Introduction

Physical industries are the main component of a national economy and are also an important source of energy consumption and carbon emissions. Currently, China’s physical industries are mainly responsible for processing, assembling, and other low-end links in the global value chain. They are characterized by high resource investment, energy consumption, and pollution emissions. Under increasingly tight resource and environmental constraints, it is theoretically and practically important to explore the low-carbon development of physical industries to achieve the two strategic goals of “manufacturing power” and “double carbon”.

At the same time, digital technology, is a knowledge-intensive “clean” production factor and is widely used in the production and operation of regional industries and enterprises. It has played an important role in reducing costs, improving efficiency, promoting innovation, and improving performance (Eichhorst et al., 2017). Digital technology has strong “permeability” characteristics that can integrate with local industries to change the economic operation mode and provide digital empowerment to surrounding areas (Bresnahan and Trajtenberg, 1995; Cai and Chen, 2019). However, there are significant regional differences in industrial structure, infrastructure, and other aspects throughout China that affect these regional differences in the development of the digital economy (Wang et al., 2022). Therefore, it is very important to study the spatial impact mechanism and effect of the digital economy on the low-carbon development of regional industries.

Currently, research on the digital economy and industrial development is increasing; it mainly focuses on the following three aspects: (1) In the study of the digital economy and total factor productivity, one view holds that digital technology is a strong driving force that improves the production efficiency of physical industrial enterprises, while the other view holds that relying too much on digital technology is not conducive to improving total factor productivity (Brynjolfsson et al., 2018; Kromann et al., 2020). (2) The research on digital technology and the global value chain indicates that digital technology enhances the degree of Chinese enterprises’ participation in the division of labor in the global value chain and also improves the status of the division of labor in the global value chain (Lv et al., 2020). (3) Research on digital technology and technological innovation suggests that digital empowerment promotes the technological innovation of enterprises through three channels: optimizing resource allocation, reducing costs, and improving the level of the labor force (Barrett et al., 2016; Chi et al., 2020; Guo and Zhang, 2021).

As China’s resource and environmental constraints continue to strengthen, low-carbon development of physical industries has begun to attract scholars’ attention. This research studies the impacts of environmental and ecological technology standards, global value chain embedding, institutional and technological innovation, financial factor agglomeration, and other factors on the low-carbon development of industry (Yuan, 2018; Shao et al., 2019; Nie and Zhang, 2019; Jin et al., 2022).

Improving the level of low-carbon industrial development in a region affects development in surrounding regions through the following mechanisms: (1) Coercion and accountability mechanisms. The accountability system for environmental protection assessment strengthens the assessment of government officials’ performance in energy conservation and emissions reduction, and performance assessments can promote the leading cadres (Yu et al., 2018). When a region strictly implements the concept of low-carbon development, it forms a “target effect” between provinces and cities, forcing surrounding regions to improve their low-carbon development of physical industries (Heberer and Senz, 2011). (2) Frequent “free rider” behavior. When a locality undertakes low-carbon restructuring of its physical industrial sector, this induces a “crowding-out effect” on energy-intensive enterprises. These entities may consequently migrate to regions with lax environmental oversight, subsequently amplifying the ecological contamination levels within proximate industries. The extant body of literature fails to delve into the intricate interplay between the digital economy and the low-carbon evolution of the industrial sector.

Wang and Tian (2018) conducted an empirical analysis of the spatial differentiation and influencing factors of China’s digital economy. Their findings suggest that the development of the digital economy varies across cities and regions, with a decreasing gradient from east to west. Huang et al. (2023) assert that digital infrastructure and a high level of marketization are the primary drivers behind spatial differentiation patterns and spatial spillover effects. Wang et al. (2023) empirically analyzed the effects of the digital economy on the real economy. Their spatial difference analysis indicated that the eastern region experienced a “crowding out effect,” whereas the central and western regions demonstrated a “promoting effect.”. Zou et al. (2024) discovered through in-depth spatial econometric analysis that the growth of the digital economy not only elevates the overall productivity of a region but also exerts substantial spatial spillover effects, thereby having a more pronounced influence on enhancing total factor productivity in regions with lower productivity and neighboring regions. Ding et al. (2022) utilized panel data from 30 provinces in China spanning 2010 to 2020 to investigate the spatial correlation and heterogeneity of digital new infrastructure for high-quality economic development, thereby boosting economic growth in other regions. Zheng et al. (2023) employed the spatial Durbin model to empirically analyze the heterogeneity and spillover effects of digital economy development on industrial carbon emission intensity. Their findings indicate that the digital economy not only diminishes local industrial carbon emission intensity but also exerts a noteworthy spatial spillover effect, thereby having a promotional impact on adjacent cities and regions. Chang et al. (2023) discovered that the growth of the digital economy helps to reduce the disparity in total factor productivity among different regional manufacturing industries. Furthermore, the digital economy’s spatial spillover accelerates the harmonious convergence of manufacturing productivity across various regions .

Compared with existing literature, this paper may make the following contributions: (1) By employing methods such as the Durbin model and Moran index, we have formulated and tested the theoretical framework delineating the influence of the digital economy on regional industries’ low-carbon total factor productivity. Furthermore, we have empirically examined the digital economy’s spatial spillover effects on regional industries’ low-carbon development. (2) Focusing on the spillover boundaries, we have assessed the genuine impact of the digital economy on empowering regional physical industries, delving into its underlying operational mechanisms and addressing the theoretical void in current research that has underutilized such mechanisms. (3) We have proposed the exogenous policy of “intellectual property protection” as a crucial institutional safeguard for fostering the digital economy, a proposition that bears significant practical implications for the sustainable development of low-carbon economies in other regions.

Theoretical analysis and research hypothesis

Mechanism of digital economy driving low-carbon development of industry from a spatial perspective

Digital technology has strong penetration, wide-coverage, substitution, and synergy, which affects the low-carbon development level of local industries, breaks through spatial constraints, and produces spatial spillover effects on the low-carbon development level of physical industries in other regions (Lily et al., 2017). Low-carbon industries refer to those that significantly reduce or eliminate carbon emissions throughout production and consumption, encompassing energy, transportation, construction, agriculture, manufacturing, services, and consumer products. They are defined primarily by their low energy consumption, minimal pollution, and low carbon emissions.

Mechanism of digital economy driving low-carbon development of local industry

The digital economy exerts a direct spillover effect on the low-carbon development of local industries through the following channels: (1) Optimizing the element structure. The application of digital technology replaces the physical elements and improves the cohesion and coordination between the elements (Zhang et al., 2024). (2) Improving the efficiency of resource allocation. The deep integration of digital technology with R&D, production, marketing, branding, and other links helps to improve the allocation efficiency of resources in all links of the industrial chain. (3) Reducing costs. Big data analysis reduces the search and matching cost of transactions, the Internet of Things greatly shortens the switching time between processes, and digital trade reduces logistics and marketing costs by breaking through the constraints of time and space. (4) Technological innovation. Through simulation experiments, digital technology helps to improve the probability of success in research and development, customizes personalized innovation schemes according to consumer needs, and reduces resource consumption (Ketteni, 2009). (5) Scale expansion. China’s physical industries mainly require high investment, high consumption, and high emissions. The increase in capacity brought about by digitalization further aggravates resource consumption. The expansion of the digital economy and the continuous improvement in the industry for low-carbon development demonstrates that the digital economy has improved the low-carbon development of local industries.

Therefore, this paper proposes research hypothesis 1: the digital economy promotes the low-carbon development of local physical industries.

Spatial spillover mechanism of the digital economy driving low-carbon development of local industry

The path and direction of the spatial spillover mechanism for low-carbon development of physical industries driven by the digital economy are refined from the local area, adjacent area, and interactions between regions. (1) Technology spillover from the digital economy. In the process of promoting deep integration of industry and digital technology, the region voluntarily or involuntarily spills over the digital economy, enabling its effect on adjacent areas, thus affecting the resource input and energy consumption of industry in the adjacent areas. (2) “Imitation effect” of adjacent areas. Promotion of the digital economy to the low-carbon development of industry in this region stimulates neighboring regions to learn and imitate, actively promote the integration of digital technology into industry, and promote the low-carbon development of industry. (3) Inter-regional spatial “interaction effect”. Development of the digital economy and the low-carbon development of physical industries in one region inevitably causes strategic interactions in other regions. This competitive situation helps each region to enhance the spatial spillover effect of the digital economy.

The digital economy facilitates the rapid dissemination of information, innovation, and best practices, thereby creating a network environment with the potential for spatial spillovers in low-carbon sectors. This can be attributed to several factors: (1) The digital economy promotes rapid exchange of information and knowledge across geographical boundaries, achieving global cooperation and networking, which can overcome geographical barriers and trigger technological diffusion. (2) Digital technology can collect and analyze a large amount of data, often helping low-carbon enterprises to more easily enter the global market. As these businesses expand, their positive impact may radiate to other regions, generating spatial spillover effects. (3) The emergence of intelligent platforms in the digital economy provides decision-makers with a means to learn from each other’s experiences and collaborate in formulating effective policies for low-carbon sectors. As successful policies are implemented in one region, other regions may adopt similar methods, resulting in contagion effects. (4) The digital economy often promotes cross-departmental integration, combining the technology and practices of one department with another, which helps to facilitate the spatial spillover of low-carbon initiatives.

Therefore, this paper proposes research hypothesis 2: the digital economy promotes the low-carbon development of physical industries in adjacent areas through spatial spillover.

The impact of urban characteristics on the spatial spillover effect of low-carbon development of industries driven by the digital economy

Using three indicators of geographical location, population size, and the degree of marketization to describe urban characteristics, this research sorted out the role of urban characteristics in the low-carbon development of industries driven by the digital economy. (1) Geographical location: In areas with relatively perfect information technology infrastructure, the digital economy has stronger penetration and synergy effects on physical industries in the surrounding areas, and the spatial spillover effect is positively correlated with the development level of the digital economy. (2) Urban population size: The larger the population size, the larger the number of customers for the development of the digital economy; on the other hand, it also increases the demand for digital technology in surrounding areas, improving the spatial spillover effect of the digital economy (Agrawal et al., 2019). (3) The degree of market integration: The higher the degree of market integration, the smoother factors circulate, including digital technology, which is conducive to the spillover effect of digital economy technology and the imitation effect in adjacent areas (Sun and Chen, 2021). (4) Administrative barriers across regions can significantly influence spatial spillover effects through various channels, including knowledge transfer and innovation, market access and expansion, policy coordination and collaboration, research and development cooperation, investment incentives, and regulatory compliance and standards. These impediments arise from the distinct regulations, policies, and administrative processes in different regions, which can either facilitate or impede spatial spillover effects.

Therefore, this paper proposes research hypothesis 3: the spatial spillover effect of the digital economy that drives the low-carbon development of physical industries is affected by the characteristics of cities; there are differences in the spatial spillover effect of the digital economy in cities with different geographical locations, population sizes, and market integration degrees.

The moderating effect of intangible asset equity protection on the spatial spillover effect of the digital economy

The regulatory role of intangible asset equity protection includes the following: (1) Intangible asset equity protection plays a crucial role in enhancing the spillover effects of digital technology. A good intangible asset equity protection system can optimize the environment for contract performance, encourage R&D and innovation of digital technology in the region, and enhance the spillover effect of digital technology (Grazi and Waisman, 2015). (2) Intangible asset equity protection strengthens the “demonstration effect” of adjacent areas. In the era of the digital economy, enterprises’ innovation achievements are more likely to be occupied (Fang et al. 2017). The intangible asset equity protection system affords digital technology enterprises a certain technological monopoly, which forces enterprises in adjacent regions to accelerate their progress in digital technology and the development of the digital economy. (3) Intangible asset equity protection promotes “spatial interaction” between regions. Improvements in intangible asset equity protection help to dispel the concerns of enterprises about digital technology innovation, promote cross-regional digital technology R&D cooperation, protect the interests of cross-regional digital element flow, and form a competitive mechanism for digital technology innovation (Barrett et al., 2015).

Therefore, this paper proposes research hypothesis 4: intangible asset equity protection has a regulatory effect on the spatial spillover effect of the digital economy, and improvements in intangible asset equity protection strengthen the role of spatial spillover effects of the digital economy in promoting the low-carbon development of physical industries.

Attenuation of spatial spillover effects of the digital economy

The spatial diffusion impact of the digital economy is anticipated to diminish progressively with escalating geographical separation and the presence of administrative delineations, indicative of the prevalence of spatial diffusion effects within regional confines. (1) Geographical distance weakens the spatial spillover effect. The transmission of invisible knowledge and technology to industry tends to decline with increases in geographical distance; thus, the spillover of digital technology and the “imitation effect” of adjacent areas will decrease with geographical distance (Ungerer et al., 2021). (2) Administrative boundaries weaken the spatial spillover effect of the digital economy. Regional barriers formed by local protection increase the cost of factor circulation, which is not conducive to cross-regional circulation of factors, including digital technology, and increases the difficulty of cooperation between regional enterprises in the field of digital industrialization and industrial digitalization, thus weakening the spatial spillover effect of the digital economy.

Therefore, this paper proposes research hypothesis 5: the spatial spillover effect of the digital economy that drives the low-carbon development of physical industries in surrounding areas attenuates over distance, and there is a certain regional boundary to spatial spillover.

Research design

Spatial econometric model setting

The spatial Durbin model (SDM) reflects the spatial interdependence of explained variables among regions and also reflects the spatial influence of explained variables in other regions; moreover, the estimation results are unbiased. Therefore, this research constructed the following SDM model to estimate the spatial impact of digital economic development on the low-carbon total factor development of industry:

$$\begin{array}{c}{\rm{In}}{{\rm {LCTF}{P}}}_{{it}}=\delta \mathop{\sum }\limits_{j=1}^{N}{w}_{{ij}}{\rm{In}}{{\rm {LCTF}{P}}}_{{jt}}+\theta {\rm{In}}{{\rm {DID}{E}}}_{{it}}+\\ \rho \mathop{\sum }\limits_{j=1}^{N}{w}_{{ij}}{\rm{In}}{{\rm {DID}{E}}}_{{jt}}+{\gamma }_{{\rm{I}}}{\rm{In}}{{\rm {Contro}{l}}}_{{jt}}+\\ \phi \mathop{\sum }\limits_{j=1}^{N}{w}_{{ij}}{\rm{In}}{{\rm {Contro}{l}}}_{{jt}}+{\mu }_{i}+{\lambda }_{i}+{\varepsilon }_{{it}}\end{array}$$
(1)

where \(i,\) \(j\) mean city; \(t\) is the year; N is the number of cities; \({{\rm {LCTF}{P}}}_{{jt}}\) means low-carbon total factor productivity; the coefficient to be estimated, \(\delta\), measures the spatial spillover effect of low-carbon of urban industrial development; \({{\rm {DID}{E}}}_{{jt}}\) represents the development level of the digital economy; the coefficient to be estimated, \(\theta\), measures the impact of the digital economy on the low-carbon development of local industries. A coefficient to be estimated, \(\rho\), represents the spatial spillover effect of the digital economy; \({w}_{{ij}}\) represents a spatial weight matrix that includes three types: the geographical distance spatial weight matrix \({w}_{{{\rm {d}}}_{{ij}}}\), the economic distance spatial weight matrix \({w}_{{{{\rm {eco}}}}_{{ij}}}\), and the economic and geographical distance-nested matrix \({w}_{{\rm {d{{eco}}}}_{{ij}}}\); \({{\rm {Control}}}\) is the set of control variables; \({\mu }_{i}\) is the urban effect; \({\lambda }_{i}\) is the time effect; and \({\varepsilon }_{{it}}\) stands for a random error term.

Direct and indirect effects

The spatial Durbin model (SDM) encompasses the spatial spillover impact of the explained variables among regions, and also incorporates the spatial spillover effect of the explained variables among regions into the dependent variables. The estimated coefficient contains interactive information between regions and cannot directly explain the relationship between dependent variables and independent variables. This research used partial differential matrix analysis to decompose the total effect of the independent variables on the dependent variables into direct effects (intra-regional spillover effects) and indirect effects (spatial spillover effects) (Keller, 2002). This can accurately reflect the impact of spatial spillover effects under the SDM and then correctly interpret the estimated coefficient of the SDM. The partial derivative matrix of the expected \(\mathrm{ln}{{\rm {LCTFP}}}\) of low-carbon development of the urban industry to the \(\mathrm{ln}{{\rm {DIDE}}}\) of the digital economy level can be written as follows:

$$\begin{array}{c}\frac{\partial E\left(\mathrm{ln}{{\rm {LCTFP}}}\right)}{\partial \mathrm{ln}{{\rm {DID}{E}}}_{1}}\frac{\partial E\left(\mathrm{ln}{{\rm {LCTFP}}}\right)}{\partial \mathrm{ln}{{\rm {DID}{E}}}_{2}}\ldots \frac{\partial E\left(\mathrm{ln}{{\rm {LCTFP}}}\right)}{\partial \mathrm{ln}{{\rm {DID}{E}}}_{N}}\\ ={\left(1-\delta \mathop{\sum }\limits_{j=1}^{N}{w}_{{ij}}\right)}^{-1}\left[\begin{array}{cccc}\theta & {w}_{12}\rho & \cdots & {w}_{1N}\rho \\ {w}_{21}\rho & \theta & \cdots & {w}_{2N}\rho \\ \vdots & \vdots & \ddots & \vdots \\ {w}_{N1}\rho & {w}_{N2}\rho & \cdots & \theta \end{array}\right]\end{array}$$
(2)

The direct effect is the mean value of all elements on the main diagonal of the matrix in Formula (2), which is the impact of the digital economy on the low-carbon development of local industries. The spatial spillover effect of the digital economy on the low-carbon development of industries in other regions is expressed in terms of the mean of the column sum of the non-diagonal elements. The total effect of the digital economy on the low-carbon development of industry is obtained by summing up the direct effect and the indirect effect.

Variables and data selection of GML index model

Explained variable: low-carbon development level of industry

Low-carbon total factor productivity is used to measure the low-carbon development level of urban industry, and the GML index model based on the SBM distance function is used to measure it. First of all, the real industrial sectors of the city are taken as the decision-making unit m, along with a combination of production factors of real industry input x = (\({x}_{1}{\cdots x}_{n}\)), producing an “expected” output y = (\({y}_{1}\cdots {y}_{n}\)) and an “unexpected” output b = (\({b}_{1}\cdots {b}_{n}\)); data envelopment analysis (DEA) is used to construct a production possibility set, including both the “expected” output and “unexpected” output. Secondly, the directional distance function of the SBM that considers the “unexpected” output is defined as \({D}_{{\rm {V}}}^{{\rm {G}}}({x}^{t{m}^{{\prime} }},{y}^{t{m}^{{\prime} }},{b}^{t{m}^{{\prime} }}{\rm{;}}{g}^{x},{g}^{y},{g}^{b})\), with \(\left({g}^{x},{g}^{y},{g}^{b}\right)\) denoting the direction vector. Then, the GML index is constructed to measure the dynamic change in low-carbon total factor productivity of industries from period t to t + 1, specifically as follows:

$${{{\rm {GML}}}}_{t}^{t+1}=\frac{1+{D}_{v}^{{\rm {G}}}({x}^{t},{y}^{t},{b}^{t}{\rm{;}}g)}{{1+D}_{v}^{{\rm {G}}}({x}^{t+1},{y}^{t+1},{b}^{t+1}{\rm{;}}g)}$$
(3)

where x is the input factor of industry, including capital, labor, and energy; y is the “expected” output, expressed in real GDP; b is the “unexpected” output, including industrial wastewater discharge, industrial \({{\rm{SO}}}_{2}\) discharge, and industrial dust discharge.

Core explanatory variable, urban digital economy development level

The digital economy development index is used to measure the digital economic development level of cities (Fleming, 2000). Considering the availability of data, the digital economy development index includes the inclusive development of digital finance and the development of the Internet (Nie and Zhang, 2021). The entropy method and principal component analysis are used to measure the digital economy development index at the city level, which is used for benchmark regression and robustness testing, respectively.

Control variables

There are seven control variables: (1) Economic development level (\({E}_{{{\rm {co}}}}\)), measured via urban per capita GDP; (2) factor endowment structure (FE), expressed as the ratio of fixed assets of industrial enterprises above a designated size to the number of employed persons at the end of the year; (3) industrial structure (IS), expressed as the proportion of the added value of the secondary industry in GDP; (4) (Inno) is expressed by the proportion of the sum of science and technology expenditure and education expenditure in the general public budget for expenditures; (5) the level of foreign investment (FI), measured by the proportion of actually used foreign capital in urban GDP; (6) environmental regulation (ER), expressed by the comprehensive utilization rate of general industrial solid waste; and (7) the degree of marketization (MK), expressed as the proportion of employment in non-public enterprises.

Data sources

In view of the availability of data, the sample constructed in this study is the panel data of 241 cities from 2012 to 2021. The original data come from the China Urban Statistics Yearbook, China Energy Statistics Yearbook, China Environmental Statistics Yearbook, and the China Digital Inclusive Finance Index. In order to eliminate data volatility and heteroscedasticity, natural logarithms were taken for the above variables. See Table 1 for the statistical description of the variables.

Table 1 Variable descriptive statistics.
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Change characteristics of digital economy development level and low-carbon development level of industry

Change characteristics of digital economy development level

The spatiotemporal evolution trends in the urban digital economy development index are as follows (Fig. 1): (1) from the perspective of time, the development level of the digital economy in each city continuously improved. In 2012, only a few cities, such as Beijing and Shenzhen, had a digital economy development index above 0.15. In 2014, the digital economy development index of Hangzhou, Nanjing, and Guangzhou exceeded 0.2. In 2016, the digital economy development indexes of Suzhou, Xiamen, Dongguan, and other cities exceeded 0.2. In 2019, the digital economy development indexes of Shanghai and Shenzhen exceeded 0.5, and the digital economy development indexes of major cities in the central and western regions also increased significantly. (2) In terms of spatial dimensions, there is spatial heterogeneity and disequilibrium in the development level of the digital economy. The top 20% of cities in the digital economy development index are mainly concentrated in coastal areas. Driven by these cities, the digital economic development level of surrounding cities is also high. In 2019, although the digital economy development index of Wuhan, Nanchang, Chengdu, Xi’an, and other central and western cities also entered a high level, these cities limited the use of the digital economy development belt in their provinces and did not develop digital economy agglomeration.

Fig. 1: The spatiotemporal evolution of spatial spillover effects of digital economy in Chinese cities.
figure 1

Changes over the years.

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Temporal and spatial evolution of low-carbon development level of industry

Temporal and spatial evolution trends of the low-carbon total factor productivity of industries in Chinese cities are shown in Fig. 2. Generally, the low-carbon total factor productivity of urban industries from 2012 to 2021 showed an initial trend of decline and then increase, and the spatial distribution also showed obvious heterogeneity and imbalance. In 2012, the number of cities with a low-carbon total factor productivity from industries >1.02 was large and widely distributed. In 2016, the low-carbon total factor productivity of industry in Beijing, Suzhou, and other strong manufacturing cities declined, and Shijiazhuang, Zhuzhou, Liuzhou, Lhasa, and other cities in the central and western regions also began to decline, indicating that the decline in total factor productivity from industry during this period shows a trend of diffusion. By 2019, the low-carbon total factor productivity of industries in cities turned upward, which is related to the implementation of measures to promote the low-carbon development of industries in the “Made in China 2025” strategy.

Fig. 2: Spatiotemporal evolution of Low-Carbon total factor productivity of the manufacturing industry in prefecture-level cities of China.
figure 2

Changes in different cities in recent years.

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The relationship between the digital economy and low-carbon development of regional industries

The data analysis reveals a notable spatial spillover effect between China’s digital economy and the growth of regional low-carbon industries, with a decreasing gradient from east to west across city blocks and regions. In 2016, Sichuan, Chongqing, and the Central China region emerged as new low-carbon development hubs thanks to continuously enhanced digital infrastructure and rising marketization levels. By 2019, the digital economy and regional low-carbon map showed a “crowding out effect” in the eastern region and a “promoting effect” in the central-western regions. Notably, in the Guangdong-Hong Kong-Macao Greater Bay Area and the Yangtze River Delta, the relatively few administrative barriers between cities, coupled with comprehensive and advanced digital infrastructure, not only enhanced the region’s low-carbon total factor productivity but also significantly reduced carbon emissions in surrounding cities and regions through spatial spillover effects. This has further bolstered the low-carbon development of industrial clusters in underproductive areas and neighboring regions.

Empirical results and analysis

Spatial correlation analysis

In this research, the Moran index is used to describe spatial autocorrelation. It can be seen from the estimation results in Table 2 that the Moran index of low-carbon total factor productivity of industry is positive and significant, indicating that the low-carbon development of industry among cities shows a strong positive spatial correlation; that is, cities with similar low-carbon development levels for industry are geographically close to each other. The development of the digital economy also shows a positive spatial correlation, indicating that the development of the digital economy among cities shows mutual influence.

Table 2 Moran’s I test results of manufacturing Low-Carbon development and digital economic development.
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Selection of spatial econometric model

The results of the spatial model selection test show the following: (1) For the LM_ spatial error and robust LM_, the spatial error statistics were 23.147 and 9.725, respectively, which were significantly positive, indicating that the selected spatial econometric model should include the spatial error term; simultaneously, the LM_ spatial lag and robust LM_ spatial lag statistics are 58.726 and 16.284, respectively, which are also significantly positive. The spatial econometric model should also include the spatial lag term of the dependent variable. (2) After checking the more general SDM model, it was found that the LR_ spatial error (15.379), Wald_ spatial error (22.153), LR_ spatial lag (16.262), and the Wald_ spatial lag (23.174) were significantly positive, indicating that the SDM is the preferred model. (3) The Hausman test showed that the fixed effect model of the SDM should be selected. (4) The LR test shows that the time and space double fixed effect model should be selected. Therefore, the optimal model is the spatiotemporal double fixed effect model of the SDM.

Spatial econometric estimation results and analysis

Benchmark estimation results of the spatial Durbin model

Under the three different spatial weight matrices, the estimated coefficients of urban digital economy development (\(\mathrm{ln}{{\rm {DIDE}}}\)) are significantly positive, indicating that the development of the local digital economy promoted low-carbon total factor productivity in local industries. The estimation coefficient of the spatial lag variable for urban digital economy development (\(w{\rm{\cdot }}\mathrm{ln}{{\rm {DIDE}}}\)) is also positive, which indicates that the development of the digital economy affects the low-carbon development of physical industries in surrounding areas through a spatial spillover effect. The spatial lag coefficient \(\delta\) of low-carbon development of industry is significantly positive, which means that there is a positive spatial interaction effect of low-carbon development on industry in cities (Table 3). Therefore, in addition to the impact of local digital economy development on the low-carbon development of local industry, the spatial spillover effect of the low-carbon development of industry and digital economic development in the surrounding areas cannot be ignored.

Table 3 Estimation results of SDM.
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Direct effect, indirect effect, and total effect of digital economy

Next, the total effect of the digital economy on the low-carbon development of industries was divided into direct effects (intra-regional spillover effects) and indirect effects (spatial spillover effects) in order to correctly interpret the impact of digital economy development. It can be seen from Table 4 that under different spatial weight matrices, the impact of the same explanatory variable on the low-carbon development of industries is basically the same. The direct effect of the digital economy on the low-carbon development of the industry is significantly positive, indicating that the development of a local digital economy is an important driving force for the low-carbon development of the industry. The spatial spillover effect of digital economic development on low-carbon industrial development is less than the direct effect, but it is also positive, indicating that developing the digital economy in surrounding areas also promotes the low-carbon development of local industries through spatial interaction. Therefore, hypothesis 1 and hypothesis 2 are verified.

Table 4 Estimation results of direct effects, indirect effects, and the total effect of the digital economy.
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Robustness test

Replace the interpreted variable

We employ carbon emission intensity as a proxy for low-carbon total factor productivity, thereby re-examining the SDM and spatial spillover effects (Dietz and Rosa, 1997). Tables 5 and 6 reveal that when the dependent variable is shifted from low-carbon total factor productivity to the carbon emission intensity of regional industries, the estimated outcomes and spatial spillover characteristics remain largely consistent with those observed in the previous analysis, suggesting that the boom of the digital economy fosters the low-carbon evolution of regional industries and incurs a positive spatial spillover effect on neighboring regions.

Table 5 Regression results of SDM for carbon emission intensity in regional industries.
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Table 6 Estimation results of effects for carbon emission intensity.
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Replace core explain variables

In order to further ensure the stability of the estimated results, based on the objective empowerment method, recalculate the digital economic development index (Nie and Zhang, 2021). Besides the digital financial inclusive development and Internet development indicators, two new indicators are added: digital industry development (the number of Internet broadband users, the number of employees in the information industry) and digital innovation capacity (the number of patents authorized and the proportion of scientific research expenditure to regional GDP), with their weights all set to 0.25, to derive a new digital economic development index, and replace the original indicators, obtaining the Durbin model and spatial spillover results (Tables 7 and 8). It can be seen from the table that when the core explanatory variable digital economic development index is recalculated, the estimated results and spatial spillover are basically consistent with the above, that is, the development and prosperity of the digital economy not only contribute to the low-carbon development of regional industries but also have a positive spatial spillover effect on the surrounding areas. Therefore, the previous estimation results have passed the robustness test, and it is more appropriate to choose the Durbin model as the research model.

Table 7 Regression results of SDM for the new digital economy development index.
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Table 8 Estimation results of effects for the new digital economy development index.
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Adjust sample period

The sample period has been shortened to 2014–2019 to mitigate the potential impact of a lack of focus on low-carbon development in earlier periods and the stringent standards applied to regional industry low-carbon development in recent years. Table 9 shows that the coefficients and significance of the estimated results remain largely unchanged after the sample period was appropriately shortened. The reduction in sample size leads to a modest decrease in \({R}^{2}\) across various spatial weight matrices, which is a normal outcome, underscoring the robustness of the original estimation conclusion.

Table 9 Estimation results of the adjusted sample period (N = 1653).
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Heterogeneity test

Geographical location heterogeneity test

To investigate the heterogeneity of geographical location, Chinese cities were divided into eight groups for regression. The results are shown in Table 10. The direct and indirect effects of digital economic development in the eastern and southern coastal areas are greater. The reason is that the digital economy of Shanghai, Hangzhou, and other cities in the Yangtze River Delta urban agglomeration is developed, and there are a large number of industrial enterprises in Suzhou, Ningbo, Wuxi, and other cities in the region. The developed digital economy and perfect manufacturing network produce spatial interaction, which enhances the spillover and spatial spillover effects in the region. Similarly, the digital economy and industry are the two wheels driving the economic development in Shenzhen and Guangzhou. Foshan and Dongguan also have developed production and manufacturing systems, so the intra-regional and spatial spillover effects of the digital economy highly promote the low-carbon development of industries. The direct promotional effect of the digital economy on the low-carbon development of industry in the northern coastal area is strong, but the spatial spillover effect is less than that in the eastern and southern coastal areas. The spatial spillover effect of urban digital economic development in southwest China is stronger than that in the middle reaches of the Yangtze River and the Yellow River. The reason is that the digital economies in Chengdu, Chongqing, and Guiyang are developing rapidly, and the development of the big data industry has natural advantages. Northeast China and northwest China are two regions with low spatial spillover effects from the digital economy. As a result of the low level of digital economic development in these two regions, the proportion of modern industries is small, and the degree of regional integration is low.

Table 10 Estimation results of SDM in different regions.
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Population size heterogeneity test

China’s cities are divided into four categories: small cities (with a permanent resident population of less than 500,000 in urban areas), medium-sized cities (with a permanent resident population of 500,000–1 million in urban areas), large cities (with a permanent resident population of 1 million–5 million in urban areas), and cities above mega cities (with a permanent resident population of more than 5 million in urban areas). The estimated results are shown in Table 11. As far as the direct effect is concerned, the digital economy’s role in promoting the low-carbon development of local industries is relatively significant, and there is no obvious change with changing urban population size. However, the spatial spillover effect is quite different. With the gradual increase in urban population size, the spatial spillover effect of digital economic development increases, which shows that the spatial spillover effect is in direct proportion to the urban population size. The larger the urban population, the more diversified the figures required for low-carbon development of industrial enterprises, which increases the input demand for digital elements in surrounding cities, thus improving the spatial spillover effect of the digital economy.

Table 11 Estimation results of the SDM model for cities with different population sizes.
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Heterogeneity test of market integration level

The price index method is used to measure the degree of market integration of each city. The degree of market integration is divided into three levels: low, medium, and high. The estimated results are shown in Table 12. Under different degrees of market integration, the direct and spatial spillover effects of the digital economy that drives the low-carbon development of the industry are heterogeneous. With improvements in the degree of market integration, the direct and spatial spillover effects increase. Enhancing market integration serves as a catalyst for the seamless dissemination of digital components. This, in turn, diminishes the operational costs incurred by enterprises that leverage sophisticated digital technologies beyond their immediate locales. Furthermore, such heightened integration optimally facilitates harnessing of the spillover effects intrinsic to the digital economy, thereby elevating the low-carbon development quotient within both local and international industries. The heterogeneity test shows that the spatial spillover effect of the digital economy is related to the geographical location, population size, market integration level, and other urban characteristics; thus, research hypothesis 3 is verified.

Table 12 Estimation results of SDM model for cities with different degrees of market integration.
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Extended analysis

Regulatory role of intangible asset equity protection

Digital technology has the characteristics of virtuality, replication and sharing, and is prone to infringement in the process of market transaction and use. Therefore, intangible asset equity protection has an important impact on the development of the digital economy and its spatial spillover effect. In this section, the cross term \(\mathrm{ln}{{\rm {DIDE}}}\cdot \mathrm{ln}{{\rm {IP}}}\) and its spatial lag variable of the digital economy and intangible asset equity protection are included in the spatial econometric model (1) to examine the regulatory role of intangible asset equity protection in the low-carbon development of industries driven by the digital economy, specified as follows:

$$\begin{array}{c}{{\rm {InLCTF}{P}}}_{{it}}=\delta \mathop{\sum }\limits_{j=1}^{N}{w}_{{ij}}{{\mathrm{ln}}}{{\rm {LCTF}{P}}}_{{jt}}+{\theta }_{1}{\mathrm{ln}}{{\rm {DID}{E}}}_{{it}}+{\theta }_{2}{\mathrm{ln}}{{\rm {DID}{E}}}_{{it}}\cdot {{\mathrm{ln}}}{{{\rm {IP}}}}_{{it}}+\\ {\rho }_{1}\mathop{\sum }\limits_{j=1}^{N}{w}_{{ij}}{{\mathrm{ln}}}{{\rm {DID}{E}}}_{{jt}}+{{\rho }_{2}\mathop{\sum }\limits_{j=1}^{N}{w}_{{ij}}({{\mathrm{ln}}}{{\rm {DID}{E}}}_{{jt}}\cdot {\mathrm{ln}}{{\rm {IP}}}})+{\gamma} _{{\rm{I}}}{\mathrm{ln}}{{\rm {Contro}{l}}}_{{jt}}+\\\phi \mathop{\sum }\limits_{j=1}^{N}{w}_{{ij}}{\mathrm{ln}}{{\rm {Contro}{l}}}_{{jt}}+{\mu }_{i}+{\lambda }_{i}+{\varepsilon }_{{it}}\end{array}$$
(4)

where \(\mathrm{ln}{\rm {{IP}}}\) represents the level of urban intangible asset equity protection; \({\sum }_{j=1}^{N}{w}_{{ij}}(\mathrm{ln}{{\rm {DIG}{I}}}_{{jt}}{\rm{\cdot }}\mathrm{ln}{{\rm {IP}}})\) is a spatial lag variable of the interaction between the digital economy and intangible asset equity protection, which is used to capture the impact of intangible asset equity protection on the spatial spillover effect of digital economic development. Table 13 shows the moderating effect of intangible asset equity protection on the low-carbon development of physical industries driven by the digital economy. The direct and indirect effects of \({\rm{In}}{\rm {{DIDE}}}\) are still significantly positive. The direct effect of focusing on the variable \({\rm{In}}{{\rm {DIDE}}}\)·\({\rm{In}}{{\rm {IP}}}\) is positive, indicating that intangible asset equity protection strengthens the intra-regional spillover effect of the digital economy driving the low-carbon development of physical industries. The indirect effect of \({\rm{In}}{{\rm {DIDE}}}\)·\({\rm{In}}{{\rm {IP}}}\) is significantly positive, indicating that in regions with higher levels of intangible asset equity protection, the level of digital economic development has a greater spatial spillover effect on the low-carbon development of physical industries in that region. Therefore, improving the level of intangible asset equity protection strengthens the spatial spillover effect of the digital economy on the low-carbon development of physical industries. Therefore, research hypothesis 4 is validated.

Table 13 The moderating role of intangible asset equity protection.
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Relationship between spatial spillover effect and geographical distance

In order to test the relationship between the spatial spillover effect of the digital economy and geographical distance, the spatial econometric model was estimated for every 20 km increase in the geographical distance between cities, and the estimated spatial spillover effect coefficients under different geographical distance thresholds were recorded. It can be seen from Fig. 3 that within a distance of 300 km, the spatial spillover effect of the digital economy is strong and the downward trend is slow, mainly because it is generally within 300 km of provincial administrative boundaries. Compared with outside the province, the mobility of digital elements among cities within the province is better, which better promotes the low-carbon development of physical industries in cities within the province through the spatial spillover effect. However, when the geographical distance exceeds 300 km, the spatial spillover effect of the digital economy suddenly decreases, and the decline rate is faster, indicating that beyond the provincial boundary, the barrier effect is stronger than the spatial spillover effect of the digital economy. When the geographical distance exceeds 520 km, the rate at which the spatial spillover coefficient of the digital economy slows down declines, which may be due to a reduction in spatial units with spatial relationships among regions. Therefore, the spatial spillover effect of the digital economy attenuates with the increase in geographical distance, and there is a certain regional boundary to spatial spillover. Thus, research hypothesis 5 is verified.

Fig. 3
figure 3

The relationship between spatial spillover effect coefficient of the digital economy and geographical distance threshold.

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Conclusions and policy recommendations

This study yields several key findings: (1) The digital economy propels the low-carbon evolution of local physical industries and stimulates low-carbon advancements in proximate industries through the spatial spillover effect. (2) The spatial spillover effect of the digital economy is contingent upon geographic location, population size, and the degree of market integration, among other urban attributes. Notably, municipalities in the southeast coastal regions, those with larger populations, and those boasting higher market integration levels exhibit more pronounced spatial spillover effects. (3) Intangible asset equity protection, as a crucial institutional underpinning for digital technology innovation, amplifies the spatial spillover effect of the digital economy, thereby steering the low-carbon development trajectory of physical industries. (4) The spatial spillover effect of the digital economy adheres to a discernible attenuation pattern. Specifically, the impact diminishes abruptly beyond a geographical distance of 300 km, which is attributed to provincial administrative boundaries. Notably, the rate of decline in the spatial spillover coefficient decelerates once the geographical distance surpasses 520 km.

This study has the following policy implications: (1) Accelerate the establishment of a unified factor market, promote the efficient, reasonable, and safe flow of data elements in a wider range, and reduce the cost of using digital elements in physical industries. Maximize the expansion, superposition, and multiplication of digital technology, and improve the spatial spillover effect of the digital economy to enable the low-carbon development of physical industries. (2) Taking into account the geographical location, population size, market integration level, and other urban characteristics, we should take measures to improve the spatial spillover effect of the digital economy. Cities with relatively lagging digital economic development in the northwest and northeast China should strengthen their cooperation with cities that have developed digital economies. Cities with small populations should increase the number of employed people in the digital economy, improve their level of market integration, and expand the spatial spillover effect dividend of the digital economy. (3) We should improve the data intangible asset equity protection system, encourage digital technology innovation, and strengthen the protection of the whole process of data production, circulation, and consumption. Safeguard the rights and interests of owners and users of digital elements, and strengthen the spatial spillover effect of the digital economy. (4) Promote the development of regional economic integration, delay the decay rate of the spatial spillover effect, and expand the spatial spillover radius of the digital economy.

Research deficiency and prospects: This article employs spatial econometric models to empirically assess the influence of the digital economy on the low-carbon evolution of regional industries. However, the analysis primarily considered the national scale, neglecting the variations in digital economy development across cities. Future research can integrate the spatial heterogeneity of individual cities into its analytical framework and employ tools like spatial convergence to investigate the pivotal role of the digital economy in fostering innovative and sustainable development in regional industries. Furthermore, the spatial spillover effects highlighted in this study might just be one aspect of the digital economy’s impact on regional industry’s low-carbon development; other influencing mechanisms might also be worth exploring in depth. Additionally, there is a reverse spillover effect in the construction of a digital economy in surrounding cities. By examining how the digital economy contributes to the low-carbon growth of regional industries through industrial restructuring, transformation, and financial development, future research can provide valuable empirical evidence for the development of low-carbon industries driven by the digital economy in the region.