Digital–Physical Integration and Carbon Productivity: An Empirical Assessment from China

Abstract

The integration of digital technologies with the physical economy has emerged as a crucial driver of sustainable and high-quality development. Drawing on a patent co-classification framework, this study constructs a provincial-level indicator of digital–real integration in China to evaluate its influence on carbon productivity and the underlying mechanisms. The empirical findings show that digital–real integration exerts a clear and statistically significant positive impact on carbon productivity. Moreover, the improvement in carbon productivity occurs mainly through three channels: green technological innovation, adjustments in industrial structure toward upgrading, and enhancements in resource allocation efficiency. Industrial upgrading is reflected in the gradual shift toward more advanced and low-carbon industrial configurations, whereas the allocation channel captures the coordinated optimization of traditional and emerging production factors. Regarding the nonlinearity, a threshold pattern is identified between digital–real integration and carbon productivity, shaped by the degree of biased technological progress. When the technological bias remains low, the productivity gains are modest; once the bias surpasses a certain critical level, the positive effect of integration intensifies substantially. The magnitude of this threshold effect also varies by bias type, with capital-biased technological progress producing the strongest influence. Overall, the results provide theoretical and policy implications for advancing digital–real integration and supporting a green and low-carbon transition.

1. Introduction

China has undergone rapid and sustained economic growth over the past four decades, transforming itself into one of the largest economies globally. Nevertheless, the country’s long-standing extensive development model—characterized by high energy consumption, heavy pollution, and low efficiency—has imposed continuous strain on the ecological environment [1] and constrained progress toward sustainable economic development [2]. According to estimates from the International Energy Agency (IEA), China’s carbon dioxide emissions reached 12.6 billion tons in 2024, accounting for around 34% of global emissions, while its primary energy consumption totaled 176.35 exajoules, approximately 27.7% of the world’s total. As the world’s largest energy consumer and carbon emitter, China has pledged to reach its carbon emissions peak before 2030 and attain carbon neutrality by 2060. The 20th National Congress of the Communist Party of China emphasized the need to integrate carbon mitigation, pollution reduction, ecological protection, and economic development within a broader framework promoting ecological conservation, efficient resource utilization, and green, low-carbon growth. Carbon productivity—measured as the economic output generated per unit of carbon emissions—functions as an essential metric for evaluating the interplay between economic growth and environmental performance. Improving carbon productivity is essential for decoupling economic expansion from carbon emissions, with technological progress acting as a fundamental catalyst. In recent years, digital technologies—including the industrial internet, artificial intelligence, big data, and cloud computing—have rapidly penetrated various industries, accelerating digitalization, intelligent transformation, and the green upgrading of the real economy [3,4,5,6]. This development pathway has emerged as a vital means for advancing the Sustainable Development Goals [7]. Therefore, examining how digital–real integration (DRI) shapes carbon productivity and through which channels this influence operates carries significant academic and policy relevance, offering insights for countries seeking to leverage digital technologies in their green transition.

A growing body of research suggests that the convergence of digital and physical economies has become a critical force promoting sustainable and high-quality development. At the firm level, combining digital tools with industrial technologies contributes to lowering enterprises’ carbon emission intensity through production optimization and improved information exchange [7]. At the macro and industrial levels, Guo et al. (2024) demonstrate that digital–real integration (DRI) markedly improves urban green total factor productivity and generates positive spatial spillover effects [4]. Other studies have also highlighted that DRI enhances cities’ capacity for green emission reduction and facilitates industrial low-carbon transformation through optimized resource utilization and strengthened innovation dynamics [8]. From a global perspective, cross-country evidence has further verified the link between digitalization and sustainable development. Yu and Liu (2024), using data from 136 countries, found that digitalization significantly boosts carbon productivity, particularly in economies with higher levels of technological accumulation [9]. Likewise, Quttainah and Ayadi (2024), focusing on Europe, revealed that digital integration promotes environmental innovation and resource efficiency, serving as a crucial pathway to corporate sustainability [10]. Taken together, the results demonstrate that digital–real integration, in both advanced and emerging economies, plays an essential function in enhancing carbon-use efficiency and advancing the transition toward greener development models.

Although prior studies have offered important insights, the existing literature broadly agrees that digital–real integration plays a positive role in promoting environmentally sustainable and low-carbon development. Nevertheless, research examining the relationship between digital–real integration and sustainable development has largely focused on metrics such as carbon intensity, green technological progress, and green total factor efficiency. In contrast, empirical evidence on carbon productivity—an indicator that more comprehensively reflects both economic performance and environmental outcomes—remains relatively scarce. Furthermore, much of the existing evidence assumes a straightforward linear linkage between digital–real integration and ecological outcomes, overlooking possible nonlinear or threshold effects arising from heterogeneity in factor endowments and the degree of digitalization.

To bridge these research gaps, this study combines theoretical analysis with empirical investigation to examine how digital–real integration affects China’s carbon productivity and through which mechanisms. A threshold regression framework is employed to identify potential nonlinear features, and the core contributions of the study are outlined below.

(i) Research perspective. This research advances the existing literature by emphasizing carbon productivity as a comprehensive indicator that jointly reflects economic and environmental performance, and by introducing biased technological progress as an external driving factor. This perspective helps illuminate the critical role of technological bias in influencing the effect of digital–real integration on carbon productivity.

(ii) Mechanism analysis. This study constructs a mechanism model from three dimensions—green technological innovation, industrial structure upgrading, and resource allocation efficiency—to systematically identify the pathways through which DRI affects carbon productivity and to further deepen the analysis of different mechanisms. Specifically, industrial structure upgrading is divided into advancement and rationalization to reveal the distinct roles of structural optimization in improving carbon productivity. Resource allocation efficiency is classified according to the attributes of production factors into emerging and traditional types, thereby analyzing the influence mechanism of DRI from the perspective of input efficiency. Meanwhile, a threshold empirical model is employed to examine the threshold effect of biased technological progress in the impact of DRI on carbon productivity, confirming that when technological progress is capital-biased, the productivity-enhancing effect of DRI becomes stronger.

(iii) Methodological innovation. Regional DRI levels are measured through a patent co-classification method, effectively capturing the technological drivers behind industrial convergence. Moreover, this study applies a slack-based DEA framework with a non-radial and non-oriented structure to derive the index of biased technological progress, thereby improving methodological robustness and ensuring the reliability of empirical findings.

The organization of the study proceeds as follows. We begin by surveying prior studies and establishing the corresponding hypotheses. Next, we outline the research design and conduct an empirical analysis of the effects of digital–real integration on carbon productivity and its transmission mechanisms. Third, we further examine the threshold role of biased technological progress. Finally, the study concludes by summarizing the key results, discussing its limitations and possible directions for subsequent research, and presenting the corresponding policy recommendations.

2. Literature Review

2.1. Research on Digital–Real Integration

The widespread penetration of digital technologies across diverse sectors has fostered the integration of digital and physical economies, increasingly influencing global economic and social evolution by creating novel growth engines and facilitating structural transformation [4,11]. This issue has garnered growing scholarly attention. Dominant definitions of digital–real integration emphasize primarily the technological aspect, depicting it as the incorporation of advanced information technologies—such as big data, cloud computing, and artificial intelligence—into real-sector operations. This process facilitates mutual interaction and a virtuous cycle between the digital and real economic domains [12]. At its core, digital–real integration is driven by digital technologies, with data becoming an important source of value. The emphasis lies in embedding data elements across the entire chain of the real economy, including production, circulation, and distribution. Through this process, digital information essential for economic development is generated, which in turn facilitates more efficient resource allocation and strengthens the coordination between supply and demand. This ultimately leads to the creation of digitalized and intelligent products and services that meet market needs [13]. During this evolution, the real economy acquires distinct digital dimensions, with its intrinsic connotation and external scope being continuously broadened, which results in the formation of a more efficient and higher-quality variant of the “new” real economy [6].

Industrial integration serves as the essential groundwork for digital–real integration. Existing studies often adopt methodologies developed for measuring industrial convergence to conduct quantitative evaluations of digital–real integration. These methods mainly fall into three categories: input–output analysis, coupling coordination models, and entropy weight approaches. These methods can be broadly grouped into three categories: input–output analysis, coupling coordination models, and entropy weight approaches. For example, some studies applied input–output analysis based on consumption coefficients to explore inter-industry linkages [14,15]. Other research adopted coupling coordination models to measure regional digital–real integration and examine its spatial dynamics [4,16,17]. In addition, existing studies have proposed evaluation frameworks that integrate foundations, enabling conditions, and application dimensions as key dimensions for assessing digital–real integration, and have employed the entropy weight method to quantify the degree of convergence between digital and real-economy sectors [18,19]. By employing the entropy weight method, they quantified the level of convergence between digital and real-economy sectors. Despite their usefulness, three methodological approaches exhibit certain deficiencies. For example, the input–output technique is constrained by the lag in statistical data, rendering it less effective in capturing the rapid transformations of digital–real integration and in providing timely evaluations of present development status. The coupling coordination model and entropy weight method rely heavily on index-based evaluation systems. As a result, the findings typically reflect integration at an aggregate level, which tends to obscure inter-industry integration relationships, thereby making it difficult to fully reflect the level of integration across different industries.

2.2. Research on the Determinants of Carbon Productivity

Enhancing carbon productivity constitutes a crucial pathway for mitigating greenhouse gas emissions, improving the efficiency of energy utilization, and supporting sustained economic growth. Moreover, it serves as an important metric for evaluating the quality of economic development, particularly in developing countries [20]. Carbon productivity measurement can be broadly categorized into two methods: single-factor and total-factor. The single-factor method captures carbon productivity by measuring the ratio of economic output to carbon dioxide emissions [21]. In contrast, total-factor methods, such as Stochastic Frontier Analysis (SFA) and Data Envelopment Analysis (DEA), assess carbon productivity within an input–output framework. Compared with total-factor measurement methods, the single-factor approach, owing to its computational tractability, has been applied in numerous studies. It has also been adopted by Meng et al. (2022) and Wang et al. (2024) to assess carbon productivity [22,23].

Prior research has explored the determinants of carbon productivity from macro-, meso-, and micro-level perspectives. At the micro level in particular, technological advancement is widely regarded as a central force driving improvements in carbon productivity [23,24,25]. Green low-carbon innovation has been shown to significantly improve carbon productivity [23,25], and intellectual capital serves as an important transmission channel in this process [26]. At the mesoscopic level, industrial agglomeration is considered a key pathway for achieving low-carbon economic growth [27]. As China advances its carbon neutrality agenda and the world continues to prioritize sustainable development, the linkage between coordinated industrial agglomeration and carbon productivity has increasingly emerged as an important subject of academic inquiry. Relevant studies suggest that improvements in carbon productivity require a foundation of high-level industrial coordination, and that upgrading industrial structure and improving production efficiency can strengthen this effect [28]. From a macroeconomic perspective, urban agglomerations, being the primary loci of carbon emissions, have become central to achieving China’s “dual carbon” commitments [29]. Empirical evidence indicates that promoting coordinated development within urban agglomerations enhances carbon productivity through multiple channels, including restructuring the energy mix, fostering eco-innovation, advancing ecological restoration initiatives, and accelerating urbanization [30].

2.3. Research on the Impact of Digital–Real Integration on Carbon Productivity

Propelled by the rapid advancement of global digital transformation, the digital economy has increasingly taken shape as a key engine driving worldwide economic revitalization and supporting collective responses to challenges such as climate change and ecological deterioration. Governments worldwide are working to balance economic growth with the pursuit of low-carbon development. Against this broader backdrop, the strengthening interaction between digital technologies and real-sector activities has become a key driver of sustainable development [31]. Meanwhile, the widespread adoption of digital technologies within real-economy industries has become an important catalyst for regional green upgrading and low-carbon transition [32]. According to the OECD (2024) [33] Digital Economy Outlook, the interplay between digitalization and decarbonization has emerged as a new driver of global green growth. The report highlights that deeper integration of data infrastructure, artificial intelligence, and blockchain into industrial systems can markedly improve carbon-emission efficiency—especially in manufacturing and energy-intensive sectors, where digital technologies enhance process optimization and intelligent energy management. In the European context, initiatives such as the EU Green Deal and the “Fit for 55” policy framework show that the broad implementation of digital management tools in energy, transportation, and industrial sectors has established an essential foundation for realizing carbon-neutral objectives [34,35].

Existing studies have examined how digital–real integration contributes to sustainable development, mainly from the perspectives of green innovation and low-carbon transition [8,16,17,36]. At the technological level, digital–industrial integration reduces marginal production costs while mitigating carbon-emission intensity through enhanced knowledge accumulation [23]. It also improves total-factor energy productivity by fostering energy–labor-biased technological progress and applying artificial intelligence technologies [31]. At the industrial level, digital–real integration enhances green innovation by easing financing constraints, advancing digital upgrading, and reinforcing firms’ social responsibility practices, which in turn contribute to higher innovation performance [17]. Moreover, it contributes to cleaner production and emission reduction, which in turn promotes industrial upgrading and societal decarbonization at the macro level [8].

In line with evidence from China, the pathways through which digitalization facilitates green development have increasingly attracted substantial attention in global academic discussions. Within OECD economies, advances in technological innovation help ease carbon-emission pressure by enhancing energy efficiency and promoting structural shifts in industrial systems [37]. In Europe, digital management systems embedded in the Green Deal framework have enhanced energy productivity and accelerated renewable energy substitution. Meanwhile, the interaction between digital integration and financial development has been shown to foster a more favorable environment for green innovation by improving information transparency and long-term investment efficiency, thus facilitating sustainable growth [10,35]. In emerging economies, the mechanisms of digital–real integration are similar to those in developed economies but differ according to development stage and industrial structure. In Turkey, studies on the manufacturing sector reveal that integrating Industry 4.0 technologies with sustainable operational practices enhances both environmental and economic performance, highlighting the significance of digital transformation for achieving sustainable manufacturing [38]. In Vietnam’s agricultural sector, digitalization and environmental innovation jointly enhance total factor productivity [39], while in Brazil and India, advancements in green technologies and resource productivity have facilitated the decoupling of economic growth from carbon emissions [40].

Overall, the literature consistently recognizes digital transformation as an essential mechanism for enhancing carbon productivity, although substantial regional heterogeneity persists due to differences in technological maturity, policy orientation, and resource endowment. Recent theoretical studies advocate embedding carbon constraints within the resource-based view (RBV) framework, arguing that the strategic significance of digital capabilities, data assets, and green technologies is conditioned by carbon intensity and environmental regulation [41]. When carbon constraints are present, firms achieve sustainable competitive advantage through the efficient configuration of low-carbon digital resources rather than through simple scale expansion [42]. This theoretical extension links micro-level digital innovation with macro-level carbon productivity, providing a comprehensive analytical framework for cross-country comparison and policy implications.

Although previous studies have underscored the importance of digital–real integration in driving green and low-carbon transformation, most have concentrated on the digital economy itself, with relatively little attention to its macroeconomic implications for carbon mitigation. As a result, the diversity and complexity of industrial activities and their broader influence on carbon productivity have not been adequately addressed. To address the above research gaps, this paper formulates a series of hypotheses that delineate the direct, mediating, and nonlinear effects through which digital–real integration influences carbon productivity, thereby providing the theoretical foundation for the subsequent empirical analysis.

3. Theoretical Framework and Research Hypotheses

3.1. The Direct Effect of Digital–Real Integration on Carbon Productivity

Endogenous growth theory posits that sustained economic expansion is fundamentally driven by technological advancement [43,44]. Within this theoretical lens, digital–real integration (DRI) functions as an internal growth mechanism that continuously stimulates innovation and efficiency enhancement. By incorporating the essential components of the digital economy—such as data assets, digital technologies, and platform applications—into real-sector operations, DRI contributes to improving carbon productivity and advancing green, low-carbon, and high-quality development.

First, data serve as the core production factor in digital–real integration. Empowered by advanced digital technologies—including the Internet, cloud computing, artificial intelligence, and big data analytics—data overcome time and space limitations, allowing their broad utilization across multiple economic and social sectors. The rapid penetration of data elements facilitates the reorganization of production factors, releases new drivers of economic growth, and provides critical support for the restructuring of industrial systems toward green transformation. In the processes of circulation and exchange, data elements more accurately match the dynamic demands of the real economy, improve the efficiency and generalizability of technological applications, and enhance firms’ productivity [45]. This digital transformation drives revolutionary changes in productivity, production relations, and institutional structures, ultimately achieving both quantitative and qualitative improvements in macroeconomic performance and carbon productivity.

Second, digital technologies—characterized by their high penetration, strong enabling capacity, and low replication cost—reshape industrial innovation systems, value chains, and factor allocation mechanisms, steering the economy toward sustainable and low-carbon development [46,47]. Empowered by these technologies, firms can overcome the constraints of traditional innovation frameworks, capture frontier technological trends with greater precision, and efficiently integrate internal and external information to continuously optimize industrial structures. The integration of digital technologies into various stages of innovation—such as idea generation, R&D design, and technological experimentation—significantly reduces R&D and search costs. Moreover, the rise in distributed innovation enhances knowledge sharing and collaborative R&D among enterprises, broadening the scope of knowledge integration and improving the overall efficiency of technological innovation.

Finally, digital platforms have given rise to new organizational forms, including platform-based, modular, ecosystem-oriented, and personalized enterprises. These emerging models support value collaboration and co-creation throughout industrial and supply chains, markedly strengthening the performance of green supply chain governance [48] and promoting the movement of value chains in the real economy toward more advanced segments.

H1: 

Digital–real integration has a positive effect on carbon productivity.

3.2. Indirect Impact of Digital–Real Integration on Carbon Productivity

3.2.1. Green Technological Innovation Effect

The convergence between digital and physical economies improves enterprises’ performance in green innovation. First, digital–real integration substantially optimizes the processes of retrieving and aligning information resources. By leveraging digital technologies to achieve interconnection, interoperability, and information sharing, it dismantles traditional information barriers and strengthens the accuracy and comprehensiveness of information accessible to market participants. This not only ensures timely and accurate market insights for firms but also helps clarify the direction of future green transformation. Second, digital–real integration reinforces the linkage between firms and consumers. The application of digital technologies facilitates consumer identification, improves transaction efficiency, and increases consumer engagement [49], thereby enabling firms to develop new products more efficiently, reduce uncertainty associated with product innovation, and lower the cost of green innovation [17]. Meanwhile, digital technologies facilitate the development and dissemination of green innovations. Third, digital–real integration contributes to expanding the knowledge stock of the entire economy. The embedding of digital technologies into real industries helps weaken the boundaries in the innovation process and significantly reduces the impact of factors such as regional fragmentation, transmission barriers, and geopolitical constraints on technological spillovers [50]. This enables enterprises to more rapidly integrate knowledge from diverse fields and apply it to emerging challenges [51]. Moreover, collaborative innovation models based on digital platforms promote knowledge sharing and cooperation among innovation entities along the industrial chain, thereby enhancing the efficiency of knowledge absorption and transformation [52]. Improvements in absorptive capacity further contribute to greater efficiency in green technological innovation across industries.

Technological innovation plays a critical role in enhancing resource use efficiency and is a key element in promoting green industrial development [53]. Green technological innovation primarily influences carbon productivity through both managerial and production dimensions. At the managerial end, the outcomes of green technological innovation can facilitate cleaner production and energy structure transformation, thereby continuously reducing the consumption of energy, raw materials, and other resources. It also strengthens low-carbon technological collaboration across industries [54], enabling green development alongside capacity expansion and promoting the green transformation of the economy. At the production end, green technological innovations optimize energy decarbonization at the source through measures such as fuel blending optimization and iterative decarbonization pretreatment technologies [55,56]; simultaneously, through equipment upgrades and renovations, a complete resource production loop is formed, enabling the resource utilization and high-value utilization of waste materials, thereby reducing the use of fossil fuels [57], ultimately achieving a dual improvement in economic and environmental benefits.

H2: 

Digital–real integration enhances carbon productivity through green technological innovation.

3.2.2. Industrial Structure Upgrading Effect

The deep integration between digital and physical economies improves carbon productivity by promoting industrial upgrading in two aspects: advancement and rationalization. Specifically, digital–real integration stimulates innovative business models, facilitates digital and intelligent transformation, and thereby drives industrial restructuring, serving as an important channel for reducing carbon emissions [58]. In particular, this process has accelerated the dissemination and uptake of advanced digital tools, such as big-data analytics, cloud-computing technologies, and artificial intelligence. Meanwhile, advancements in internet and information technologies have stimulated a rising demand for cultural and knowledge-intensive forms of consumption. This transformation has fostered the emergence of novel business models and progressively shaped digital industrial chains. In particular, it has promoted the expansion of green, low-carbon, and environmentally sustainable industries, thereby driving industrial upgrading and propelling sectors toward higher positions within the value chain. Moreover, digital technologies have integrated product R&D, production, and marketing processes within traditional industries, driving their transformation and upgrading, and enabling improvements in quality, cost-efficiency, and productivity [5]. Second, digital–real integration contributes to industrial rationalization by enhancing management coordination and professional specialization. With the support of digital platforms, data can be exchanged across various stages of the industrial chain, improving responsiveness and collaborative efficiency [36]. At the same time, the application of intelligent production management systems advances production processes toward greater intelligence, precision, and specialization. By enabling more flexible allocation of capital, labor, and energy inputs, enterprises can continually enhance the efficiency of resource use and advance green development.

Upgrading of the industrial structure represents an important avenue for improving carbon productivity. The optimization of industrial structures exerts beneficial effects on the environment by facilitating the transformation of production systems toward resource-saving practices and circular modes of utilization. This process guides production factors toward industries characterized by low energy consumption, high value-added, and low pollution, thereby reducing energy consumption in resource-intensive sectors. Through the advancement of a low-carbon and high-efficiency economy, overall energy use efficiency can be significantly improved.

H3: 

Digital–real integration promotes carbon productivity via industrial structure upgrading.

3.2.3. Resource Allocation Effect

According to neoclassical growth theory, efficient resource allocation maximizes economic output by allowing production factors to flow freely toward their most productive uses [59]. However, market distortions and information asymmetries often lead to resource misallocation and efficiency losses [60]. Digital–real integration (DRI) mitigates these inefficiencies by enhancing information transparency, lowering transaction costs, and improving factor-matching efficiency, thereby optimizing resource allocation and ultimately enhancing carbon productivity.

On one hand, DRI improves allocation efficiency and promotes carbon emission reduction by reducing factor search and transaction costs [8]. The integration of data elements with traditional production factors increases the marginal returns of capital and labor, generating amplification and multiplier effects that stimulate economic growth. This process refines input–output relationships, reduces transaction costs, and enhances resource utilization efficiency. Furthermore, DRI continuously stimulates the emergence of new industries, business forms, and organizational models, enabling faster and more accurate dissemination of factor information. These dynamics reduce information search and bargaining costs and further optimize resource allocation [45]. On the other hand, DRI effectively alleviates price distortions and supply–demand mismatches in factor markets. By embedding digital technologies into production processes, enterprises can streamline workflows, extract insights from market demand and consumer preferences, and make more accurate forecasts. These capabilities enhance firms’ ability to track technological frontiers [15], reduce investment risks, and direct capital toward more innovative and environmentally sustainable projects [17]. Meanwhile, DRI increases labor market transparency, facilitating the precise matching of labor supply and enterprise demand, which improves labor allocation efficiency and strengthens overall social productivity.

Improvements in resource allocation efficiency further advance the green economy. Optimized allocation channels production factors toward high-efficiency sectors, improving the overall quality of economic development [61]. During this process, scarce resources—such as capital and labor—tend to shift toward the tertiary sector [17], promoting the scaling-up and market-oriented development of green industries. Consequently, DRI helps reduce carbon emission intensity, fosters synergy between environmental protection and economic growth, and promotes the transition toward sustainable and high-quality development.

H4: 

Digital–real integration improves carbon productivity by optimizing resource allocation efficiency and reduces factor misallocation.

3.3. Threshold Effects of Digital–Real Integration on Carbon Productivity

Biased technological progress serves as an important catalyst for advancing the transition toward a low-carbon economy and society. On one hand, driven by profit-seeking motives, firms tend to asymmetrically enhance the productivity of specific factors, thereby reducing production costs and mitigating carbon emissions. On the other hand, biased technological change alters the marginal rate of substitution among production factors, leading to changes in their marginal productivity. This adjustment helps optimize factor allocation, reduce undesirable outputs, and indirectly improve carbon productivity. Previous studies have demonstrated that the effect of biased technological progress on carbon productivity exhibits significant stage-dependent characteristics. When the accumulation of technological progress is insufficient, its productivity-enhancing effect remains limited; however, once innovation surpasses a critical threshold, spillover and synergy effects become substantially amplified, thereby generating a distinct threshold effect [62]. This finding is consistent with economic growth theory, which posits that technological progress and efficiency improvement exhibit nonlinear characteristics, reflecting the varying capacities of economic systems to absorb and transform innovation across different stages of development [43,44,63].

As digital technologies continue to advance swiftly and become deeply embedded across industries, data has increasingly been integrated with traditional production inputs throughout the value-creation process. This integration enhances the productivity of conventional factors and has become an important engine of modern economic growth. This study further explores the influence of biased technological progress on industrial digitalization, ecological transformation, and intelligent upgrading. Using the slack-based measure (SBM) model and the Malmquist–Luenberger (ML) index to examine low-carbon technological progress in China’s industrial sector, the empirical results show that such progress exhibits a pronounced threshold pattern in shaping the influence of digital–real integration on carbon productivity. Accordingly, we contend that biased technological progress gives rise to a nonlinear nexus between digital–real integration and carbon productivity, with the magnitude and direction of this impact varying by the type of factor bias (Figure 1).

H5: 

The effect of digital–real integration on carbon productivity exhibits a nonlinear threshold pattern shaped by biased technological progress, with the marginal impact becoming more positive beyond the threshold level.

4. Research Design

4.1. Model Setup

4.1.1. Baseline Econometric Specification

Based on the identified determinants of carbon productivity and the characteristics of the dataset, the study employs a bidirectional fixed-effects framework to analyze how digital–real integration affects carbon productivity.

$${CP}_{it}=a_0+a_1{DRI}_{it}+a_2{X}_{it}+{\mu }_i+v_t+{\epsilon }_{it}$$

(1)

In this model, $i$ indexes provinces and $t$ indexes years. The dependent variable ${CP}_{it}$ measures carbon productivity for province $i$ at year $t$, and ${DRI}_{it}$ serves as a measure of digital–real integration for province $i$ at time $t$. The control vector $X_{it}$ comprises factors that may influence carbon productivity, including investment intensity, population size, foreign direct investment, and trade openness. Province-fixed effects ${\mu }_i$ and year-fixed effects $v_t$ are incorporated to address unobserved heterogeneity across provinces and over time, and ${\epsilon }_{it}$ represents the idiosyncratic error term.

4.1.2. Mechanism Model

Following Jiang (2022) [64], this study investigates the mechanisms through which the core explanatory variable influences relevant intermediaries, and specifies the corresponding econometric model as follows:

$${Med}_{it}={\beta }_0+{\beta }_1{DRI}_{it}+{\beta }_2{X}_{it}+{\mu }_i+v_t+{\epsilon }_{it}$$

(2)

In this model, ${Med}_{it}$ captures the group of mechanism variables used in the analysis, namely green technological innovation, industrial structure upgrading, and resource allocation efficiency. The evaluation of industrial structure upgrading is conducted along two dimensions, namely industrial advancement and industrial rationalization, whereas resource allocation efficiency is assessed across capital, labor, and aggregate efficiency dimensions. The remaining variables follow the same definitions as those used in Model (1).

4.1.3. Threshold Model

For robustness verification, this study adopts Hansen’s (1999) panel threshold approach to explore how biased technological progress exerts stage-specific influences on the nexus between digital–real integration and carbon productivity [65]. The following panel threshold effect model is constructed:

$${CP}_{it}={\gamma }_0+{\gamma }_1{DRI}_{it}I\left(q_{it}\le \tau \right)+{\gamma }_2{DRI}_{it}I\left(q_{it}>\tau \right)+{\gamma }_3{X}_{it}+{\mu }_i+{\epsilon }_{it}$$

(3)

$${CP}_{it}={\gamma }_0+{\gamma }_1{DRI}_{it}I\left(q_{it}\le {\tau }_1\right)+{\gamma }_2{DRI}_{it}I\left({\tau }_1<q_{it}\le {\tau }_2\right)+{\gamma }_3{DRI}_{it}I\left(q_{it}>{\tau }_2\right)+{\gamma }_4{X}_{it}+{\mu }_i+{\epsilon }_{it}$$

(4)

In this model, $I\left(·\right)$ denotes the indicator function, while the threshold variable ($q_{it}$) corresponds to biased technological progress ($BTECH$), capital–labor–biased technological progress ($BiasKL$), energy–capital–biased technological progress ($BiasEK$), and energy–labor–biased technological progress ($BiasEL$). The parameter $\tau$ represents the estimated threshold point. $X_{it}$ denotes the vector of control variables, ${\mu }_i$ captures the province-specific fixed effects, and ${\epsilon }_{it}$ represents the random disturbance term. Beyond the single-threshold framework, the model further incorporates the possibility of multiple thresholds by formulating a double-threshold specification, as shown in Equation (4).

4.2. Variable Description

4.2.1. Dependent Variable: Carbon Productivity

In line with Wang et al. (2024) and Zhou et al. (2024) [23,66], carbon productivity is measured as the ratio of gross regional product to carbon emissions, expressed in units of ten thousand RMB per ton. This measure serves as a systematic indicator that captures the relative balance between inputs and outputs and is widely recognized as a key metric of regional sustainable performance. For estimating carbon emissions, we follow the method proposed Zhu et al. (2018), calculating emissions separately from fossil-fuel combustion and cement production [67]. Fossil energy use is further divided into seven types, including coal, coke, petroleum products (gasoline, kerosene, diesel, and fuel oil) and natural gas. The corresponding calculation equation is expressed as follows:

$$CP={\displaystyle \frac{GDP}{E}}$$

(5)

$$E={\sum }_{k=1}^7{E}_k\times {CF}_k{\times CC}_k\times {COF}_k\times {\displaystyle \frac{44}{12}}+Q\times {EF}_{cement}$$

(6)

Here, $GDP$ denotes gross domestic product; $E$ represents the total amount of CO₂ emissions; $E_k$ indicates the consumption of energy type $k$ in each province; ${CF}_k$ denotes the heating value of the corresponding energy type; ${CC}_k$ represents its associated carbon content; and ${COF}_k$ indicates the corresponding oxidation factor. $Q$ stands for cement output, while ${EF}_{cement}$ represents the emission coefficient for cement production. The CO₂ emission factor for each energy type is calculated as ${CF}_k{\times CC}_k\times {COF}_k\times \left(44/12\right)$. To remove the effect of price fluctuations, GDP is deflated using the GDP deflator, with 2000 as the base year.

4.2.2. Explanatory Variable: Digital–Real Integration

The foundation of digital–real integration lies in industrial integration, which is, in turn, predicated on the technological convergence across industries. This study conceptualizes digital–real integration as a dynamic process through which the real economy increasingly incorporates digital elements, such as data and digital technologies, thereby acquiring digital attributes and continuously expanding both its intrinsic connotation and external boundaries. This study measures the extent of digital–real integration through the patent co-classification method [68,69]. From a technology-driven industrial integration perspective, technical association data are obtained through patent classification codes, and the correspondence between technologies and industries is used to map technological integration into industrial integration data, thereby measuring the level of digital–real integration. First, utilizing International Patent Classification (IPC) data, a co-occurrence matrix is established. The IPC codes, as standardized classification identifiers, are allocated by examiners to reflect the specific technological domains addressed in patent applications. The co-occurrence frequency $x_{ij}$ indicates how many times ${IPC}_i$ and ${IPC}_j$ co-occur in the complete set of patents $p$. Secondly, the International Patent Classification (IPC) codes are matched with subcategories of national economic industries. Drawing on the Reference Table of International Patent Classification and National Economic Industry Classification (2018), this study links IPC codes to their respective sub-industries and constructs an industry co-occurrence matrix $X_{ij}$ for each pair of ${IPC}_i$ and ${IPC}_j$. Subsequently, the degree of industrial integration is derived. Third, the level of industrial integration is calculated. Based on the matched industry co-occurrence matrix $R$, the co-occurrence frequency between two industries is obtained by summing across rows (or columns) within each sub-industry. The self-integration indicators of individual industries are then excluded to construct the final industrial integration matrix $Z$. Finally, the measurement of digital–real integration is established. Following the Statistical Classification of the Digital Economy and Its Core Industries (2021), the first four principal sectors of the digital economy are identified, and industries are classified into digital sectors ($D_i$) and real industries ($R_i$) according to their sub-sector codes. The sub-matrix $Z_{DR}$ is extracted from the industrial integration matrix to represent cross-sector linkages, and the aggregate integration level is derived by computing a weighted average of the industry factor values contained within $Z_{DR}$.

In addition, the study applies Pearson correlation tests to assess the validity of the primary explanatory variable. In particular, the digitally real integration ($DRI$) index constructed using the patent co-classification method is compared against provincial-level indicators of digital–real integration ($MDI$), digital economy development (DEDI), and real economy development (REDI), as well as two authoritative datasets, namely the China Academy of Information and Communications Technology index (DEI_CA) and the global digital economy index (DEI_TI).

Table A1. Pearson Correlation Test.

Variable	DRI	MDI	DEDI	REDI	DEI_CA	DEI_TI
DRI	1.0000
MDI	0.7782	1.0000
DEDI	0.9056	0.9125	1.0000
REDI	0.8046	0.9349	0.8619	1.0000
DEI_CA	0.3955	0.3681	0.3713	0.2469	1.0000
DEI_TI	0.3404	0.2542	0.2814	0.1671	0.9546	1.0000

presents the corresponding correlation coefficients—0.7782, 0.9056, 0.8046, 0.3955, and 0.3404—each of which is significant at the 1 percent level. These findings demonstrate that the DRI index adopted in this study accurately reflects regional digital–real integration levels, thereby supporting the methodological validity and reliability of the measurement approach. Moreover, this measurement system exhibits strong generalizability and can be extended to evaluate digital–real integration in other countries or regional settings.

4.2.3. Mechanism Variables

(1) Green Technological Innovation. Green technological innovation ($GTE$) is proxied by the number of authorized green patents per capita at the regional level [70]. Compared with green patent applications, authorized patents undergo a rigorous substantive examination process, providing a more accurate reflection of regional green innovation outcomes. Furthermore, the number of green innovations per capita provides a more accurate and intuitive reflection of a region’s green innovation capability [66].

(2) Industrial Structure Upgrading. Industrial structure upgrading is assessed along two dimensions: sophistication ($RIS$) and rationalization ($AIS$), following the indicators proposed by Gan et al. (2011) [71]. Specifically, Industrial structure advancement is proxied by the ratio of tertiary to secondary sector output, which reflects the overall trend in structural upgrading. Industrial structure rationalization is evaluated using the Theil index, with its calculation defined as follows:

$${AIS}_{ijt}=\sum _{j=1}^3{y}_{ijt}\mathrm{l}\mathrm{n}\left(y_{ijt}/l_{ijt}\right), j = 1, 2, 3$$

(7)

Here, $y_{ijt}$ measures the share of industry j’s output in province $i$ at time $t$ within GDP, and $l_{ijt}$ denotes its corresponding employment share. Rationalization of the industrial structure indicates enhanced sectoral coordination and reinforced inter-industry linkages.

(3) Resource Allocation Efficiency.

Efficient resource allocation refers to a state under market mechanisms in which the free flow of production factors maximizes social output, while resource misallocation reflects the deviation from this optimal allocation. Following Xu et al. (2025), Bai and Liu (2018), and Zhang and Hu (2024), this study classifies resource allocation efficiency into two dimensions based on the types of production factors: new production factors and traditional production factors [8,72,73]. Specifically, the level of data factor marketization ($Dmc$) is employed as a proxy for the allocation efficiency of new production factors, measured by software business revenue. Meanwhile, the factor misallocation index is used to represent the allocation efficiency of traditional production factors, which includes both capital misallocation ($Kmis$) and labor misallocation ($Lmis$). The calculation process is as follows:

$$Kmi\mathrm{s}={\displaystyle \frac{1}{{\gamma }_{Ki}}}-1, Lmi\mathrm{s}={\displaystyle \frac{1}{{\gamma }_{Li}}}-1$$

(8)

Among them, ${\gamma }_{Ki}$ and ${\gamma }_{Li}$ are the relative price distortion coefficients, representing the markup of resources relative to the undistorted scenario. The calculation formulas are as follows:

$${\hat{\gamma }}_{Ki}=\left({\displaystyle \frac{K_i}{K}}\right)/\left({\displaystyle \frac{s_i{\beta }_{Ki}}{{\beta }_K}}\right),{\hat{\gamma }}_{Li}=\left({\displaystyle \frac{L_i}{L}}\right)/\left({\displaystyle \frac{s_i{\beta }_{Li}}{{\beta }_L}}\right)$$

(9)

In Equation (9), $s_i=y_i/Y$ represents the share of regional output $y_i$ in province $i$ relative to the national total $Y$. The parameters ${\beta }_{Ki}$ and ${\beta }_{Li}$ capture the output elasticities of capital and labor in province $i$, respectively. Aggregate capital contribution is given by ${\beta }_K=\sum _i^N{s}_i{\beta }_{Ki}$, representing the output-share–weighted elasticity of capital. The ratio $K_i/K$ indicates the actual proportion of capital allocated to province $i$ in a given year, whereas $s_i{\beta }_{Ki}/{\beta }_K$ represents the theoretically optimal share under efficient allocation. The comparison of these two measures reflects the degree of capital misallocation across provinces. A value above one implies excess allocation of capital, reflecting higher capital utilization costs relative to the national average, while a value below one suggests insufficient allocation.

The estimation of the two-factor misallocation indices relies on the Solow residual approach, which is applied to derive the output elasticities $\beta$ of capital and labor. The estimated elasticities are then substituted into Equation (9) to calculate the relative price distortion coefficients, which are further used in Equation (8) to derive the capital and labor misallocation indices. A lower index indicates improved resource allocation efficiency. To ensure consistency in the direction of the regression results, the absolute values of the two-factor misallocation indices are used in this study.

4.2.4. Threshold Variable: Biased Technological Progress

The measurement of biased technological progress in existing research is generally approached through three methods: the standard supply-side system, the stochastic frontier analysis (SFA), and data envelopment analysis (DEA). Among these, DEA is extensively utilized owing to its non-parametric nature, independence from functional form assumptions, and ability to provide objective and accurate estimates. Building upon this, the study applies a non-radial and non-parametric approach to assess biased technological progress [74]. Detailed descriptions of all variables are provided in

Table A2. Variable Definitions and Calculation Methods.

Variable Type	Variable Name	Indicator		Specific Measure	Deflator
Explained Variable	Digital–Real Integration (DRI)	—		Patent co-classification analysis	—
Core Explanatory Variable	Carbon Productivity	—		Regional gross output/Carbon emissions	—
Mediating Variables	Green Technological Innovation (GTE)	—		Number of authorized green patents per region/Regional population	—
	Industrial Structure (IND)	Structural upgrading		Output value of tertiary industry/Output value of secondary industry	—
		Structural rationalization		Theil index	—
	Resource Allocation Efficiency	Data factor allocation efficiency (Dmc)		Software business sales revenue	—
		Capital Misallocation Index(Kmis)/Labor Misallocation Index(Lmis)	Output (Y)	R&D output	Deflated by GDP deflator
			Capital (K)	Actual R&D expenditure	Deflated by GDP deflator
			Labor (L)	R&D personnel	—
Threshold Variable	Biased Technological Progress (BTECH)	Capital (K)		Net value of industrial fixed assets	Deflated by fixed asset investment price index
		Labor (L)		Average number of industrial employees by region	—
		Energy (E)		Energy consumption per unit of GDP	—
		Desired output (Yg)		Industrial value added	Deflated by producer price index
		Undesired output (Yb)		Environmental pollution index (entropy method) based on: total industrial wastewater discharge (10,000 tons), industrial smoke and dust emissions (10,000 tons), general industrial solid waste generation (10,000 tons), and industrial SO2 emissions (10,000 tons)	—

. To incorporate environmental pollution into the production framework, this study treats each province as a decision-making unit ($DMU$), with resource and environmental elements explicitly integrated into the production process. Each $DMU$ employs $N = 3$ input factors $X = X_1, \dots , X_N$ to generate both desirable outputs $y = {(y}_1, \dots ,y_M$) and undesirable outputs $b = {(b}_1, \dots , b_I$), where the vectors $Y$ and $B$ denote the sets of desirable and undesirable outputs, respectively. For each period $t=\mathrm{1,2}, \dots , T$ and province $k=\mathrm{1,2}, \dots , K$, the input–output combination is represented as $\left(x^{k,t},y^{k,t},b^{k,t}\right)$. Accordingly, the production possibility set $P\left(X\right)$ is defined as:

$$p^t\left(x^t\right)=\{(y^t,b^t):{\sum }_{k=1}^K{\lambda }_k^t{y}_{km}^t\ge y_{km}^t,\forall m,{\sum }_{k=1}^K{\lambda }_k^t{x}_{kn}^t\le x_{kn}^t,\forall n,{\sum }_{k=1}^K{\lambda }_k^t{b}_{ki}^t=b_{ki}^t,\forall i,{\sum }_{k=1}^K{\lambda }_k^t=1,{\lambda }_k^t\ge 0,\forall k\}$$

(10)

In this framework, ${\lambda }_k^t$ denotes the weight assigned to each cross-sectional observation. When ${\lambda }_k^t$ is restricted to being non-negative and required to sum to one, the model corresponds to variable returns to scale (VRS). If ${\lambda }_k^t$ is limited solely by the non-negativity condition, the production technology is assumed to exhibit constant returns to scale (CRS). Capital, labor, and energy inputs are proxied by the net value of industrial fixed assets, average employment, and total energy consumption, respectively. The desirable output ($Y$) is measured by industrial value added, whereas the undesirable output ($B$) is captured through an environmental pollution index.

To simultaneously account for resource utilization and environmental constraints, this study adopts a non-radial, non-oriented directional distance function incorporating slack variables [75]. Based on this framework, the Slack-Based Measure (SBM) directional distance function is defined as follows:

$$D\left(x^{k,t},y^{k,t},b^{k,t},g^x,g^y,g^b\right)=\underset{s^x,s^y,s^b}{\max }{\displaystyle \frac{\frac{1}{N}\sum _{n=1}^N\frac{s_n^x}{g_n^x}+\frac{1}{M+I}(\sum _{m=1}^M\frac{s_m^y}{g_m^x}+\sum _{i=1}^I\frac{s_i^b}{g_i^b})}{2}}$$

(11)

$$\left\{\begin{array}{c}{\displaystyle \sum _{t=1}^T}{\displaystyle \sum _{k=1}^K}{\lambda }_k^t{x}_{kn}^t+s_n^x=x_{k,n}^t,\forall n\\ {\displaystyle \sum _{t=1}^T}{\displaystyle \sum _{k=1}^K}{\lambda }_k^t{y}_{km}^t-s_m^y=y_k^t\\ {\displaystyle \sum _{t=1}^T}{\displaystyle \sum _{k=1}^K}{\lambda }_k^t{b}_{ki}^t+s_i^b=b_k^t\\ {\displaystyle \sum _{t=1}^T}{\displaystyle \sum _{k=1}^K}{\lambda }_k^t=1,{\lambda }_k^t\ge 0,\forall k\\ s_n^x\ge 0,\forall n;s_m^y\ge 0,s_i^b\ge 0\end{array}\right.$$

(12)

Here, $(x^{k,t},y^{k,t},b^{k,t})$ correspond to the vectors of inputs, desirable outputs, and undesirable outputs for province $k$ at time $t$, respectively. The directional vector ${(g}^x,g^y,g^b)$ specifies the orientations of input contraction, desirable output augmentation, and undesirable output abatement. The slack variables ${(s}_n^x,s_m^y,s_i^b)$ capture the inefficiencies linked to inputs and outputs. A positive $s_n^x$ or $s_i^b$ indicates that the actual value exceeds the frontier, implying excessive input use or excessive environmental pollution. Conversely, a positive $s_m^y$ suggests that the observed desirable output does not reach the production frontier, indicating a shortfall in output performance.

Subsequently, this study employs the Malmquist–Luenberger (ML) index and its decomposition framework are applied to calculate the index of biased technological progress [76,77,78]. Building upon the SBM directional distance function, the ML productivity index is formulated as follows:

$$ML=\sqrt{{\displaystyle \frac{D^t(x^{t+1},y^{t+1},b^{t+1};g)}{D^t(x^t,y^t,b^t;g)}}\times {\displaystyle \frac{D^{t+1}(x^{t+1},y^{t+1},b^{t+1};g)}{D^{t+1}(x^t,y^t,b^t;g)}}}$$

(13)

The expressions ${\displaystyle \frac{D^t(x^{t+1},y^{t+1},b^{t+1};g)}{D^t(x^t,y^t,b^t;g)}}$, ${\displaystyle \frac{D^{t+1}(x^{t+1},y^{t+1},b^{t+1};g)}{D^{t+1}(x^t,y^t,b^t;g)}}$ correspond to the indices of efficiency variation. In turn, total factor productivity ($ML$) can be decomposed into two components: the efficiency change index ($EFFCH$) and the technical change index ($TECH$).

$$ML={\displaystyle \frac{D^{t+1}\left(x^{t+1},y^{t+1},b^{t+1};g\right)}{D^t\left(x^t,y^t,b^t;g\right)}}\times \sqrt{{\displaystyle \frac{D^t\left(x^t,y^t,b^t;g\right)}{D^{t+1}\left(x^t,y^t,b^t;g\right)}}\times {\displaystyle \frac{D^t\left(x^{t+1},y^{t+1},b^{t+1};g\right)}{D^{t+1}\left(x^{t+1},y^{t+1},b^{t+1};g\right)}}}=EFFCH\times TECH$$

(14)

In order to identify biased technological progress, this study employs the $TECH$ decomposition framework, wherein the technical change index ($TECH$) is partitioned into neutral progress ($MTECH$) and biased progress ($BTECH$) [76].

$$TECH=MTECH\times BTECH={\displaystyle \frac{D^t\left(x^{t+1},y^{t+1},b^{t+1};g\right)}{D^{t+1}\left(x^{t+1},y^{t+1},b^{t+1};g\right)}}\times \sqrt{{\displaystyle \frac{D^t\left(x^t,y^t,b^t;g\right)}{D^{t+1}\left(x^t,y^t,b^t;g\right)}}\times {\displaystyle \frac{D^{t+1}\left(x^{t+1},y^{t+1},b^{t+1};g\right)}{D^t\left(x^{t+1},y^{t+1},b^{t+1};g\right)}}}$$

(15)

$$BTECH=\sqrt{{\displaystyle \frac{D^t\left(x^t,y^t,b^t;g\right)}{D^{t+1}\left(x^t,y^t,b^t;g\right)}}\times {\displaystyle \frac{D^{t+1}\left(x^{t+1},y^{t+1},b^{t+1};g\right)}{D^t\left(x^{t+1},y^{t+1},b^{t+1};g\right)}}}$$

(16)

Building on Weber and Domazlicky (1999) [79], this study develops a factor bias index to quantify deviations in technological change across different production factors. The ratio $\left(i^{t+1}/j^{t+1}\right)/\left(i^t/j^t\right)$ captures the rate at which the marginal substitutability between factors $i$ and $j$ changes over time. The indicator $BTECH$ is employed to identify the direction of technological change, distinguishing between progress and regression, while ${Bias}_{pq}$ captures the relative bias between factors $p$ and $q$. Specifically, when $BTECH>1$, a positive ${Bias}_{pq}>0$ indicates that technological progress favors factor $p$, whereas a negative ${Bias}_{pq}$ reflects a bias toward factor $q$. Conversely, when $BTECH<1$, a positive ${Bias}_{pq}$ suggests that technological regression is biased toward factor $p$ (or progress is biased toward factor $q$), and a negative value implies the opposite. A value of $BTECH=1$ characterizes Hicks-neutral technological progress. The corresponding calculation is given as follows:

$${Bias}_{pq}=\left({\displaystyle \frac{i^{t+1}/j^{t+1}}{i^t/j^t}}-1\right)\times (BTECH-1)$$

(17)

Accordingly, using the biased technological progress index in conjunction with factor bias measures, technological advancement is differentiated into three categories: capital–labor-biased progress, energy–capital-biased progress, and energy–labor-biased progress. The subsequent analysis investigates how these distinct forms of biased technological progress generate nonlinear effects on the nexus between digital–real integration and carbon productivity.

4.2.5. Control Variables

To reduce potential biases arising from omitted variables, the study incorporates several control variables commonly adopted in prior research [4,5,17,58]. These controls include investment intensity, population size, foreign direct investment, and openness. Investment intensity ($INV$) is measured as the ratio of fixed asset investment to real GDP. Population size ($PS$) is represented by the logarithm of the permanent urban population. Foreign direct investment ($FDI$) is computed as the proportion of actual foreign capital utilized in real GDP, with provincial data converted to RMB using the average annual USD exchange rate. The openness indicator ($OPEN$) is approximated using the logarithm of the annual contracted amount of inbound foreign investment.

4.3. Data Sources and Descriptive Statistics

The study constructs a provincial-level panel dataset consisting of 30 regions in China for the period 2000–2023. Due to substantial data gaps, Tibet, Hong Kong, Macao, and Taiwan are excluded from the sample. The data are obtained from multiple sources, including the China Statistical Yearbook, China Industrial Statistical Yearbook, China Energy Statistical Yearbook, China Urban Statistical Yearbook, the official website of the National Bureau of Statistics (https://www.stats.gov.cn/, accessed on 25 April 2025), the patent application database, the China Research Data Service Platform (CNRDS), and the CEIC China Economic Database. For limited missing values in individual provinces, linear interpolation is applied to ensure completeness. In total, 720 provincial-level observations are assembled. Summary statistics for the principal variables are reported in

Table 1. Descriptive Statistics.

Variable	Definition	N	Mean	SD	Min	Max
DRI	Digital–Real Integration	720	19.3857	48.5392	0.0029	441.0297
CP	Carbon Productivity	720	1854.1630	1207.5816	205.0371	9375.2266
GTE	Green Technological Innovation	720	0.5705	1.0545	0.0037	8.8518
RIS	Rationalization of Industrial Structure	720	1.1040	0.6330	0.4944	5.6898
AIS	Upgrading of Industrial Structure	720	0.2030	0.1353	−0.2142	0.7139
Dmc	Data factor allocation efficiency	720	0.1290	0.2861	0.0000	2.6693
Kmis	Capital Misallocation Index	720	0.5738	0.5399	0.0010	6.1671
Lmis	Labor Misallocation Index	720	0.3316	0.2917	0.0004	2.3815
BTECH	Biased Technological Progress	690	1.0564	0.1069	1.0000	1.6316
BiasKL	Capital–Labor Bias Index	660	0.0094	0.0832	−0.2981	1.9884
BiasEK	Energy–Capital Bias Index	660	−0.0024	0.0122	−0.0851	0.1130
BiasEL	Energy–Labor Bias Index	660	0.0060	0.0723	−0.3073	1.7720
INV	Investment Intensity	720	2.6304	2.6685	−10.5821	12.7774
PS	Population Size, log of urban residents	720	75.1076	7.7485	51.9040	91.6775
FDI	Foreign Direct Investment	720	0.2639	4.6485	0.0004	124.5472
OPEN	Degree of Openness	720	5.9848	2.5024	−1.2894	10.5097

, and province-specific statistics for the main explanatory indicators are provided in Appendix A 

Table A3. Descriptive Statistics of Major Variables Across Provinces.

Province	DRI					CP
	N	Mean	SD	Min	Max	Mean	SD	Min	Max
Beijing	24	68.0154	73.542	2.4022	227.6915	5595.0738	1639.7977	3236.5579	9375.2266
Tianjin	24	11.2442	12.6463	0.216	39.2868	2243.6757	316.5193	1623.7842	2782.5277
Hebei	24	8.4297	12.1373	0.1238	36.6392	1161.9514	264.6863	877.3545	1868.2028
Shanxi	24	2.8729	4.3416	0.0456	13.9796	462.4271	73.7765	341.5846	579.1537
Inner Mongolia	24	1.7409	2.9771	0.0154	10.5919	530.986	325.6471	205.0371	1270.6649
Liaoning	24	8.7404	10.2186	0.381	31.8322	1498.2051	313.9967	1068.9821	2142.3563
Jilin	24	4.538	6.494	0.244	22.6187	1720.1221	247.6613	1325.9672	2160.088
Heilongjiang	24	4.0246	4.9896	0.0917	16.5338	1590.9416	446.5651	986.7488	2457.5572
Shanghai	24	37.8487	38.6245	1.0679	116.7996	3444.0658	435.9065	2946.7437	4722.5145
Jiangsu	24	77.8537	102.244	1.0908	287.9265	2293.1297	775.7811	1712.97	4214.0837
Zhejiang	24	45.6979	56.2487	0.458	164.4807	2706.1657	624.4173	2303.4512	4359.5201
Anhui	24	22.1303	31.2859	0.1219	90.7304	1427.874	371.8202	1081.2868	2335.9243
Fujian	24	17.3296	23.021	0.1311	68.0403	2904.088	1365.4895	2021.1878	6711.9557
Jiangxi	24	7.3966	11.0443	0.0386	33.3354	1817.538	594.566	1340.6807	3313.5168
Shandong	24	24.8052	34.5137	0.2687	101.5082	1758.3315	699.8248	1170.4272	3891.8218
Henan	24	12.1915	16.3944	0.0982	45.8099	1571.9815	419.8039	1198.6602	2722.8078
Hubei	24	21.1519	30.3491	0.2501	90.5158	1840.1315	341.2107	1415.7946	2930.7898
Hunan	24	12.2061	16.2487	0.1025	43.724	2139.9385	695.1969	1731.1638	4348.4646
Guangdong	24	135.7188	146.987	1.8852	441.0297	3351.6825	735.2328	2760.7966	5242.4471
Guangxi	24	4.4861	6.0956	0.049	17.3623	2058.0374	674.0843	1361.7017	3580.1241
Hainan	24	0.954	1.7082	0.0037	5.4805	2562.6821	1312.359	1648.583	6096.7782
Chongqing	24	8.6445	12.5237	0.0561	39.3126	1728.6277	347.4216	1331.5799	2389.4713
Sichuan	24	18.2655	23.2495	0.2221	73.7571	1869.9383	440.1934	1421.7267	3058.3598
Guizhou	24	3.1503	4.7844	0.0144	15.8107	739.6405	119.0006	623.9591	1043.2008
Yunnan	24	3.2378	5.1854	0.0224	17.4815	1433.0066	409.4314	1101.9901	2598.5527
Shaanxi	24	13.8352	18.6093	0.126	58.3505	1253.1974	566.6472	730.5105	2545.7319
Gansu	24	1.8789	2.831	0.0218	9.1013	1103.6632	298.8345	770.3087	1707.4884
Qinghai	24	0.6989	1.1468	0.0055	4.1915	1128.1957	410.8315	740.7208	2222.063
Ningxia	24	1.0735	1.8313	0.0029	7.2644	680.8526	884.2229	210.5389	4346.9169
Xinjiang	24	1.4097	2.248	0.0195	7.7969	1008.7403	572.4705	419.3448	2041.9394

.

5. Empirical Analysis

5.1. Baseline Test

Table 2. Baseline Regression Results.

Variable	CP
	(1)	(2)	(3)	(4)	(5)
DRI	2.5886 **	2.5495 **	2.5102 **	2.4828 **	2.4956 **
	(2.2169)	(2.2083)	(2.2132)	(2.1906)	(2.2191)
INV		−38.1519 ***	−30.9847 ***	−30.6175 ***	−33.0308 ***
		(−4.0708)	(−3.4932)	(−3.4344)	(−3.5704)
PS			−62.8993 ***	−62.5502 **	−67.5107 ***
			(−2.6014)	(−2.5822)	(−2.7252)
FDI				−3.9206 **	−3.9513 **
				(−2.1429)	(−2.1476)
OPEN					47.4856 **
					(2.3837)
Constant	1803.9807 ***	1905.0949 ***	6611.2233 ***	6585.6039 ***	6680.0877 ***
	(72.8418)	(66.6081)	(3.6425)	(3.6220)	(3.6656)
Province Effect	Yes	Yes	Yes	Yes	Yes
Year FE	Yes	Yes	Yes	Yes	Yes
N	720	720	720	720	720
R2	0.8374	0.8404	0.8419	0.8421	0.8427

**, and *** indicate significance at the 5%, and 1% levels. The values shown in parentheses represent the corresponding t-statistics.

reports the estimation results based on the two-way fixed effects specification. Column (1) provides the benchmark regression, indicating that digital–real integration exerts a significantly positive influence on carbon productivity, thereby lending preliminary support to Hypothesis 1. Columns (2)–(5) progressively introduce additional controls to mitigate omitted-variable bias. Across all specifications, the coefficient of digital–real integration remains positive and statistically significant, with its magnitude showing little fluctuation. On average, a one-unit increase in digital–real integration corresponds to an improvement of approximately 2.4956 units in carbon productivity, suggesting that integration of digital and real sectors contributes meaningfully to efficiency gains in low-carbon development. This effect is mainly attributed to the digital economy framework supported by data elements, digital technologies, and digital platforms, which enhances the accuracy and completeness of information collection in the innovation process. Consequently, this promotes higher innovation efficiency at the front end of the innovation chain, fosters an industry upgrading path aligned with green and collaborative innovation, and ultimately facilitates low-carbon and green economic development.

5.2. Robustness Test

To strengthen the reliability of the empirical findings and reduce possible sources of bias, the study conducts multiple robustness exercises, such as instrumental-variable estimation, introducing lagged explanatory variables, adding additional control variables, and modifying the sample scope.

(1) Instrumental Variable Approach. To alleviate endogeneity problems related to reverse causality, omitted variables, and sample selection, an instrumental-variable technique is used to enhance the consistency of the main results. Following previous literature [8,12], we construct an instrument by interacting annual postal and telecommunication volumes with time dummies. Additionally, considering the role of digital infrastructure investment in promoting digital–physical integration and its potential impact on carbon productivity, we introduce the lagged digital infrastructure investment (with a 1-year lag) as an additional instrument. Digital infrastructure is a key enabler of digital–physical integration, and its investment level drives the adoption and diffusion of digital technologies. By using lagged digital infrastructure investment, we mitigate potential reverse causality issues arising from contemporaneous endogeneity. Furthermore, incorporating regional fixed effects helps ensure that the instrumental variable meets both relevance and exogeneity requirements. Using the two-stage least squares (2SLS) approach, we further address potential endogeneity and verify the validity of the instruments through weak identification and over-identification tests. The corresponding results are reported in columns (1)–(2) of

Table 3. Robustness Tests (1).

Variable	2SLS		Lagged Independent Variables
	First Stage	Second Stage	Lagged by 1 Period	Lagged by 2 Periods	Lagged by 3 Periods
	(1)	(2)	(3)	(4)	(5)
IV1_DRI	6.8683 ***
	(11.7854)
IV2_DRI	35.2655 *
	(1.8948)
DRI		5.9325 ***	2.6379 **	2.9529 **	3.2850 **
		(3.4363)	(2.1658)	(2.2261)	(2.1402)
INV	1.1488 ***	−28.1050 ***	−28.6415 ***	−25.0038 ***	−21.7342 ***
	(3.5224)	(−3.7451)	(−3.3133)	(−3.0802)	(−2.9127)
PS	6.9242 ***	−66.0689 ***	−70.5653 ***	−71.1557 **	−56.9682 **
	(4.9494)	(−2.6874)	(−2.6044)	(−2.3885)	(−2.2454)
FDI	0.0802	−2.1540	−3.3028 *	−2.2114	−1.0121
	(1.0501)	(−1.3194)	(−1.8717)	(−1.4934)	(−0.9181)
OPEN	−3.9740 ***	50.3392 **	48.0202 **	45.0480 **	32.5772 **
	(−3.1942)	(2.5377)	(2.5109)	(2.4631)	(2.1503)
Constant	−700.5436 ***	9584.7947 ***	6863.4682 ***	6879.5382 ***	5841.1569 ***
	(−6.2937)	(4.8534)	(3.4262)	(3.1122)	(3.0773)
Kleibergen–Paap rk LM Statistic	62.94 ***	62.937 ***
	[0.0000]	[0.0000]
Kleibergen–Paap rk Wald F Statistic	69.63	69.631
	{19.93}	{19.93}
Hansen J statistic		0.791
		[0.3738]
Province Effect	Yes	Yes	Yes	Yes	Yes
Year FE	Yes	Yes	Yes	Yes	Yes
N	690	690	690	660	630
R2	0.7738	0.8526	0.8604	0.8758	0.8970

[ ] indicate p-values, and { } represent the critical values of the Stock–Yogo weak identification test at the 10% significance level. *, **, and *** represent statistical significance at the 10%, 5%, and 1% levels, respectively.

. Compared with the baseline estimates, the effect of digital–real integration remains significantly positive after controlling for endogeneity, confirming the robustness of our findings. Specifically, the estimated coefficient of DRI increases from 2.4965 in the baseline regression to 5.9325 under 2SLS. This substantial rise indicates that the 2SLS procedure effectively corrects the attenuation bias caused by endogeneity, thereby strengthening the credibility of the causal interpretation.

(2) Lagged explanatory variable. Considering that the influence of digital–real integration on carbon productivity may occur with a time lag, the explanatory variable is introduced using one- and multi-period lag structures. As reported in columns (3)–(5) of Table 3, the estimated coefficients stay positive and highly significant, providing additional confirmation of the robustness of the empirical findings.

(3) Adjustment of sample range. The year 2014 is generally recognized as a critical turning point in the evolution of digital–real integration [11], marked by the emergence of extensive discourse on the industrial internet. With the industrial internet steadily maturing, the incorporation of digital technologies into real-sector activities progressed into a more advanced stage. Consequently, the analysis is limited to the years 2014–2023. As reported in column (1) of

Table 4. Robustness Tests (2).

Variable	Restricted Sample	Additional Controls	Interaction Fixed Effects
	(1)	(2)	(3)
DRI	2.7887 ***	1.6334 *	3.5407 ***
	(3.0751)	(1.6580)	(6.5454)
INV	3.4886	−21.5379 ***	27.4234 ***
	(0.9968)	(−2.6380)	(3.3789)
PS	−71.3235	−74.2600 ***	−79.5055 **
	(−0.9932)	(−3.0845)	(−2.4461)
FDI	0.0076	−4.7679 ***	4.1117 *
	(0.0112)	(−2.6330)	(1.7282)
OPEN	111.4146 ***	32.8650 *	−0.0948
	(2.6708)	(1.7832)	(−0.0036)
FD		421.3340 *
		(1.7134)
INF		−153.8061 ***
		(−5.6317)
Constant	6280.5383	7813.9838 ***	7684.3427 ***
	(1.1612)	(4.3110)	(3.1570)
Province Effect	Yes	Yes	Yes
Year FE	Yes	Yes	Yes
Province-Year FE	No	No	Yes
N	300	720	720
R2	0.9653	0.8588	-

*, **, and *** represent significance at the 10%, 5%, and 1% levels, respectively.

, the estimated coefficients remain consistent and robust.

(4) Incorporation of Additional Control Variables. To reduce potential biases arising from model specification, the methodology proposed by Pang et al. (2025) is referenced, and the control variable set is further enriched by incorporating regional-level factors [16]: (i) fiscal decentralization ($FD$), measured as fiscal revenue relative to GDP, and (ii) infrastructure ($INF$), proxied by per capita road area. The results presented in column (2) of Table 4 indicate that the coefficient on digital–real integration remains significantly positive, thereby offering additional support for the robustness of the findings.

(5) Adjusted Regression Model. For additional robustness verification, an alternative panel regression is estimated by incorporating province–time interaction fixed effects into the baseline specification. The results, presented in column (3) of Table 4, show that the estimated coefficient of digital–real integration is 3.5407 and remains significant at the 1% level, thereby reinforcing the reliability of the main findings.

(6) Granger Causality Test. To examine short-term dynamics and causal direction between digital–real integration (DRI) and carbon productivity (CP), a Granger causality analysis is conducted. The outcomes, reported in

Table 5. Granger causality analysis.

Null Hypothesis	Test Statistic	p-Value	Result
DRI fails to Granger-cause CP	3.499 ***	0.0005	Reject
CP fails to Granger-cause DRI	0.557	0.5776	Accept

*** represents significance at the 1% levels.

, reveal that DRI Granger-causes CP at the 1% significance level, implying a strong short-run influence of DRI on carbon productivity. In contrast, the reverse causal effect is not supported, as CP fails to Granger-cause DRI.

5.3. Mechanism Test

Building on the theoretical framework proposed earlier, digital–real integration is posited to improve carbon productivity through three primary channels: fostering green technological innovation, enhancing the efficiency of resource allocation, and facilitating industrial upgrading. To empirically examine these transmission pathways, this study develops separate models to assess the role of each mechanism variable.

5.3.1. Green Technological Innovation

Table 6. Mechanism Analysis Results.

Variable	Med1	Med2		Med3
	(1)	(2)	(3)	(4)	(5)	(6)
DRI	0.0114 ***	0.0013 **	0.0004 ***	0.0048 ***	−0.0010 ***	−0.0011 ***
	(7.21)	(2.39)	(4.97)	(11.92)	(−2.73)	(−3.05)
INV	−0.0454 ***	−0.0164 **	−0.0055 ***	−0.0069 ***	0.0070	0.0167 ***
	(−3.72)	(-2.26)	(−3.98)	(−2.78)	(1.37)	(4.85)
PS	−0.0882 ***	−0.0753 ***	−0.0081	−0.0160 **	−0.0350 **	−0.0013
	(−3.20)	(-5.92)	(−1.46)	(−2.27)	(−2.31)	(−0.13)
FDI	0.0022 *	0.0060 ***	0.0005 ***	−0.0005	0.0001	−0.0039 ***
	(1.69)	(6.68)	(3.91)	(-1.12)	(0.03)	(−4.05)
OPEN	0.0008	−0.0351 ***	0.0125 ***	0.0045	0.0079	0.0144
	(0.05)	(-3.46)	(3.51)	(1.22)	(0.41)	(1.35)
Constant	7.0906 ***	6.9823 ***	0.7412 *	1.2275 **	3.1543 ***	0.3181
	(3.44)	(7.36)	(1.80)	(2.35)	(2.89)	(0.45)
Province Effect	Yes	Yes	Yes	Yes	Yes	Yes
Year FE	Yes	Yes	Yes	Yes	Yes	Yes
N	720	720	720	696	720	720
R2	0.810	0.857	0.775	0.872	0.529	0.451

*, **, and *** represent significance at the 10%, 5%, and 1% levels, respectively.

reports the estimation outcomes for the impact of digital–real integration on green technological innovation. Column (1) indicates that the estimated coefficient of digital–real integration is both positive and statistically significant. This evidence suggests that digital–real integration promotes carbon productivity through the channel of green technological innovation, thereby supporting Hypothesis 2. The underlying mechanism is that deeper integration of the digital and real economies reduces costs associated with temporal, spatial, and informational frictions, thereby improving the alignment between technological innovation outcomes and market demand. The resulting knowledge spillovers substantially reinforce green innovation capacity. Furthermore, the widespread adoption of green technologies not only lowers energy demand but also improves energy utilization efficiency, ultimately promoting higher carbon productivity.

5.3.2. Industrial Structure Upgrading

Table 6 (columns 2 and 3) reports the estimation results for the mechanism associated with industrial structure upgrading. Column (2) shows that digital–real integration has a positive effect on industrial structure advancement, producing a coefficient of 0.0013 that is statistically significant at the 5 percent level. Column (3) reports the estimation results for industrial structure rationalization, where the coefficient associated with digital–real integration is 0.0004 and remains positively significant at the 1% level. These findings suggest that digital–real integration facilitates both the upgrading and rationalization of industrial structures, thereby promoting structural transformation and improving carbon productivity. Hence, Hypothesis 3 is validated.

Furthermore, the results indicate that digital–real integration has a stronger effect on industrial structure advancement than on rationalization. This can be explained by the fact that integration between the digital and real economies provides a more direct impetus for advancing industrial structure, primarily by facilitating the emergence of new business models and upgrading existing industries. On one hand, new business forms, through rapid vertical and horizontal industrial differentiation, form new clusters of digital industries and drive the agglomeration of production factors into high-productivity sectors [80]. On the other hand, traditional industries with lower productivity are constrained by weak digital infrastructure and mismatched labor skills. These limitations result in a longer required coordination period for digital technologies to take effect across the industrial chain, with improvements often confined to specific segments. As such, they fall short of enabling comprehensive industrial structure optimization within a short timeframe.

5.3.3. Resource Allocation Efficiency

Columns (4)–(6) of Table 6 present the estimation results for testing the mechanism of resource allocation efficiency. The coefficients for data, capital, and labor factors are 0.0048, −0.0010, and −0.0011, respectively, all significant at the 1% level. These results indicate that digital–real integration (DRI) enhances carbon productivity by improving the efficiency of resource allocation across production factors, thereby supporting Hypothesis 4. Further analysis reveals that DRI primarily promotes carbon productivity through the improvement of data factor allocation efficiency, while the marginal effects on traditional factors such as capital and labor are relatively weak. This suggests that, with the continuous development of digital technologies and the gradual improvement of the data factor market system, DRI plays an increasingly important role in optimizing factor allocation efficiency. A plausible explanation is that DRI strengthens the matching efficiency between data and traditional production factors, reduces transaction costs and information frictions, and alleviates market distortions, thereby facilitating the optimal flow of resources across industries. Consequently, the production mode has shifted from an extensive allocation pattern dominated by single-factor inputs to a collaborative multi-factor allocation framework centered on data factors. Through this process, the overall efficiency of resource allocation has been substantially improved, accelerating the agglomeration of capital and labor toward green and low-carbon industries, and thus promoting green transformation and high-quality economic development.

6. Further Discussion

As discussed earlier, the effect of digital–real integration on carbon productivity may vary depending on the type of biased technological progress. To capture potential nonlinearities, a threshold regression model is employed for empirical analysis. In addition to examining overall biased technological progress, the analysis further decomposes it into capital–labor, energy–capital, and energy–labor dimensions to investigate threshold effects across factor types. For the threshold estimation, 100 grid points are employed, and bootstrap procedures are used to examine whether threshold values exist. As reported in

Table 7. Threshold Effect Test of Biased Technological Progress.

Threshold Variable	Number of Thresholds	F-Statistic	10%	5%	1%	Threshold Value	p-Value	95% Confidence Interval
Biased Technological Progress	Single	336.41 ***	73.142	108.218	242.083	1.0156 ***	0.000	[1.0137, 1.0161]
	Double	56.58 *	54.016	76.271	138.434	1.0382 *	0.090	[1.0362, 1.0387]
	Triple	17.53	65.350	79.005	100.464		0.860
Capital–Labor-Biased Technological Progress	Single	212.59 ***	20.029	39.671	155.904	0.0019 ***	0.000	[0.0016, 0.0020]
	Double	15.27 **	11.075	12.752	19.115	0.0061 **	0.027	[0.0050, 0.0066]
	Triple	32.32	66.969	77.943	111.653		0.487
Energy–Capital-Biased Technological Progress	Single	285.13 ***	40.887	71.759	290.216	−0.0031 ***	0.013	[−0.0033, −0.0030]
	Double	14.12 *	13.189	15.990	22.313	0.0012 *	0.077	[0.0007, 0.0013]
	Triple	14.24	38.495	45.388	61.477		0.783
Energy–Labor-Biased Technological Progress	Single	114.95 ***	23.124	36.434	78.730	−0.0015 ***	0.007	[−0.0016, −0.0013]
	Double	111.10 ***	18.201	23.458	110.876	0.0020 ***	0.010	[0.0018, 0.0020)
	Triple	10.55	32.614	36.234	45.047		0.720

F-statistics, p-values, and the critical values at the 10%, 5%, and 1% significance levels are computed via bootstrapping with 300 replications. *, **, and *** represent significance at the 10%, 5%, and 1% levels, respectively.

, both the single and double threshold models are significant, whereas the triple-threshold specification is not supported. Therefore, the double-threshold specification is selected for the empirical analysis.

Table 8. Estimated Parameters of the Threshold Model of Biased Technological Progress.

Variable	Dependent Variables: CP
	(1)	(2)	(3)	(4)
	BTECH	BiasKL	BiasEK	BiasEL
$\mathrm{DRI} (q_{it}\le {\tau }_1)$	0.1695	0.6594	23.2586 ***	21.2282 ***
	(0.3918)	(0.6100)	(18.9080)	(16.1261)
$\mathrm{DRI} ({\tau }_1<q_{it}\le {\tau }_2)$	9.5628 ***	15.7752 ***	0.5491	0.5675
	(4.4095)	(3.2589)	(0.5493)	(0.5212)
$\mathrm{DRI} (q_{it}>{\tau }_2$)	22.1572 ***	22.8575 ***	10.7214 ***	15.7239 ***
	(14.6365)	(10.0142)	(5.0366)	(3.4485)
INV	−11.1064	−6.2898	2.5956	−16.6882
	(−0.6697)	(−0.2765)	(0.1142)	(−0.7365)
PS	−144.4184 ***	−145.4366 ***	−139.2783 ***	−133.8236 ***
	(−6.2853)	(−6.0537)	(−5.4692)	(−5.3752)
FDI	−1.4808 **	427.6695	263.9529	461.2048
	(−2.3041)	(0.8562)	(0.5534)	(0.8875)
OPEN	−119.7202 **	−107.2205 **	−100.5573 **	−104.0785 **
	(−2.5845)	(−2.4375)	(−2.2358)	(−2.3889)
Constant	13,287.6400 ***	13,271.3441 ***	12,783.8124 ***	12,420.7911 ***
	(7.7679)	(7.3890)	(6.6136)	(6.6703)
Province Effect	Yes	Yes	Yes	Yes
Year FE	No	No	No	No
N	690	660	660	660
R2	0.5677	0.4908	0.5300	0.4983

**, and *** represent significance at the 5%, and 1% levels, respectively.

reports the regression outcomes, with Columns (1)–(4) presenting the estimated parameters for the models corresponding to overall, capital–labor, energy–capital, and energy–labor-biased technological progress, respectively. The estimated threshold functions for these models are visualized in Figure A1, which clearly illustrates the nonlinear relationships between digital–real integration and carbon productivity under different types of biased technological progress.

6.1. Overall Biased Technological Progress

Column (1) of Table 8 reports the threshold regression estimates for overall biased technological progress. Two threshold values, 1.0156 and 1.0382, are identified, suggesting a phased intensification of the positive effect of digital–real integration on carbon productivity. When biased technological progress is below 1.0156, the effect is statistically insignificant. Between the first and second thresholds, digital–real integration significantly promotes carbon productivity, with a coefficient of 9.5628. Beyond the second threshold, the stronger technological bias further amplifies this effect, raising the coefficient to 22.1572 at the 1% level—approximately 1.32 times higher than in the previous stage. These results imply that gains in carbon productivity from digital–real integration depend on the accumulation of a sufficient level of biased technological progress. At lower levels, digital infrastructure and technologies remain inadequate, and the participation of digital intelligent technologies in green, low-carbon innovation is limited, constraining efficiency improvements and emission reductions. Importantly, after incorporating biased technological progress into the model, the coefficient of digital–real integration rises from 2.4956 to 22.1572, confirming that biased technological progress substantially reinforces the positive role of digital–real integration in enhancing carbon productivity and functions as a critical driver of its emission-reduction effect.

6.2. Biased Technological Progress by Factor Type

Drawing on the average value of the biased technological progress index (greater than 1) and the sign of the factor-bias indices used as threshold variables, the direction of technological bias can be further identified. According to the estimates in column (2) of Table 8, the threshold values for capital–labor-biased technological progress are 0.0019 and 0.0061. The threshold effects display a stage-wise and significantly increasing pattern, consistent with the overall model. In this case, technological progress is mainly biased toward capital, and only when the degree of capital bias surpasses a certain level does digital–real integration significantly promote carbon productivity. Specifically, when the capital–labor-biased technological progress index exceeds the first threshold value of 0.0019, the positive effect of digital–real integration on carbon productivity becomes statistically significant for the first time. After surpassing the second threshold (0.0061), the estimated coefficient increases from 15.7752 to 22.8575, representing a 44.90% improvement. This indicates that a stronger capital bias substantially enhances the carbon-reduction efficiency gains brought by digital–real integration. A plausible explanation is that deeper digital–real integration requires strong digital infrastructure and the extensive application of digital technologies. When capital investment is inadequate, the diffusion and application of digital technologies are constrained, thereby limiting the capacity of the digital economy to realize its scale and multiplier effects in production processes [81].

In column (3) of Table 8, for energy–capital biased technological progress, the threshold values of the factor bias index are −0.0031 and 0.0012. When the index is below −0.0031, capital-biased technological progress significantly amplifies the positive effect of digital–real integration on carbon productivity. As the bias shifts from capital toward energy, the effect remains positive but loses statistical significance, reflecting that the capital-intensive growth model increases energy consumption and emissions, while energy-biased progress has not yet developed an effective substitution mechanism to enhance low-carbon efficiency. Beyond the second threshold, further increases in the bias index continue to reinforce the positive impact of digital–real integration on carbon productivity. This indicates that under capital-biased technological progress, the productivity-enhancing role of digital–real integration is stronger. Compared with energy-biased progress, the reinforcing effect is considerably more pronounced when technological progress is biased toward capital: the marginal impact of digital–real integration increases from 10.7214 to 23.2586, representing an expansion of approximately 1.17 times. The results for energy–labor-biased technological progress exhibit a similar pattern, characterized by a significant U-shaped threshold structure. Under labor-biased technological progress, the effect of digital–real integration on carbon productivity rises from 15.7239 to 21.2282, corresponding to a 35.01% increase. These findings further confirm the heterogeneous nonlinear responses across different types of technological bias.

Overall, the relationship between digital–real integration and carbon productivity exhibits threshold effects shaped by biased technological progress, with marked heterogeneity across bias types. Capital-biased technological progress exerts the strongest effect, followed by labor-biased, while energy-biased progress is relatively weaker. This pattern accords with factor-matching theory, which holds that the effectiveness of digital–real integration depends on alignment with factor bias characteristics. Deep integration requires robust digital infrastructure, efficient allocation of data elements, and breakthroughs in core technologies—all of which are heavily capital-driven—explaining the pronounced role of capital bias. Capital-biased technological progress exhibits stronger compatibility with digital–real integration. It not only deepens the fusion of digital technologies with the real economy through capital-intensive investment, but also mitigates carbon emission pressures by optimizing capital input structures, thereby fostering energy conservation and emission reduction [23,82]. In comparison, labor-biased technological progress provides indirect support for digital–real integration by increasing the supply of highly skilled labor and enhancing skill premiums. Nevertheless, the lengthy processes of education and skill transformation weaken its short-term effectiveness relative to capital-biased progress. In the Chinese context, energy-biased technological progress is subject to a “carbon lock-in” effect [83], which constrains its capacity to curb emissions. Only when effectively combined with digital technologies and capital inputs can it deliver simultaneous benefits of low-carbon transition and sustained economic growth.

7. Conclusions and Policy Implications

7.1. Conclusions

Using panel data for 30 Chinese provinces from 2000 to 2023, this study examines how digital–real integration (DRI) affects carbon productivity by combining theoretical insights with empirical investigation. The main conclusions are as follows:

(i) The baseline regressions indicate that digital–real integration has a significantly positive impact on carbon productivity, and this conclusion persists under a series of robustness evaluations.

(ii) The mechanism assessment shows that the increase in carbon productivity induced by digital–real integration operates mainly through three pathways: fostering green technological innovation, promoting industrial upgrading, and improving resource allocation efficiency. Among these channels, green technological innovation emerges as the principal driving mechanism. By embedding digital technologies into innovation activities, digital–real integration facilitates knowledge accumulation and the transformation of green innovation achievements, thereby simultaneously improving economic performance and environmental efficiency.

(iii) In the mechanism through which digital–real integration influences carbon productivity via industrial upgrading, the advancement of industrial structure exerts a greater effect. Digital–real integration accelerates the digitalization and intelligent transformation of traditional industries, guiding them toward high value-added and low-carbon development, and generating both technological spillover and synergistic effects. Within the mechanism of resource allocation efficiency, digital–real integration strengthens the synergy between data factors and traditional production factors such as capital and labor, optimizes the structure and utilization efficiency of production factors, and promotes the transition of industries toward greener and cleaner development.

(iv) Further analysis reveals that biased technological progress induces a double-threshold pattern in how digital–real integration relates to carbon productivity. Higher levels of bias amplify the positive contribution of DRI.

(v) The threshold effects associated with biased technological progress differ across various factor-bias categories, with capital-biased progress showing the strongest positive influence on how digital–real integration interacts with carbon productivity.

7.2. Discussion

This study still leaves several avenues for further exploration.

First, in terms of sample scope, this research employs provincial-level panel data from China to provide macro-level evidence that informs regional sustainability and policy design. Nevertheless, it lacks verification from micro-level perspectives. Most existing works have investigated digital–real integration at the regional scale, focusing mainly on green total factor productivity and green development efficiency [4,5]. Unlike earlier research, this study provides a systematic evaluation of how digital–real integration jointly affects economic outcomes and environmental performance by examining carbon productivity. Future analyses could broaden this framework by incorporating firm-level data, such as from China’s A-share listed enterprises or international samples, to enable cross-regional comparisons under different policy, infrastructure, and energy conditions. Building on firm-level evidence from Tianren and Sufeng (2024) [7], subsequent studies may also explore how digitalization differentially shapes industrial and corporate carbon performance via distinct transmission pathways.

Second, with respect to the mechanisms, this paper identifies three major pathways through which digital–real integration influences carbon productivity: promoting green technological innovation, optimizing industrial structure, and enhancing resource allocation efficiency. These findings extend existing research by offering a more detailed understanding of the underlying mechanisms. Nevertheless, due to limitations in data availability and model specification, the mechanism analysis could be further deepened. Future studies may employ moderated mediation models to examine how regional characteristics—such as industrial composition, economic development level, and digital infrastructure—shape the strength and direction of each mechanism, thereby uncovering the conditional heterogeneity in how digital–real integration enhances carbon productivity. Meanwhile, subsequent research could also focus on factor coordination and virtual agglomeration effects, emphasizing the dynamic coupling relationships among core production factors and their evolutionary patterns during the process of digital–real integration. Such analysis would provide a richer understanding of complex mechanisms governing resource allocation efficiency and innovation diffusion.

Finally, the methodological approach adopted in this study captures only a portion of the nonlinear linkage between digital–real integration and carbon productivity. Although the patent co-classification approach adopted here effectively reflects the technological linkages between the digital and real sectors, it is still subject to certain limitations inherent in the International Patent Classification (IPC) system. Differences in classification standards across countries may constrain international comparability and the granularity of measurement. Future research could extend this framework by incorporating the Cooperative Patent Classification (CPC) system to conduct sensitivity and robustness analyses, thereby enhancing data compatibility and improving the precision of digital–real integration metrics across different regions. In addition, cross-country panel models could be employed to examine how technological direction, institutional constraints, and innovation absorptive capacity interact to shape the relationship between digital–real integration and carbon productivity. Comparative studies between developed and emerging economies would help uncover the differentiated pathways and policy adaptability through which digital–real integration promotes low-carbon transformation and sustainable growth. Compared with Wang et al. (2024) [23], although both studies investigate the threshold effects of biased technological progress on carbon productivity, the present study places greater emphasis on the role and nonlinear impact of technological bias within the context of accelerating digital–real convergence. In addition, drawing on the theoretical perspective of Acemoglu and Johnson (2023) [84], future research may conceptualize technological progress as a socially directed process jointly shaped by institutional arrangements, incentive structures, and governance mechanisms. From this institutional and evolutionary perspective, future work could further explain how digital–real integration influences the directional evolution of technological progress, thereby deepening the theoretical understanding of the threshold effects of biased technological change.

7.3. Policy Recommendations

Based on the above results, several policy-oriented insights can be proposed:

First, reinforce the substantive integration between the digital economy and the real sector to create sustained momentum for sustainable development. This study finds that digital–real integration significantly enhances carbon productivity. Policymakers should focus on embedding and transforming digital technologies within industrial innovation processes and outcomes, enabling digital tools to effectively empower the real economy. At the same time, digital governance systems should be improved to foster a sound and orderly innovation ecosystem. Drawing on the experience of regions such as the European Union, integrating digital management systems with carbon governance can simultaneously enhance innovation efficiency and environmental performance, thereby providing continuous momentum for green economic transformation.

Second, cultivate new drivers of digital–real integration and broaden regional pathways toward green transformation. Policy efforts should emphasize three key mechanisms: green technological innovation, industrial upgrading, and resource allocation efficiency. For developed economies, the key task is to strengthen the sophistication and the breadth of green technological innovation. Digital–real integration should serve as a core driver of innovation, relying on mature industrial internet platforms to promote the adoption of advanced digital management tools in carbon-intensive sectors such as energy and manufacturing. This can enhance energy productivity and accelerate renewable energy substitution. Meanwhile, the synergy between digital governance and green finance should be strengthened to create an institutional environment that encourages innovation diffusion, technological spillovers, and sustained low-carbon growth. For developing and emerging economies, policy focus should shift toward building digital capacity and promoting digitally empowered industrial upgrading. Digital technologies enable the smart upgrading of conventional industries throughout the entire production chain, helping them shift toward higher value-added positions within global production networks. In addition, improving digital finance systems and developing data factor markets can enhance resource allocation efficiency, foster innovation diffusion, and accelerate regional green transformation.

Third, optimize the input structure of production factors to support a low-carbon economic transition. To begin with, investment in digital infrastructure and green R&D should be intensified. Social capital needs to be directed toward areas such as digital infrastructure, renewable energy, and low-carbon technologies, enabling firms to restructure their energy systems and enhance efficiency through capital deepening. In addition, the attraction and cultivation of high-quality human capital should be strengthened. As digital–real integration stimulates the formation of new industries and innovative business models, it becomes essential to broaden employment opportunities, strengthen labor–skill alignment, and build platforms for knowledge exchange and open innovation in order to attract and retain high-level talent. Such efforts will help upgrade the structure of human capital and facilitate the coordinated advancement of digitalization and low-carbon transformation.

Fourth, develop differentiated and phased strategies for digital–real integration based on regional technological foundations. For regions with strong innovation capacity and high levels of technological accumulation, priority should be given to deepening digital–real synergy, accelerating the application of intelligent technologies, and promoting large-scale upgrades of digital infrastructure. For regions with weaker technological foundations, efforts should first focus on strengthening basic digital infrastructure, improving human capital, and enhancing the diffusion and absorptive capacity of digital technologies. At the same time, governments should establish differentiated fiscal support systems that correspond to regional development stages and technological conditions. Regions with limited fiscal capacity may adopt a phased investment approach supported by central–local co-financing arrangements, whereas more developed regions can accelerate infrastructure deployment through diversified financing channels such as digital economy industrial investment funds, green credit instruments, and public–private partnership (PPP) models. By aligning the intensity of policy interventions with regional development stages, technological endowments, and fiscal constraints, governments can promote the productivity-enhancing and emission-reducing effects of digital–real integration in a more balanced and sustainable manner. Such differentiated strategies ensure that policy measures match regional technological foundations and development constraints, enabling digital–real integration to generate sustained and equitable improvements in carbon productivity across regions and providing stronger support for long-term efficiency gains and low-carbon benefits.