and COF_i is the carbon oxidation factor for each energy type. The factor 44/12 represents the molecular weight ratio of carbon dioxide to carbon.

4.3.2. Explanatory Variable

The core explanatory variable in our study is the digital economy development Index. Drawing on the relevant research [58,59,60], and data availability, our study constructs a three-level indicator system based on three dimensions: infrastructure, industrial application, and innovation environment (as shown in

Table 1. Digital Economy Development Indicators.

Fundamentals	Primary Indicators	Secondary Indicators	Unit	Weight Coefficient
Digital Infrastructure	Internet infrastructure construction	Mobile Telephone Penetration Rate	subscriptions per 100 inhabitants	1.80%
		Optical Fiber Cable Density	fiber-km/104 km2	7.21%
		Base Station Density	units/km2	8.13%
		Internet Broadband Access Port Density	ports/km2	9.42%
Industry Integration	Digital industrialization	per Capita Software Revenue	CNY/capita	10.67%
		The proportion of employed persons in the ICT industry to total urban employment.	%	5.97%
		per Capita Telecom Service Volume	CNY/capita	6.46%
		Digital Inclusive Finance Index	/	1.52%
	Industrial digitization	Enterprises with websites per 100 establishments	Websites/100 est.	0.46%
		Percentage of Enterprises with E-commerce Transactions	%	1.70%
		E-commerce sales	100 million yuan	7.10%
		Number of Internet domain names	10 thousand units	7.60%
Innovation Capacity	Innovation input	Intramural Expenditure on R&D	10 thousand yuan	5.93%
		Full-Time Equivalent (FTE) Personnel in R&D	person-year	5.61%
	Innovation output	Valid Invention Patents of Above-Scale Industrial Enterprises	item	10.00%
		Total Transaction Value of Technology Contracts	10 thousand yuan	10.36%

). The index is constructed using an improved entropy method, with the formula drawing on the work of Du and Wang (2024) [61].

4.3.3. Moderating Variable

The degree of industrial structure transformation and upgrading serves as the moderating variable in our study. Drawing on the perspectives of scholars [62,63,64], our study uses industrial structure rationalization (ISR) and industrial structure advancement (ISA) to calculate the degree of moderating variable. The industrial structure rationalization primarily reflects the quality of industrial agglomeration and the efficiency of resource utilization in industrial development. It represents the degree of balanced allocation and coordinated development among different industries. Our study draws on the approach of Ausloos and Miśkiewicz (2010) [65], employing the Theil index to measure ISR, as shown in Equation (11):

$$TL={\displaystyle \sum _{i=1}^n(\frac{Y_i}{Y})}\ln ({\displaystyle \frac{Y_i}{L_i}}/{\displaystyle \frac{Y}{L}})$$

(11)

In the formula, i takes values from 1 to 3, representing the primary, secondary, and tertiary industries of China. Y_i denotes the output value of industry i, L_i represents the number of employees in that industry, Y_i/Y reflects the industrial structure of the region, and Y/L represents labor productivity.

The measurement of industrial structure advancement is based on the Petty-Clark theorem, which emphasizes that as socio-economic development advances, industries transition progressively from the primary sector to the secondary sector and then to the tertiary sector [66]. Accordingly, our study draws on the research of Sánchez-Bayón (2023) and Zhang et al. (2024) [8,67], employing the ratio of the tertiary sector to the secondary sector to assess the trend of industrial structure.

4.3.4. Control Variables

Based on a review of existing literature and considering data availability [68,69,70], the following control variables are selected:

(1) Urbanization Level (URB): Represented by the proportion of the urban population to the total local population.

(2) Labor Force Quality (LAB): Represented by share of the employed population with a college degree or higher.

(3) Economic Development Level (ECO): Calculated as the logarithm of per capita GDP.

(4) Level of Openness (OPEN): defined as the ratio of total trade volume (imports plus exports) to regional GDP.

(5) Energy Structure (ES): Measured as the share of coal in total energy consumption.

5. Empirical Results Analysis

5.1. Data Sources, Descriptive Statistics and Correlation Analysis

Considering the significant lack of data for certain digital economy development indicators prior to 2010, our study conducts empirical research based on data from 30 Chinese provinces during the period 2011–2022 (excluding Tibet, Hong Kong, Macau, and Taiwan due to substantial data gaps). The primary data sources include the China Statistical Yearbook, China City Statistical Yearbook, China Energy Statistical Yearbook, and provincial statistical yearbooks. Missing values were supplemented using linear interpolation.

The descriptive statistics of the relevant variables are presented in

Table 2. Descriptive Statistics of Variables.

Variable Name (Unit)	Notation	Mean	Median	SD	Min	Max
Total Factor Carbon Productivity	TFCP	0.285	0.232	0.184	0.130	1.243
Digital Economy Development Index	DED	0.173	0.112	0.169	0.0180	0.737
Industrial Structure Rationalization	ISR	0.161	0.145	0.104	0.00600	0.498
Industrial Structure Advancement	ISA	1.266	1.112	0.722	0.518	5.297
Urbanization Level	URB	0.600	0.587	0.122	0.350	0.938
Labor Force Quality	LAB	0.021	0.020	0.006	0.008	0.044
Economic Development Level	ECO	10.872	10.835	0.461	9.682	12.161
Level of Openness	OPEN	0.272	0.146	0.281	0.00800	1.464
Energy Structure	ES	0.371	0.382	0.149	0.00600	0.687

. The VIF for the variables has a mean value of 4.48, indicating that multicollinearity is not a concern among the variables, the data values are deemed reasonable.

To mitigate the potential influence of outliers on the empirical results, our study first conduct a Pearson’s correlation analysis of all variables used in the model (as shown in

Table 3. Variable Correlation Analysis.

Variable	TFCP	DED	ECO	OPEN	URB	ES	LAB	ISR
DED	0.773 ***
ECO	0.755 ***	0.856 ***
OPEN	0.664 ***	0.454 ***	0.582 ***
URB	0.766 ***	0.746 ***	0.866 ***	0.662 ***
ES	−0.632 ***	−0.720 ***	−0.661 ***	−0.552 ***	−0.616 ***
LAB	0.322 ***	0.432 ***	0.532 ***	0.317 ***	0.608 ***	−0.274 ***
ISR	−0.540 ***	−0.609 ***	−0.698 ***	−0.578 ***	−0.648 ***	0.577 ***	−0.389 ***
ISA	0.737 ***	0.762 ***	0.525 ***	0.359 ***	0.548 ***	−0.642 ***	0.321 ***	−0.476 ***

*** p < 0.01.

). The digital economy development Index (DED) demonstrates a significant 0.773 correlation coefficient with total factor carbon productivity (TFCP), passing the p < 0.01 significance test, indicating its potential to enhancetotal factor carbon productivity. ISR and ISA exhibit correlations of −0.540 and 0.737 with total factor carbon productivity, indicating their possible moderating effects on the TFCP-DED relationship.

5.2. Spatiotemporal Trends Analysis

Our study employs the undesirable-output global super-efficiency SBM model to evaluate the carbon productivity of 30 Chinese provinces over the period 2011–2022. Based on the calculated efficiency values, regional distribution maps of carbon productivity for 2011 and 2022 were drawn according to quartiles (Figure 1). Figure 1 shows that regions with high carbon productivity efficiency (efficiency values above 0.6) were absent in 2011, but by 2022, Beijing and Shanghai had emerged as high-efficiency regions. Regions with medium-high efficiency values (0.4–0.6) were concentrated in the three developed coastal provinces of Zhejiang, Jiangsu, and Guangdong, maintaining their leading positions nationwide from 2011 to 2022. The number of third-tier regions (efficiency values of 0.2–0.4) increased significantly during the observation period, rising from 9 regions in 2011 to 19 regions in 2022. Conversely, the number of low-efficiency regions (efficiency values of 0.0–0.2) decreased significantly over the same period.

The three-dimensional kernel density map of carbon productivity (Figure 2) further corroborates two evolutionary trends in national carbon productivity. First, the primary peak shows a gradual rightward shift, confirming the conclusion from Figure 1 that carbon productivity has been steadily improving. Second, since 2014, a secondary peak has emerged on the right-hand side of the primary peak, with an increasing gap between the two peaks. This indicates that several regions have experienced significant improvements in carbon productivity, leading to the emergence of a “head divergence” effect.

The trends observed in Figure 1 and Figure 2 confirm that China’s carbon productivity has been improving overall, transitioning from being dominated by low-efficiency regions to being primarily composed of medium- and low-efficiency regions. However, it is important to acknowledge that China’s aggregate carbon productivity remains at a comparatively modest level. Additionally, the eastern coastal regions exhibit significant development advantages compared to the central and western regions, with a trend of increasing regional disparity. The northeastern and some underdeveloped northwestern regions face particularly severe challenges in carbon emission management.

The observed disparities are attributed to differences in the stages of industrialization across regions, as well as variations in local economic and technological development levels and the degree policy priority that local governments assign to environmental protection. The eastern regions benefit from abundant resources such as capital, technology, and talent, providing more favorable conditions for transitioning their economic development models. By optimizing economic and industrial structures, these regions are better equipped to balance economic growth with resource and environmental constraints, demonstrating stronger regional governance capabilities in green development and ecological civilization construction.

5.3. Markov Transition Trend Prediction

To investigate the long-term dynamics of regional carbon productivity, our study first employs a traditional Markov matrix to predict and analyze regional carbon productivity. Using the quartile method, regional carbon productivity is categorized into four levels: low, medium-low, medium-high, and high. Based on lagged data from the previous period (time t), the Markov transition probability matrix for carbon productivity (time t + 1) is calculated, as shown in

Table 4. Traditional Markov Matrix of Carbon Productivity.

t/t + 1	Low	Medium-Low	Medium-High	High
Low	0.8372	0.1512	0.0116	0
Medium-Low	0.0824	0.7529	0.1529	0.0118
Medium-High	0	0.0250	0.9000	0.0750
High	0	0	0	1

.

The results indicate that the values along the main diagonal of the matrix are significantly higher than those in the off-diagonal regions, suggesting that regional carbon productivity exhibits high stability, with the highest probability of maintaining its current state over time. Among the off-diagonal regions, the probabilities of transitioning from medium-low efficiency to high efficiency (15.29%) and from medium-high efficiency to high efficiency (7.5%) are notably higher than the probabilities of transitioning to lower levels (8.24% and 2.5%, respectively), indicating that China’s carbon productivity is on a stable upward trajectory, with an optimistic overall trend of improvement.

Given the spatial agglomeration effects of carbon productivity, neighboring regions’ carbon productivity may influence local productivity. To account for this, the study further incorporates a spatial Markov matrix model to analyze the evolution of carbon productivity (

Table 5. Spatial Markov Matrix of Carbon Productivity.

Neighboring Level	t/t + 1	Low	Medium-Low	Medium-High	High
Low	Low	0.9375	0.0625	0	0
	Medium-Low	0.0769	0.9231	0	0
	Medium-High	0	0	1	0
	High	0	0	0	1
Neighboring level	t/t + 1	Low	Medium-Low	Medium-High	High
Medium-Low	Low	0.8235	0.1569	0.0303	0
	Medium-Low	0.0303	0.7179	0.1795	0.0256
	Medium-High	0	0.0417	0.9167	0.0417
	High	0	0	0	1
Neighboring level	t/t + 1	Low	Medium-Low	Medium-High	High
Medium-High	Low	0.6667	0.3333	0	0
	Medium-Low	0.0938	0.0938	0.1875	0
	Medium-High	0	0.0294	0.9412	0.0294
	High	0	0	0	1
Neighboring level	t/t + 1	Low	Medium-Low	Medium-High	High
High	Low	1	0	0	0
	Medium-Low	0	1	0	0
	Medium-High	0	0	0.8182	0.1818
	High	0	0	0	1

). The results show that when neighboring regions are at low, medium-low, medium-high or high levels, the probabilities along the main diagonal remain the highest, followed by the probabilities of transitioning to the next higher level. When neighboring regions are at a high level, medium-low regions are highly likely to transition to medium-high levels, indicating that while regional carbon productivity exhibits high spatial stability, it is also significantly influenced by neighboring high-efficiency regions.

Additionally, high-efficiency regions consistently maintain the most stable states across all neighboring conditions (with probabilities of 1 when neighboring regions are at low, medium-low, medium-high or high levels). Medium-high efficiency regions also demonstrate relatively high stability (with probabilities of 100%, 91.67%, 94.12%, and 81.82%, respectively, under different neighboring conditions). This suggests that, compared to low-efficiency regions, high-efficiency regions possess a stronger ability to maintain their productivity levels, validating the existence of a “club convergence” phenomenon in carbon productivity. This finding aligns with the conclusions of Han et al. (2022) [41] that regions with similar structural characteristics—such as levels of economic development, industrial composition tend to exhibit internal homogeneity, leading to foster convergence in their carbon productivity performance.

5.4. Spatial Econometric Analysis

5.4.1. Spatial Agglomeration Effects Analysis

To further validate Hypothesis 1 regarding the spatial effects of carbon productivity, our study conducts a spatial correlation test. The results indicate that the Global Moran’s I index remains at a high level of statistical significance (

Table 6. Global Moran’s I of TFCP.

Year.	2011	2012	2013	2014	2015	2016	2017	2018	2019	2020	2021	2022
Z	5.098	5.099	5.297	5.213	5.182	5.236	5.107	5.010	4.693	4.931	4.881	4.833
p-value	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
Moran’s I	0.201	0.201	0.211	0.205	0.198	0.198	0.190	0.180	0.165	0.176	0.173	0.170

), confirming the existence of significant spatial correlation in carbon productivity across China. This provides empirical support for Hypothesis 1.

5.4.2. Spatial Regression Model Specification

To determine the most appropriate econometric model for this study, we followed a stepwise test procedure. First, the Lagrange Multiplier (LM) tests for both spatial lag (LM-lag) and spatial error (LM-error) dependencies yield statistics that are significant at the 1% level, indicating that a spatial econometric approach is superior to a traditional OLS model. Then we examine the robust LM tests and show that the robust LM-error statistic is significant while the robust LM-lag statistic is not, providing preliminary evidence that the SEM might be a suitable specification. However, to ascertain whether the more general SDM is preferable to the SEM, a likelihood-ratio test is conducted and the result supports the use of the SDM. Having established the SDM as the appropriate model form, we then perform a Hausman test to choose between fixed and random effects. The test result (p < 0.001) provides decisive evidence in favor of the fixed-effects specification. Subsequently, we compare the goodness-of-fit for the SDM under three different fixed-effects settings: individual fixed, time fixed, and time-and-individual fixed. Based on the log-likelihood values and the Akaike Information Criterion (AIC), the model with time-and-individual fixed effects demonstrates the best statistical fit. Therefore, our study ultimately employs the SDM with time and individual fixed effects for the empirical analysis.

5.4.3. Empirical Analysis of the Spatial Regression Models

To further explore the impact of digital economy development on carbon productivity, our study employs SDM, SAR and SEM, respectively, for regression analysis. The empirical results (as shown in

Table 7. Impact of Digital Economy Development on Carbon Productivity.

Variable	(1)		(2)	(3)	(4)	(5)	(6)
	SDM		SAR	SEM	Direct Effects	Indirect Effects	Total Effects
	Main	Wx
DED	−0.0790 *** (0.0107)	−0.0852 (0.0598)	−0.0709 *** (0.0105)	−0.0710 *** (0.0105)	−0.0773 *** (0.0110)	−0.0425 (0.0447)	−0.1199 *** (0.0454)
DED2	0.0071 *** (0.0006)	0.0118 *** (0.0029)	0.0059 *** (0.0005)	0.0062 *** (0.0005)	0.0069 *** (0.0006)	0.0070 *** (0.0023)	0.0138 *** (0.0024)
URB	−0.0929 ** (0.1518)	0.2113 * (0.1094)	−0.4955 *** (0.1397)	−0.5056 *** (0.1339)	−0.01344 (0.1522)	0.16043 * (0.8458)	0.14699 * (0.8446)
LAB	−0.3367 ** (0.1687)	1.0659 (0.9831)	−0.5329 *** (0.1735)	−0.49661 *** (0.1729)	−0.3719 ** (0.1681)	0.4169 (0.7647)	0.0450 (0.7548)
ECO	0.1558 *** (0.0349)	0.0833 (0.1695)	0.1876 *** (0.0340)	0.1908 *** (0.0329)	0.1551 *** (0.0344)	0.0246 (0.1358)	0.1798 * (0.1299)
OPEN	−0.0808 ** (0.0346)	−0.2123 (0.1743)	−0.0763 ** (0.0352)	−0.0776 ** (0.0340)	−0.0763 ** (0.0350)	−0.1417 (0.1285)	−0.2179 * (0.1225)
ES	−0.0898 * (0.0528)	−0.2500 (0.2273)	−0.0484 (0.0513)	−0.0546 (0.0504)	−0.0836 (0.0540)	−0.1537 (0.1726)	−0.2373 (0.1774)
R2	−0.0790 *** (0.0107)	−0.0852 (0.0598)	−0.0709 *** (0.0105)	−0.0710 *** (0.0105)	−0.0773 *** (0.0110)	−0.0425 (0.0447)	−0.1199 *** (0.0454)
Log- likelihood	755.4764		736.7537	738.6103

Notes: The numbers in parentheses are the corresponding standard errors, the asterisks ***, **, * represent 1%, 5%, 10% of significance levels, respectively.

, Columns 1–3) reveal a non-linear relationship between digital economy and carbon productivity. Specifically, the coefficient on the linear term for digital economy development is consistently negative and significant at the 1% level, whereas the coefficient on the quadratic term is positive and significant. This pattern provides strong evidence of a U-shaped curve, suggesting that while the initial stages of digitalization may inhibit carbon productivity, its environmental dividends become apparent as the digital economy matures.

These findings align with the conclusions of Li and Zhou (2024) [71], who argue that digital economy development, factors such as technological limitations, industrial environments, and energy structures lead to a significant increase in carbon emissions at the early stage. However, as the digital economy evolves to higher levels, it can significantly enhance carbon productivity by promoting technological transformation, optimizing management efficiency, and improving energy efficiency. This partially validates Hypothesis 1.

Additionally, the coefficient of the quadratic interaction term between the digital economy development indicator and the spatial weight matrix (W_x) is also significantly positive, suggesting that further advancement of digital economy development in neighboring regions generates significant positive spatial spillover effects on local carbon productivity.

Regarding the control variables, labor force quality, economic development level, and openness to foreign investment all exhibit significant positive relationships with carbon productivity. The result implies that improvements in labor quality, economic growth, and openness to foreign investment can significantly enhance carbon productivity at the current stage of development. Conversely, urbanization level shows a significant negative correlation. A plausible explanation is that urbanization drives population growth and economic expansion, which are accompanied by substantial increases in resource input and energy consumption, thereby suppressing carbon productivity. The significant negative effect of energy structure on carbon productivity highlights that the traditional energy structure has a clear adverse impact on carbon productivity. This underscores the urgent need to improve the energy structure and emission-reduction technologies.

5.4.4. Analysis of Spatial Spillover Effects

Lesage and Pace (2009) [72] pointed out that the SDM may produce biased point estimates of spatial effects. To address this, spatial decomposition based on partial derivatives is required to estimate the direct, indirect, and total effects. Accordingly, our study decomposes the spatial effects of the SDM, and the results are presented in Table 7 (Columns 4–6).

The coefficients for digital economy development exhibit a significant negative effect for the linear term and a significant positive effect for the quadratic term in both the direct and total effects. This indicates that the spatial impact of the digital economy on carbon productivity remains primarily confined to regions with close economic ties and geographic proximity. However, the spatial spillover effects on regions with greater geographic distance and significant economic disparities remain limited, providing partial support for Hypothesis 2.

Regarding the control variables, economic development level positively contributes to local carbon productivity but has limited positive effects on neighboring regions. This suggests that economic development in one region may attract social resources, talent, and capital from other regions, creating a “siphon effect” that negatively impacts the carbon productivity of surrounding areas. However, from an overall perspective, the total effect of economic development remains significantly positive, indicating that economic growth underpins the long-run transition to a low-carbon economy.

Urbanization level shows a significant negative impact on local carbon productivity. This suggests that China is still in the early stages of digital economy development, where factors such as infrastructure construction and industrial transformation driven by urbanization significantly increase local carbon emissions, consistent with the Environmental Kuznets Curve (EKC) hypothesis that environmental quality deteriorates with income growth in the early stages of economic development [73]. While the local impact of urbanization is negative, its positive spillover effects on neighboring regions are notable. This indicates that the industrial upgrading and resource allocation practices associated with urbanization have a technological diffusion and demonstration effect on surrounding areas.

The degree of openness also shows a significant negative effect with carbon productivity, indicating that the ‘pollution paradise’ effect still exists in some parts of China during the sample period. Although China has significantly improved its industrial development level in recent years through a series of industrial upgrading policies, some underdeveloped regions still undertake a large amount of energy-intensive production in foreign trade, which lowers the overall carbon productivity.

It should be noted that study shows a significant negative correlation in labor quality. One possible reason is that the employment of current China’s college graduates is mainly concentrated in non-energy-intensive industries such as services, where their carbon productivity is already at a high level. The tertiary industry, due to factors such as salary and working environment, is highly attractive to talents, leading to talent hollowing out in industrial sectors and slowing down the pace of carbon productivity improvement. The significant negative coefficient on the energy structure variable underscores the detrimental impact of a coal-dominated energy mix on carbon productivity. This underscores the urgent need to improve the energy-saving and emission-reduction technologies.

5.4.5. Analysis of Spatial Heterogeneity

In light of the significant regional disparities in technological conditions, economic development, and energy structures, our study employs two methods for heterogeneity analysis. The first method based on the regional distribution, divides the 30 provinces into three spatial dimensions—eastern, central, and western regions—to explore the spatial heterogeneity of the impact of digital economy development on carbon productivity. The second method, based on the “China Digital Economy Development Index Report (2024)” released by the Ministry of Industry and Information Technology of People’s Republic of China [74], categorizes the 30 provinces into three tiers according to their differences in digital economy development levels, exploring how variations in digital economy development affect carbon productivity. For the selection of the spatial weight matrix, our study employs a composite economic-geographic weight matrix integrated both geographic distance and economic attributes.

The empirical results (

Table 8. Heterogeneity Tests.

Variable	Baseline Regression	East	Central	West	First Tire	Second Tire	Third Tire
DED	−0.0790 *** (0.0107)	−0.1265 *** (0.0157)	−0.0508 ** (0.0238)	0.0253 ** (0.0100)	−0.0994 *** (0.0164)	−0.0137 (0.0221)	−0.0147 (0.0128)
DED2	0.0071 *** (0.0006)	0.0075 *** (0.0007)	0.0110 ** (0.0048)	0.0000 (0.0009)	0.0078 *** (0.0007)	0.0024 (0.0021)	0.0030 ** (0.0013)
W*DED	−0.0724 (0.0566)	−0.1335 * (0.0807)	0.2159 ** (0.0916)	0.0640 (0.0564)	−0.2789 *** (0.0790)	0.0838 (0.0801)	−0.0633 (0.0503)
W*DED2	0.0110 *** (0.0028)	0.0160 *** (0.0031)	−0.0294 * (0.0154)	0.0089 (0.0057)	0.0173 *** (0.0026)	0.0041 (0.0075)	0.0066 (0.0053)
Controlled Variable	YES	YES	YES	YES	YES	YES	YES
R2	0.5922	0.5973	0.6017	0.6644	0.7729	0.6819	0.4055
Log-likelihood	755.4764	283.8762	281.0313	461.7946	254.0304	409.2298	337.0064

Notes: The numbers in parentheses are the corresponding standard errors, the asterisks ***, **, and * represent 1%, 5%, and 10% of significance levels, respectively.

, Columns 2–4) reveal notable spatial differences. In the eastern and central regions, the coefficients for the linear term of digital economy development are significantly negative, while the coefficients for the quadratic term are significantly positive. However, the linear term coefficient is significantly positive in the western region, while the quadratic term coefficient is significantly negative. This finding highlights a pronounced developmental disparity that, compared to the eastern and central regions, the overall development trajectory and construction outcomes in the western region remain at a relatively low level. Consequently, the marginal effects of digital economy development are greater in the western region, giving it a stronger latecomer advantage in achieving the “dual carbon” goals. Nevertheless, due to limitations in technological conditions and infrastructure construction, the deep application of the digital economy in the western region may lead to a rapid increase in carbon emissions, thereby suppressing carbon productivity. This could result in a “high-carbon lock-in” effect, causing negative impacts on carbon productivity.

Table 8 (Columns 5–7) illustrates the heterogeneous impacts of regional disparities in digital economy development on carbon productivity growth. In the first-tier provinces, the relationship between digital economy and carbon productivity aligns with national trends, demonstrating a pronounced “U-shaped” pattern. This indicates that rapid digital expansion in these frontier regions, accompanied by massive digital infrastructure investments and substantial energy consumption, initially suppresses carbon productivity. However, after crossing the regional inflection point, advanced digital technologies begin delivering significant green dividends through optimized energy allocation, enhanced production efficiency, and smart energy management, becoming a key driver of carbon productivity improvement. These effects, however, are not fully observed in the second and third-tier provinces. In the second tier, digital economy’s carbon reduction efficacy shows significant negative correlation with carbon productivity, and its quadratic coefficient remains statistically insignificant. This is primarily due to these provinces being in a phase of rapid digital expansion, where massive investments in emerging infrastructure have not yet achieved deep green transformation of traditional energy-intensive industries, leading to a decrease of carbon productivity. The third-tier provinces exhibit lower overall digital economy development levels, as their economies remain predominantly traditional. While the carbon reduction impact is not significant here, the quadratic coefficient demonstrates notable positive effects. This is mainly due to the fact that some regions, driven by policies, have given priority to the development of digital and green industries like photovoltaic and wind power, which have substantially boosted carbon productivity in these regions.

5.4.6. Robustness Tests

Analysis Through Alternatives to the Spatial Weight Matrix

Three types of matrices are used to assess the robustness of our main findings: adjacency matrix, distance matrix, and geoeconomic weight matrix. The adjacency matrix is constructed based on whether provinces are geographically adjacent. The element w_ij equals 1 if provinces i and j share a common border, and 0 otherwise. This specification assumes spatial interactions occur exclusively between physically adjacent units. The distance matrix is constructed by row-standardizing a matrix where each element w_ij the inverse of the shortest highway distance between the provincial capitals of region i and region j. The geoeconomic weight matrix is constructed by assigning equal weights (50%) to the inverse of the per capita GDP difference and the inverse of geographic distance, both standardized, for the period 2011–2022.

The empirical results are presented in Table 9 (Columns 1–3). After introducing the adjacency matrix, distance matrix, and geoeconomic weight matrix, the coefficients for the linear term of digital economy development remain significantly negative at the 1% level, while the coefficients for the quadratic term exhibit significant positive effects. These findings are consistent with the spatial regression results presented earlier, confirming the robustness of the conclusions.

Replacing the Explanatory Variable

Our study reconstructs the digital economy indicator system using variables such as digital industrialization and industrial digitalization [75,76]. It selects variables including internet penetration rate, mobile internet user numbers, internet workforce size, per capita telecom service volume, digital inclusive finance, and government R&D expenditure ratio. The entropy method is applied to calculate the new digital economy index, replacing the original indicator. The results are shown in Table 9 (Column 4). The robustness of our main finding is affirmed, as the coefficients for the linear and quadratic terms of the digital economy retain their respective negative and positive signs and statistical significance.

Table 9. Results of Robustness Tests with Alternative Matrices.

Variable	Adjacency Matrix	Distance Matrix	Geoeconomic Weight Matrix	Variable Replacement
DED	−0.0897 *** (0.0098)	−0.0793 *** (0.0102)	−0.0773 *** (0.0115)	0.5275 ** (0.2058)
DED2	0.0071 *** (0.0004)	0.0069 *** (0.0005)	0.0066 *** (0.0006)	−0.6608 *** (0.2149)
W*DED	0.1095 *** (0.0212)	0.0984 *** (0.0230)	0.0309 (0.0290)	−1.6413 * (0.9351)
W*DED2	−0.0021 * (0.0011)	−0.0026 ** (0.0010)	−0.0000 (0.0014)	0.5335 (0.9350)
Controlled Variable	YES	YES	YES	YES
R2	0.8096	0.6198	0.7820	0.3413
Log-likelihood	794.2891	800.7231	739.7103	691.2335

Notes: The numbers in parentheses are the corresponding standard errors, the asterisks ***, **, and * represent 1%, 5%, and 10% of significance levels, respectively.

Table 9. Results of Robustness Tests with Alternative Matrices.

Variable	Adjacency Matrix	Distance Matrix	Geoeconomic Weight Matrix	Variable Replacement
DED	−0.0897 *** (0.0098)	−0.0793 *** (0.0102)	−0.0773 *** (0.0115)	0.5275 ** (0.2058)
DED2	0.0071 *** (0.0004)	0.0069 *** (0.0005)	0.0066 *** (0.0006)	−0.6608 *** (0.2149)
W*DED	0.1095 *** (0.0212)	0.0984 *** (0.0230)	0.0309 (0.0290)	−1.6413 * (0.9351)
W*DED2	−0.0021 * (0.0011)	−0.0026 ** (0.0010)	−0.0000 (0.0014)	0.5335 (0.9350)
Controlled Variable	YES	YES	YES	YES
R2	0.8096	0.6198	0.7820	0.3413
Log-likelihood	794.2891	800.7231	739.7103	691.2335

Notes: The numbers in parentheses are the corresponding standard errors, the asterisks ***, **, and * represent 1%, 5%, and 10% of significance levels, respectively.

5.4.7. Analysis of the Moderating Mechanism

To explore the moderating role of industrial structure transformation and upgrading, our study introduces three pathways based on Hypothesis 3: industrial structure rationalization, industrial structure advancement, and their combined effects (as shown in

Table 10. Results of the Moderating Mechanism.

Variable	(1)		(2)		(3)
	Main	Wx	Main	Wx	Main	Wx
DED	−0.0780 *** (0.0107)	−0.0785 (0.0615)	−0.0916 *** (0.0157)	−0.0024 (0.0824)	−0.0988 *** (0.0154)	0.0790 (0.0867)
DED2	0.0070 *** (0.0006)	0.0108 *** (0.0029)	0.0050 *** (0.0012)	0.0033 (0.0058)	0.0063 *** (0.0012)	−0.0050 (0.0064)
DED*ISR	0.1674 *** (0.0569)	0.6293 ** (0.2809)			0.1689 *** (0.0542)	−0.0138 (0.2841)
DED2*ISR	−0.0214 ** (0.0087)	−0.0981 ** (0.0470)			−0.0188 ** (0.0081)	−0.0379 (0.0453)
ISR	0.1131 (0.1003)	−0.6572 (0.4861)			0.0523 (0.0976)	0.4443 (0.4917)
DED*ISA			0.0238 *** (0.0051)	0.0081 (0.0327)	0.0200 *** (0.0051)	−0.0316 (0.0337)
DED2*ISA			−0.0008 *** (0.0003)	0.0001 (0.0019)	−0.0008 *** (0.0003)	0.0029 (0.0020)
ISA			−0.0515 ** (0.0234)	0.1616 (0.1094)	−0.0148 (0.0244)	0.1613 (0.1132)
Controlled Variable	YES		YES		YES

Notes: The numbers in parentheses are the corresponding standard errors, the asterisks *** and ** represent 1% and 5% of significance levels, respectively.

, columns 1–3).

The interaction terms between digital economy development and both industrial structure rationalization and industrial structure advancement are both found to be positive and significant at the 1% level. It demonstrates that the industrial structure and the digital economy are highly compatible at the current stage. The digital economy plays a significant role in promoting industrial structure optimization and upgrading, which in turn contributes to reducing carbon emissions, thereby validating Hypothesis 3. However, the study also reveals that the interaction terms between the quadratic term of digital economy development and the two moderating variables have negative coefficients. This suggests that numerous mechanism-related obstacles persist. If the pace of digital technology development accelerates further and becomes misaligned with the rate of industrial structure transformation, the resulting mismatch could negatively impact carbon productivity.

The rationalization of industrial structure shows a positive impact on carbon productivity, but the significance is insufficient. While industrial structure advancement exhibits a significant negative impact on carbon productivity. The results indicate that, although China’s industrial structure has been continuously optimized and the transformation has achieved notable results, the traditional manufacturing-oriented industrial structure and the coal-dominated energy structure remain critical components of social development. The existence of structural contradictions significantly hinders improvements in carbon productivity in the process of promoting industrial structure transformation and upgrading, especially in the initial stage.

6. Conclusions and Recommendations

6.1. Conclusions and Discussion

Drawing on panel data from China covering the period from 2011 to 2022, our study constructs a digital economy development index and calculates carbon productivity. Through the kernel density estimation method and Markov matrix analysis, the spatiotemporal distribution and its evolutionary trends of carbon productivity are examined. Meanwhile, based on spatial regression analysis, we explored the spatial impact of digital economy development on China’s carbon productivity and its potential moderating effects. Our research mainly reveals the following findings:

Firstly, China’s carbon productivity shows a steady upward trend, while significant regional differentiation exists. The eastern region of China, leveraging advantages in capital, technology, and talent resources, has created more favorable conditions for economic model transformation. By optimizing the economic industrial structure, these regions demonstrate stronger capabilities in green governance and ecological civilization construction, showing greater advantages in balancing economic growth with resource and environmental constraints. During the observation period, the carbon productivity in central and western China also exhibited a clear upward trend, primarily due to the effective measures taken by local governments and enterprises in recent years to reduce carbon emissions. These measures include improving energy efficiency and resource conversion rates through technological upgrades, phasing out outdated production capacities, adopting clean energy, and developing a circular economy.

Secondly, China’s carbon productivity exhibits significant regional stability and spatial aggregation. The spatial correlation test and Markov Transition Trend Prediction confirm that high-efficiency regions demonstrate stronger stability in maintaining productivity levels, validating the “club convergence” phenomenon in the development of carbon productivity. The study also shows that high-efficiency regions play a positive demonstration role in enhancing carbon productivity for surrounding areas. Therefore, by supporting high-carbon productivity regions to become sources of green technology innovation and policy innovation, and by transferring green industries and energy-saving technologies, we can actively drive the improvement of carbon productivity in surrounding medium-and low-efficiency regions.

Thirdly, the development of the digital economy has significantly boosted carbon productivity, though this relationship shows marked regional and developmental disparities. In eastern and central regions, the digital economy’s impact on carbon productivity follows a “U-shaped” trajectory, indicating that after reaching a certain economic threshold, its influence shifts from negative to positive. Conversely, western regions exhibit an “inverted U-shaped” pattern, suggesting that extensive digital adoption in these areas may trigger a “high-carbon lock-in effect,” leading to rapid carbon emission growth. Across different development stages, high-level digital economy cities demonstrate consistent “U-shaped” characteristics, while similar trends remain absent in lower-tier regions. It indicates that underdeveloped digital infrastructure, weak industrial digital transformation capabilities, and uneven new energy deployment in these areas have hindered significant improvements in carbon productivity.

Fourthly, the transformation and upgrading of industrial structure play a positive moderating role in the relationship between digital economy development and carbon productivity. Research confirms that the digital economy plays a pivotal role in promoting the optimization and upgrading of industrial structure, thereby significantly reducing carbon emissions. However, it should not be overlooked that although China’s industrial structure continues to optimize, the industrial structure dominated by traditional manufacturing and the energy structure dominated by thermal power will still persist for a long time. Structural contradictions may hinder the further improvement of carbon productivity.

6.2. Recommendations

Achieving carbon peaking and carbon neutrality entails a profound and systemic transformation that requires coordinated efforts across the entire nation. For China, as the world’s largest developing economy, advancing the “dual carbon” goals is not only crucial for achieving high-quality, green economic growth and building a modern society characterized by harmony between humans and nature but also a strategic approach to reshaping growth drivers, enhancing competitive advantages, and realizing modernization during the current period of global economic restructuring. Based on the findings of our study, the following policy recommendations are proposed:

(1) Strengthen the integration of digital and green economies through technological innovation

A region’s ability to maintain digital leadership, adapt to energy transition trends, and seize opportunities in clean energy development will determine its future economic competitiveness. On one hand, digital innovation can be leveraged to develop new renewable and clean energy sources and explore innovative energy production and consumption models. For instance, embedding carbon efficiency modules into industrial internet platforms can enable real-time monitoring and optimization of carbon emissions throughout a product’s lifecycle. On the other hand, the scope and efficiency of digital applications should be expanded in areas such as digital infrastructure, energy management, and green governance to support the stable development of a green and low-carbon economy.

(2) Implement region-specific policies to promote balanced carbon productivity development

Given the significant regional disparities in the spillover effects of the digital economy on carbon productivity, policy design should fully consider the economic foundations and technological development levels of different regions. Tailored pathways for enhancing carbon productivity should be constructed to align with the digitalization stages of each region. For the eastern region, as the current leader in carbon productivity, efforts should focus on transitioning the digital economy from large-scale expansion to technological deepening by establishing green innovation centers for digital technologies to overcome the inflection point of the U-shaped curve. Meanwhile, developed regions should strengthen collaboration with neighboring underdeveloped areas, facilitating the flow of advanced technologies, data resources, and talent across regions. For the central and western regions, priority should be given to improving digital infrastructure to reduce the costs of low-carbon transitions for enterprises, seizing opportunities from industrial restructuring and energy system reforms to achieve differentiated and sustainable development while avoiding the diminishing returns of the post-U-shaped curve.

(3) Optimize resource allocation to facilitate industrial structure transformation and upgrading

Empirical evidence from our study indicates that the carbon reduction effects of the digital economy depend on the synergy between digital development and industrial structure upgrading. To fully leverage the digital economy in driving industrial transformation, it is essential to enhance policy support and financial investment in green and low-carbon industries, guiding social capital to prioritize sectors such as renewable energy, smart agriculture, and other low-carbon service fields. Simultaneously, efforts should be made to accelerate the digital transformation of traditional industries by introducing intelligent manufacturing to optimize production processes, fostering a clean, efficient, and low-carbon energy consumption structure. Additionally, building an intelligent ecological system to modernize traditional industrial forms will help establish a digitalized and low-carbon industrial structure.