Multidimensional agglomeration, industrial digitalization, and the development of new quality productive forces: an analysis based on Marxist political economy Open Access

The world is currently witnessing a new wave of technological revolution and industrial transformation fueled by advancements in digital technologies. The deep integration of the digital economy with the real economy has emerged as a new engine for economic and social development. In this context, the nature of productive forces is undergoing profound changes. Emerging technologies such as artificial intelligence, big data, and the internet of Things are not only reshaping the combination of traditional factors of production but also giving rise to a more innovative and dynamic form of productive forces, namely, new quality productive forces (NQPF).

Agglomeration, a key feature of regional economic development, has become closely intertwined with industrial digitalization. However, existing studies have not systematically explained how industrial digitalization promotes the development of NQPF through concrete mechanisms, nor have they fully clarified the specific relationships between multidimensional agglomeration and industrial digitalization. Addressing these gaps requires both theoretical refinement and empirical validation.

Grounded in the theoretical framework of Marxist political economy, this study focuses on industrial digitalization as a new component of productive forces. It aims to uncover both the logic and practical pathways for developing NQPF while also investigating the interconnections between multidimensional agglomeration and industrial digitalization.

Theoretically, this study identifies the channels and mechanisms through which the digital economy enhances high-quality new productive forces. Specifically, it argues that industrial digitalization improves productivity through three key channels: direct production processes, indirect labor reproduction processes, and inter-industry linkages. The core mechanism lies in increasing the organic composition of capital. Furthermore, this study analyzes how agglomeration in different dimensions relates to industrial digitalization by examining three aspects: industrial agglomeration (at the industrial level), digital industry agglomeration, and overall economic agglomeration at the city level.

Empirically, drawing on the labor theory of value, this study constructs an indicator system based on input-output data covering agglomeration, industrial digitalization, and productive forces. It then employs econometric analysis to test how industrial digitalization contributes to the development of NQPF and how various forms of agglomeration relate to industrial digitalization.

The remainder of this paper is structured as follows: Section 2 provides a comprehensive review of the literature on NQPF, industrial digitalization, and agglomeration. Section 3 outlines the theoretical framework and formulates the research hypotheses. Section 4 details the econometric model, data sources, and methodology. Section 5 presents and discusses the empirical results. Section 6 concludes by summarizing the key findings and their policy implications.

Theoretical studies on new quality productive forces primarily concentrate on their formation logic and defining characteristics. First, the formation logic of NQPF can be explored from theoretical, historical, and practical perspectives. Based on dialectical materialism, Marx and Engels examined productive forces within the dynamic contradiction between production and social relations, grounding the study of productivity research in historical materialism. Historically, traditional productive forces at a certain stage of development provide the basis for the emergence of NQPF. This evolutionary process is typically accompanied by technological revolutions (Zhao and Ji, 2024). The ongoing technological revolution has not only liberated manual labor but also increasingly replaced mental labor, thereby giving rise to new qualitative features of productive forces (Ren, 2024).

Second, quantitative and qualitative dimensions can clarify the connotation of NQPF. Liu (2024) argues that emphasizing total factor productivity (TFP) improvements as a hallmark of NQPF does not negate the labor theory of value; rather, it reflects higher output and market value in price terms. There is a growing academic consensus that artificial intelligence and the digital economy constitute essential domains for developing NQPF (Wang and Liu, 2024; Wang, 2024).

Two main approaches are used to measure the new quality of productive forces. The first treats them as measurement targets and constructs an index system to evaluate their development level. The second approach considers general productive forces as the measurement target, first identifying the specific components of new quality and then assessing their impact. Most studies adopt the first approach, commonly using the entropy method to build indicator systems based on the three elements of productivity—laborers, means of labor, and objects of labor—by selecting variables from the digital economy, AI, and new energy sectors (Wang and Wang, 2024; Han and Zhang, 2024). However, such studies vary significantly in their indicator systems, making comparative research challenging.

The second approach offers greater flexibility than the first. Qiao and Ma (2024) proposed using the labor theory of value and a “labor conversion” approach to evaluate productivity with Total Labor Productivity (TLP). While TFP is widely used in existing research, it has been criticized for being detached from actual production (Shaikh, 1974; Xie et al., 2019), inconsistent with empirical reality (Young, 1992), failing to fully capture efficiency improvements (Zheng, 2007), and lacking a clear economic interpretation (Bai and Zhang, 2014). In contrast, TLP directly aligns with Marx's theory of productive forces, making it a theoretically sound and practically feasible method. Given that the components and manifestations of NQPF are still evolving, the second approach is better suited for long-term empirical inquiry.

Against the backdrop of the ongoing technological and industrial transformation, the impact of the digital economy on productivity has emerged as a key area of academic inquiry. Jiang and Jin (2022) highlight how digital technologies enhance firm efficiency and industrial coordination through service-oriented division of labor, digital twinning, and supply chain optimization. Hong and Ren (2024) conceptualize data and algorithms as digital productive forces, arguing that integration between the digital and real economies gives rise to new quality digital productive forces.

At the micro level, the majority of studies suggest that digitalization significantly enhances productivity through technological advancement and resource reallocation. Brynjolfsson and Hitt (2003) demonstrate that IT investment enhances TFP growth rates in U.S. firms, with lasting effects. Utilizing firm-level data from China, Wang et al. (2007) found that information technology investment improves firm efficiency, with the effect being scale-dependent. Bloom et al. (2012) note that U.S. multinationals achieve greater productivity gains compared to their European counterparts, primarily due to more effective IT utilization. At the macro level, Jorgenson et al. (2005) attributed U.S. economic growth to the expansion of IT capital stock. However, Acemoglu et al. (2014) argue that observed productivity gains are more closely associated with reductions in labor input than increases in technology investment.

Research findings demonstrate variability across dimensions such as firm size, management quality, and regional development. Larger firms and those with better managerial capabilities benefit more from digitization (Atrostic and Nguyen, 2005; Wang et al., 2007). Dewan and Kraemer (2000) observe that IT contributes more significantly to productivity in developed countries, whereas its effects in developing countries are more constrained. Furthermore, studies employing input–output tables at the regional and city levels also suggest that both digital equipment and services make substantial contributions to productivity enhancement (Qiao and Ma, 2024; Qiao and Liu, 2025).

Digitalization has also exerted a profound impact on labor. He et al. (2019) find that IT exhibits a strong complementary relationship with high-skilled labor, thereby enhancing productivity growth, while its substitution effect on low-skilled labor remains modest. Bai and Zhang (2021) emphasize that although digital transformation poses challenges to the rights of low- and mid-skilled workers, it also creates new opportunities.

Digitalization represents a critical strategy for firms navigating the digital economy, yet it hinges heavily on capital and human resource investment. This requires substantial investments in infrastructure, research and development, as well as workforce training (Eller et al., 2020). Firm size exerts a decisive influence on digitalization (Lashkari et al., 2024; Sommer, 2015). Large manufacturing firms possess comparative advantages owing to returns to scale (Müller et al., 2018). In contrast, small and medium-sized enterprises (SMEs) face significant constraints on resources and capabilities. SMEs often view digitalization as overly complex, costly, and irrelevant to their operations (Bley et al., 2016). The high breakeven points of digital investment may further deter SMEs from undertaking transformation (Rüttimann and Stöckli, 2016), while staggered investment strategies can complicate system integration (Sony et al., 2022). Empirical studies confirm that SMEs adopt digital technologies at lower rates than their larger counterparts (Kennedy and Hyland, 2003). Remane et al. (2017) show that larger firms with larger workforces are better equipped to pursue digitalization.

Beyond firm size, industrial clusters facilitate digitalization through knowledge spillovers and agglomeration economies, thereby enhancing innovation capabilities (Götz and Jankowska, 2017). Firms within clusters acquire and diffuse tacit knowledge more readily, often facilitated by geographic proximity and face-to-face interactions (Kogut and Zander, 1992). Clusters also foster collaboration and knowledge accumulation, thereby enhancing firms’ competitive advantage (Keeble and Wilkinson, 2000, pp. 12-13).

While firm-level studies emphasize returns to scale, an industry-level perspective reveals another important mechanism. From the viewpoint of Marxian political economy, digital inputs deployed across sectors function similarly to fixed capital. To dilute the costs of such capital and capture returns to scale, production tends to agglomerate geographically. This spatial concentration supports efficiency and facilitates expanded reproduction, indicating that industrial agglomeration may serve as a key channel through which digitalization drives productivity (Qiao and Liu, 2025).

In summary, existing studies have explored the formation logic and characteristics of NQPF, as well as how digitalization enhances productivity and how agglomeration facilitates digital transformation. However, the mechanisms by which industrial digitalization promotes NQPF, as well as the interrelationships between multidimensional agglomeration and industrial digitalization, remain underexplored. Addressing these research gaps calls for a more integrated theoretical and empirical investigation.

This study addresses these limitations in two dimensions. Analytically, it advances the understanding of the economic essence of NQPF by focusing on industrial digitalization as a core driver and exploring its productivity-enhancing pathways. It further investigates how agglomeration across industrial sectors, digital sectors, and urban economies interacts with digitalization processes. Empirically, this study adopts the second approach discussed above, measuring productivity and testing the impact of industrial digitalization as an identified component. Three types of agglomeration indicators are constructed to examine how industrial digitalization fosters industrial agglomeration and how city-level agglomeration in both the digital and overall economy accelerates industrial digitalization.

The primary contribution lies in the development of a comprehensive framework rooted in Marxian political economy. This framework integrates theoretical mechanisms, empirical strategy, and quantitative evidence to explain how industrial digitalization promotes the development of NQPF with multidimensional agglomeration functioning as an interactive factor.

Productive forces reflect humanity's capacity to utilize and transform the natural environment. On the one hand, they constitute material forces that facilitate the transformation of nature through the interaction of physical substances, thereby enabling production. On the other hand, they represent social forces whose level of development determines the stage of socioeconomic advancement.

In terms of composition, productive forces comprise three elements: laborers, means of labor, and labor objects. The latter two are collectively referred to as the means of production. However, these three elements do not constitute productive forces. Instead, they represent material components that must be organically integrated—based on a scientific understanding of natural laws—to generate effective productive capacity.

According to the labor theory of value, the value of a commodity is determined by the socially necessary labor time required for its production. The undifferentiated human labor embedded in a commodity consists of both objectified and living labor. As productive forces develop, the combination of laborers and means of production transforms, leading to greater output with less labor input. Consequently, the development of productive forces is directly manifested in increased productivity, namely, an increase in output per unit of labor time, or equivalently, a decrease in the labor time required to produce each unit of output.

Among the three elements, laborers constitute the most essential and dynamic element. Their skills and qualities play a pivotal role in driving productivity growth. Through education and training, workers develop skills aligned with contemporary demands, thereby enhancing productivity in the production process. As indicators and instruments of changes in production methods and relations, the means of labor significantly influence the development of productive forces through their continual improvement and innovation. For instance, the advent of machinery and mechanical systems has brought about a historic transformation in the means of production, substantially boosting productivity. This is because machine-based production drastically reduces the amount of objectified labor compared with labor-intensive production. Likewise, the quality of objects of labor constituting essential preconditions for production directly impacts productivity. The incorporation of new objects of labor into the production process facilitates labor conservation and enhances operational efficiency.

Changes in the combination of laborers, means of labor, and objects of labor can give rise to new industries, innovative business models, and emerging growth drivers, thereby facilitating the development of productive forces. For instance, information technologies and the Internet have fostered platform-based industrial ecosystems, transforming production from standardized mass production into diversified and customized models. Consequently, the development of productive forces encompasses both an internal transformation of their components and a reconfiguration of their combinations.

Grounded in the principles of Marxian political economy, industrial digitalization promotes the development of productive forces through three primary channels: First, digital inputs directly transform the production process. During the production phase, digital inputs interact with the means of production to substitute and economize on living labor, thereby improving productivity. Second, digital inputs indirectly influence labor reproduction. A portion of workers' wage income is directed toward the consumption of digital goods and services, which can enhance their skills and overall competence. This, in turn, improves individual labor productivity and contributes to higher overall efficiency in production processes. Third, digital inputs promote productivity through inter-industrial production networks. Specific production techniques manifest as particular input–output relations, whereby the production of any given commodity relies on inputs from other sectors. Consequently, digital input enhances productivity through interindustry linkages and production networks.

The mechanism through which industrial digitalization enhances productive forces lies in its capacity to raise the organic composition of capital—the value ratio of constant capital to variable capital—determined by the technical composition of capital. Mechanized production overcomes the physical, precision, and endurance limitations of manual labor, driving a leap in industrial productivity.

In this context, technological change typically reflects tendencies of increased capital intensity and labor-saving. The rising technical composition of capital leads to a sustained increase in its value. In the digital economy era, novel forms of means of production—exemplified by artificial intelligence—establish the material and technical conditions for intelligent machines to substitute human labor, for machines to produce machines, and for the development of machine-centered production networks.

Moreover, industrial digitalization expands the scope of objects of labor by incorporating new elements such as data, while ongoing advancements in algorithmic innovation, such as machine learning, continuously improve intelligent production processes. Consequently, through the enhancement of the organic composition of capital, industrial digitalization can significantly enhance productivity.

Industrial digitalization not only transforms traditional modes of production but also fosters the emergence of new industrial forms, serving as a catalyst in developing NQPF. This transformation is closely associated with industrial agglomeration. Existing studies show that larger firms and economies demonstrate distinct advantages in the digitalization process (Lashkari et al., 2024). Qiao and Liu (2025) offer systematic empirical evidence that production agglomeration within industrial sectors is the key mechanism through which digitalization promotes productivity. Notably, these studies vary in their analytical perspectives and research field. To further contribute to this line of inquiry and explore how city-level agglomeration—as an external contextual factor—influences industrial digitalization, this study incorporates and comparatively analyzes three forms of agglomeration: industrial agglomeration, urban digital industry agglomeration, and urban overall economic agglomeration.

Industrial agglomeration refers to the geographic concentration of specific industries in particular regions and cities. Industrial digitalization necessitates substantial investments in non-transferable digital equipment to achieve automation, digitization, and intelligent production. Such equipment entails high fixed capital costs and is subject to economies of scale. Agglomeration enables the distribution of these fixed costs across a larger number of firms, thereby lowering the digital investment entry threshold. It also improves equipment utilization, minimizes idle capacity, and shortens capital turnover cycles, ultimately enhancing capital efficiency. Furthermore, it facilitates information flow, accelerates knowledge diffusion, and fosters technological spillovers, allowing digitally transformed industries to achieve productivity gains at an accelerated pace. In conclusion, industrial digitalization plays a crucial role in promoting industrial agglomeration.

Urban digital industry agglomeration denotes the geographic concentration of digital industries in cities. It encompasses not only the clustering of digital enterprises but also the concentration of complementary digital infrastructure and services. Agglomeration optimizes information infrastructure, accelerates data transmission speeds, and lowers communication costs, thereby providing essential material support for industrial digitalization.

As digital industries become increasingly concentrated in urban areas, information flows improve in efficiency, the diffusion of digital technologies accelerates, and the pace of industrial digitalization quickens. Urban digital industry agglomeration is thus both a manifestation of digital industrialization and a foundational support for industrial digitalization, driven by infrastructure development and network effects.

Urban overall economic agglomeration generally refers to the expansion of a city’s economic scale. On the one hand, it drives the upgrading of urban infrastructure and facilitates the concentration of key resources such as talent, capital, and technology, which are essential drivers of digital industrialization and the digital transformation of industries. On the other hand, the expanded market demand resulting from economic agglomeration encourages firms to increase their digital investments. To address large-scale and diverse consumer demands, firms leverage digital tools to optimize product design and enhance the intelligence of the production process. This results in increased output and improved service quality, thereby driving both industrial digitalization and urban economic growth.

Based on the aforementioned theoretical analysis, this study formulates the following testable hypotheses:

This study investigates the role of industrial digitalization in fostering the development of NQPF. According to the Statistical Classification of the Digital Economy and Its Core Industries (2021), issued by the National Bureau of Statistics of China, the digital economy consists of two key components: digital and industrial digitalization. Digital industrialization encompasses sectors such as the manufacturing of computers, communications, and other electronic equipment, as well as telecommunications and broadcasting services, which constitute the material foundations of the digital economy. Industrial digitalization, by contrast, refers to the application of digital technologies and data resources in traditional industries to enhance output and productivity ^[1].

Based on this classification, the study identifies two primary categories of digital inputs: digital devices, which represent manufacturing sectors that produce digital infrastructure, and digital services, which encompass information transmission, software, and related services. These inputs are further classified into direct digital inputs, which are incorporated directly into the production process, and indirect digital inputs, which are consumed in labor reproduction. These four types of inputs are considered manifestations of industrial digitalization and function as explanatory variables for assessing the impact of industrial digitalization on productivity.

To quantify this relationship, a two-way fixed effects model is employed to examine the impact of each type of digital input, in conjunction with inter-sectoral production networks, on relative total labor productivity. The econometric specifications are presented as follows:

where $i$⁠, $j$ and $t$ denote industry, city, and year, respectively. $TLPRijt$ denotes the relative total labor productivity of sector $i$ in city $j$ at time $t$⁠; $Dijt$ represents different relative digital input ratios: digital device input, digital service input, direct digital input, and indirect digital input; $oTLPijt$ is the weighted average TLP of all other industries in other cities, calculated based on direct consumption coefficients; $uij$ and $vt$ denote industry-city effects and year fixed effects, respectively; $εijt$ is the error term. The use of relative TLP and the digital input ratio enables the model to control structural differences across industries.

This study further examines the role of agglomeration in industrial digitalization through a three-dimensional framework: Industrial agglomeration denotes the spatial concentration of specific industries within urban areas; urban digital industry agglomeration reflects the geographic clustering of digital industries and infrastructure; and urban overall economic agglomeration captures the aggregate expansion of total economic activity at the city level.

Similarly, by employing a two-way fixed effects model, we first examine the impact of industrial digitalization on agglomeration at the industrial level. Subsequently, we analyze how urban digital agglomeration and overall economic agglomeration influence the extent of industrial digitalization. The econometric model specifications are presented as follows.

where $Dijt$ retains its definition as the digital input level, indicating the degree of industrial digitalization. The variable $priijt$ denotes industrial agglomeration, calculated as the share of industrial output value in total urban production. $Aggijt$ encompasses urban agglomeration indicators: $dlqijt$ represents digital industry agglomeration, measured by the location quotient (LQ) of digital industries, and $ppijt$ denotes overall economic agglomeration, measured by the total production value. Detailed calculation methods for these indicators are elaborated in section 4.3.

The empirical analysis is conducted using input-output tables for prefecture-level cities in China for the years 2012, 2015, and 2017, obtained from the Carbon Emission Accounts and Datasets (CEADs) database. The dataset encompasses 313 cities and 42 industries. Drawing upon the principles of Marxist political economy, these industries are divided into 33 productive and 9 non-productive sectors.

To calculate value-added and production prices, the following procedures are applied: Labor time is estimated by integrating input-output data with data from the China Labour Statistical Yearbook; Intermediate s are adjusted to align with the structure of domestic production, and consumption matrices are constructed based on the expenditure patterns of urban and rural households.

The distinction between productive and non-productive labor derives from sectoral classification. Although mixed labor forms may exist across sectors, data limitations necessitate maintaining this dichotomy. This analysis refrains from differentiating simple and complex labor for two reasons: first, empirical exchange ratios between labor types are unavailable; second, inter-industry transactions obscure inherent differences in labor complexity. This methodological alignment conforms to established practices in empirical Marxist research (Feng, 2016; Qiao et al., 2022).

Okishio (1959) established that the value embodied in a unit of output across all sectors corresponds to the sum of the materialized and living labor expended in its production. This concept of unit value is calculated based on production input coefficients. Building upon this theoretical framework, Ochoa (1989) extended the model by incorporating fixed capital and accounting for its depreciation. In this study, we employ the SON (Sraffa-Okishio-Nakatani) method to address the treatment of fixed capital, integrating an endogenous depreciation rate. This approach synthesizes and extends the foundational contributions of Sraffa (1960), Okishio and Nakatani (1975), as well as Li (2017).

Here, $A$⁠, $D$⁠, $L$ and $λ$ represent the matrices of intermediate inputs, fixed capital depreciation, labor inputs, and value coefficient, respectively. Since $A$ and $D$ quantify materialized labor, $(A+D)λ$ denotes the amount of materialized labor measured in working hours. $L$⁠, measured directly in terms of working hours, reflects the new value generated by living labor. $λ$ is derived using the Leontief inverse matrix. While this model is based on calculations involving physical input coefficients, the scarcity of physical input-output data necessitates their substitution with value-based input matrices adjusted according to market prices, following the approach proposed by Marelli (1983). Consequently, the results are interpreted as working hours per monetary unit, leading to the derivation of the value coefficient matrix $λ$⁠.

After clarifying the methodology for value calculation, the city-level and national-level values for each industrial sector can be computed separately. The city-level value is calculated based on $AC$⁠, $DC$⁠, $LC$ for each city. Assuming there are $m$ cities and $n$ industrial sectors in a country, $AC$ and $DC$ are the matrices of $(n×m)×(n×m)$⁠, and $LC$ is the matrix of $(n×m)×1$⁠. The national-level value necessitates computation based on specific period averages of national $AN$⁠, $DN$ and $LN$⁠. To achieve this, the aggregation eliminates city-level dimensions from national-level input-output tables, preserving only the industrial sector dimensions, thereby reflecting the national average productivity. Consequently, $AN$ and $DN$ are the matrices of $n×n$⁠, and $LN$ a matrix of $n×1$⁠. Using these methods, the matrix of the value coefficient for cities $λC$ and the matrix of the value coefficient of the nation $λN$ can be computed.

Production prices are determined through the equalization of the profit rate, adhering to the principle that equivalent amounts of capital should generate equivalent profits. Production prices consist of cost prices and the average profit rate. The calculation procedure is outlined as follows:

The depreciation rate of fixed capital $φi(r)$ is a function of the interest rate $r$ and can be calculated based on the depreciation period $τi$⁠. The generalized input coefficient matrix $M(r)$ embodies the condition of uniform profit rates across all sectors. $φ(r)$ is a diagonal matrix of $φi(r)$⁠. Let $I$ denote the identity matrix, $K$ the fixed capital stock coefficient matrix, and $b$ the real wage matrix. Let $p$ denote the vector of production prices, which correspond to the eigenvector corresponding to the eigenvalue 1 of the matrix $M(r)$⁠. According to the Perron–Frobenius theorem, there exists a unique non-negative eigenvector that carries economic significance. However, any positive scalar multiple of the eigenvector $p$ is also an eigenvector corresponding to the same eigenvalue, which requires further normalization to uniquely determine $p$⁠.

To uniquely determine the production price vector $p$⁠, the condition that the total value equals the total production price is imposed. The calculation method is presented as follows:

Let $x$ denote the gross output vector of productive sectors, and let $x′$ represent the aggregate gross output vector of all sectors. The national economic system consists of both productive and non-productive sectors. While the creation of value is exclusive to productive sectors, all sectors participate in the process of profit rate equalization. Consequently, value calculations are confined to the productive sectors, whereas production price calculations must encompass all the sectors within the economic sector.

Grounded in the labor theory of value, this study introduces a labor conversion framework to Total Labor Productivity (TLP), an indicator of productivity levels. Within this framework, the means of production utilized during the production process are conceptualized as embodied labor and are converted into labor time. This value is then combined with the living labor time contributed by workers, yielding the total labor input (L). TLP is subsequently measured as the amount of output generated per unit of total labor time, providing a basis for assessing changes in productive forces over time.

Let $λijt$ denote the value contained in one unit of currency of the sector $i$ in the city $j$⁠; its reciprocal represents the monetary expression of labor time. This value is defined as $TLPijt$ shown in Equation (9). To enable meaningful comparisons of TLP across different years, cities, and sectors, we compute the national average level of TLP in the sector $i$⁠, across all cities for a given year, denoted as $TLPitAverage$⁠. Taking the sector- and city-specific $TLPijt$ as the numerator and $TLPitAverage$ as the denominator, we derive the relative TLP, $TLPRijt$⁠, as shown in Equation (10).

Next, we identify industrial digitalization. Drawing upon the concept of digital industrialization as outlined by the National Bureau of Statistics of China, and based on the sector classification detailed in the input-output tables, the sector responsible for supplying digital devices is identified as the “Communication Equipment, Computers, and Other Electronic Equipment” sector. Correspondingly, the sector delivering digital services is categorized under the “Information Transmission, Software, and Information Technology Services” sector. As indicated by the aforementioned analysis, digital inputs across all sectors can be classified into two categories: direct inputs, which are associated to the production process itself, and indirect inputs, which pertain to the reproduction of labor. Both categories of input originate from the digital device and digital service sectors.

Table 1 presents the input indicators developed in this study to quantify cross-sector digital inputs.

Equations (11) and (12) specify the calculation methods. These indicators measure the share of digital qualitative inputs within the inputs of each sector and city, based on production price ratios. The subscript $i(i∈n)$ denotes the sector, $pi$ represents the national production price of the sector $i$⁠, and $Xij$ denotes the total output of the sector $i$ in the city $j$⁠. Consequently, $piXij$ represents the total production price. $pdd$ and $pds$ denote the national production prices of the digital device sector and the digital service sector, respectively.

The calculations are based on input-output data, where $Dij$ and $Dij′$ represent intermediate input matrices; $Cij$ and $Cij′$ denote wage consumption matrices, all measured in monetary terms. Specifically:

$Dij$ denotes the intermediate input from the digital devices sector to sector $i$ in city $j$⁠, while $pddDij$ represents the total production price paid by sector $i$ in city $j$ for digital devices, indicating the direct digital device input. $Dij′$ denotes the intermediate input from the digital services sector to sector $i$ in city $j$⁠, and $pdsDij′$ is the total production price paid by sector $i$ in the city $j$ for digital services, reflecting the direct digital service input. Similarly, $pddCij$ and $pdsCij′$ represents the indirect digital device input and the indirect digital service input, respectively.

In summary, the four indicators defined in Equation (11), namely $ddd$⁠, $dds$⁠, $idd$⁠, and $ids$ represent the shares of direct digital device input, direct digital service input, indirect digital device input, and indirect digital service input, respectively. Let $dd$ and $ds$ denote the total shares of digital device input and digital service input, respectively. Similarly, let $di$ and $indi$ represent the overall shares of direct digital input and indirect digital input, respectively. Consequently, the overall share of digital input $dtotal$ can be obtained by aggregating these classifications. To ensure comparability of digital input shares across years and sectors, the national average levels of each digital input for the sector $i$ are used as denominators. The ratios of the sector- and city-specific shares to these national averages reflect the relative levels of digital device input $ddrijt$⁠, digital service input $dsrijt$⁠, direct digital input $dirijt$ and indirect digital input $indirijt$⁠.

Further consideration of the impact of the production network based on inter-sectoral linkage leads to the formulation of Equation (14), which presents the calculation method for the direct consumption coefficient $α$ between sectors. In this context, $piXij$ denotes the total production price of sector $i$ in city $j$⁠, $px$ denotes the production price of sector $x$ at the national level, $Axy−ij$ represents the intermediate input from sector $x$ in city $y$ to sector $i$ in city $j$⁠. Accordingly, $pxAxy−ij$ represents the total production price of this intermediate input. The coefficient $αxy−ij$ reflects the extent of direct consumption between city-sector pairs, thereby indicating the strength of interconnections within the urban industrial network. Equation (15) employs the direct consumption coefficients as weights to calculate a weighted average of aggregate labor productivity for all city-sectors that provide inputs to the sector $i$ in city $j$⁠, excluding the weighted productivity of the sector $i$ in the city $j$ itself. This results in the weighted average TLP $oTLPijt$ of other city-sectors relative to the sector $i$ in the city $j$⁠. This indicator enables analysis of how productivity improvements in other sectors and cities within the production network influence the productivity of a specific sector in a specific city.

This study examines the impact of three dimensions of agglomeration on industrial digitization. Equation (16) defines the calculation method for industrial agglomeration, which can be represented by a city's share within the overall industry. Specifically, it is measured as the ratio of the total production price of the sector $i$ in the city $j$⁠, namely, $piXij$⁠, to the national total production price of the sector $i$⁠, namely, $∑j=1piXij$⁠. Equation (17) outlines the calculation method for city-level digital industry agglomeration. The digital industry agglomeration level in the city $j$ is determined using the location quotient (LQ) of its digital sector, $dlq$⁠.The numerator represents the share of the total production price of the digital sector in the city $j$ relative to the city's total production price, while the denominator is the share of the national digital sector production price relative to the national total production price. This indicator measures the relative concentration of the digital economy in the given city. A value greater than 1 indicates that the city's digital economy agglomeration exceeds the national average, while a value below 1 suggests a lower-than-average level of agglomeration. Equation (18) measures the city-level overall economic agglomeration, proxied by the city's total production price, serving as an indicator of the city's economic scale.

Table 2 presents the descriptive statistics of the variables. Owing to missing or anomalous values in certain input-output data during the calculation process, the final sample size is smaller than the maximum number of city-sector observations covered by the input-output data ^[2].

This study investigates the effects of digital device input, digital service input, direct digital input, indirect digital input, and the aggregate TLP of other city-sector pairs within the production network on the relative TLP of a specific sector in a specific city. Columns (1) to (5) of Table 3 report the regression results based on Equations (1) and (2), while Columns (1) to (4) of Table 4 present the results based on Equation (3). All regressions control for individual (city sector) fixed effects and time fixed effects.

The results in Tables 3 and 4 indicate that digital device input, digital service input, direct digital input, and production network linkages have a significant positive effect on the relative level of TLP. In contrast, indirect digital input suppressed the relative level of TLP.

According to the earlier theoretical analysis, the core mechanism through which industrial digitalization promotes productivity development is consistent with the theory of machine-based large-scale industry as articulated in Marxist political economy. Investment in digital devices, the auxiliary role of digital services, and the integration of direct digital inputs into the production process collectively create favorable conditions for the substitution of labor by machine. Consequently, digital device input, digital service input, and direct digital input drive an increase in the organic composition of capital, thereby enhancing production efficiency.

However, because indirect digital input influences the reproduction process of labor power, an increase in indirect input leads to higher variable capital costs in production, which in turn reduces the organic composition of capital, thus hindering the improvement of current production efficiency.

The organic composition of capital, determined by the technical composition of capital, is represented by the ratio of constant capital $C$ to variable capital $V$⁠, with its calculation method provided in Equation (19).

Consistent with the baseline regression, this study employs a fixed-effects model to examine the roles of the organic composition of capital and spatial production agglomeration as underlying mechanisms. The regression model is specified as follows:

Table 5 presents the results of the mechanism test. The regression outcomes reveal that digital device input, digital service input, and direct digital input exert significant positive effects on the organic composition of capital, whereas indirect digital input exhibits a negative impact. The coefficient and significance level of $ln⁡oTLP$ demonstrate that productivity improvements in other sectors contribute to an increase in the organic composition of capital within the sector under study. This observation is consistent with the theory of machine-based large-scale industry, which posits that the application of machinery and the formation of machine systems can enhance production efficiency by elevating the organic composition of capital.

Given that an increase in indirect digital input may reduce the organic composition of capital and thus exert a short-term suppressive effect on productivity, the observed negative impact of indirect digital input on productivity in the current period aligns with theoretical expectations. From a long-term perspective, however, indirect digital input contributes to the enhancement of workers' skill levels and overall quality, thereby positively affecting labor productivity.

Equation (21) presents the calculation formula for labor productivity $LP$⁠, where $Xijt$ denotes the total output value (measured in monetary terms), and $Lijt$ denotes the total hours of living labor input (measured in hours). Accordingly, $LPijt$ represents the output generated per unit of living labor hour and serves as an indicator of labor productivity.

Based on this, this study further analyzes the long-term effects of digital input on labor productivity. Specifically, an empirical model is developed, incorporating current-period digital inputs as independent variables and future-period labor productivity as the dependent variable in order to assess the long-term impact of digital inputs on labor productivity.

The regression results reported in Table 6 indicate that digital device and digital service inputs have no significant impact on future labor productivity. When examining the effects of current-period direct and indirect digital inputs, the results show that the current direct digital input tends to constrain future labor productivity, whereas the current indirect digital input contributes positively to future labor productivity.

By integrating these findings with the earlier analysis of the effects of direct digital input in the production process and indirect digital input in the labor reproduction process on the organic composition of capital, the role of indirect digital input can be summarized as follows: on the one hand, an increase in indirect digital input reduces the organic composition of capital in the current production period, which is not conducive to the improvement of current TLP; on the other hand, it contributes positively to enhancing future labor productivity. The impact of direct digital input exhibits the opposite pattern.

As previously discussed, the theoretical framework of this study identifies industrial agglomeration at the industry level as a key mechanism through which industrial digitalization promotes the development of productive forces. Meanwhile, city-level digital industry agglomeration and overall economic agglomeration are regarded as the driving forces behind industrial digitalization.

The results presented in Table 7 suggest that digital device input significantly promotes industrial agglomeration, whereas digital service input does not demonstrate a statistically significant impact. Moreover, direct digital input positively contributes to industrial agglomeration, whereas indirect digital input exerts a negative effect.

This finding can be attributed to the structural adjustment of production inputs induced by digitalization: as industrial digitalization advances, industries increase their investment in digital devices and elevate the proportion of direct digital inputs within the production process—inputs that exhibit the characteristics of fixed capital. Production tends to concentrate geographically in order to dilute unit production costs and fully realize returns to scale.

In contrast, digital services are inherently less reliant on spatial proximity due to their capacity to transcend time and space constraints. Indirect digital input, which corresponds to wage-related expenses, not only displaces direct digital input but also facilitates remote work, exerting a negative effect on industrial agglomeration.

To build upon existing studies that consider returns to scale at the firm level as a driving force of digitalization, and to address potential endogeneity arising from the bidirectional causality between industrial digitalization and industrial agglomeration, this paper introduces an instrumental variable (IV), i.e. $dtotal̅it×phonej$⁠. It is constructed as the interaction between the average level of total digital investment $dtotal̅it$ in the sector $i$ in year $t$ and the number of fixed-line telephones $phonej$ in the city $j$ as recorded in 1984. Fixed-line telephones serve as an initial mode of Internet access, influencing the city's capability and readiness to adopt digital technologies without directly impacting current productivity levels. To simplify the interpretation of the endogeneity correction results, the total digital investment level of the city-industry pair was used as the explanatory variable to access the causal impact of industrial digitalization on industry-level agglomeration. Table 8 reports the results of the instrumental variable estimation for the two-step GMM. The first-stage regression confirms the validity of the selected instrument, and the second-stage regression demonstrates that industrial digitalization significantly promotes industry-level agglomeration.

The results reported in Table 9 indicate that enhanced urban digital industry agglomeration significantly promotes digital device, digital service, direct digital, and indirect digital inputs. As digital sectors within cities expand and mature, digital infrastructure becomes more complete, and the diffusion of digital technologies accelerates, thereby laying a solid foundation for increased digital investment across various industrial sectors.

On the one hand, improved accessibility to digital devices and services facilitates greater adoption; on the other hand, an optimized digital economic environment also strengthens firms' willingness to adopt digital tools, thereby promoting simultaneous growth in both direct and indirect digital inputs.

The regression results presented in Table 10 indicate that the improvement of a city's economic development significantly promotes digital device input, digital service input, and direct digital input. Conversely, it exhibits a suppressive effect on indirect digital input. The scale effects and capital accumulation resulting from economic development encourage cities to prioritize digital devices, digital services, and direct inputs in the production process. As a result, there is a displacement of indirect digital inputs linked to the labor reproduction process.

Drawing on the principles of Marxist political economy, this study analyzes how industrial digitalization contributes to the development of NQPF. IT also explores the interplay between multidimensional agglomeration and industrial digitalization. The theoretical framework posits that digital inputs—representing components of the new productive forces—promote productivity through three primary channels: direct impacts on production processes, indirect effects on labor reproduction, and diffusion through industrial linkages. The core mechanism underlying this productivity enhancement is the increase in organic composition of capital. Furthermore, this study investigates how industrial digitalization facilitates industrial agglomeration, and how urban digital industry agglomeration and overall economic agglomeration accelerate the process of industrial digitalization.

Empirically, this study initially employs TLP to measure the overall development level of productive forces. It then identifies digital inputs as a proxy for new quality factors and quantifies their levels. Subsequently, the study constructs a set of indicators to assess the degree of agglomeration across three dimensions of the industry. Finally, drawing on input-output data encompassing over 300 Chinese cities and 33 production sectors, the study conducts an econometric analysis to provide empirical validation for the theoretical mechanisms. The key findings are as follows: (1) industrial digitalization significantly promotes the development of NQPF; (2) the key mechanism through which this occurs is the increase in the organic composition of capital; and (3) industrial digitalization promotes industry-level agglomeration, while city-level digital and economic agglomeration accelerates the process of industrial digitalization.

To further harness the digital economy in fostering NQPF, corresponding transformations of production relations are essential. The following policy recommendations are proposed:

First, deepen reforms within the science and technology system and strengthen innovation as the driving force of the digital economy. This involves advancing an innovation-driven development strategy, improving the new nationwide system for innovation, enhancing intellectual property protection, accelerating the commercialization of digital technologies, and reforming education and talent development systems, with a special emphasis on establishing world-class digital talent hubs and innovation centers.

Second, deepen economic reforms to create a more favorable environment for the development of digital economy in the region. This entails establishing mechanisms for the distribution of returns from emerging production factors, such as data, regulating and supporting the platform economy, fostering an ecosystem of innovation centered around technology-based enterprises, and creating the necessary infrastructure and institutional safeguards for the development of NQPF.

Third, construct a modern industrial system. This requires advancing new industrialization through smart and green development, industrial clustering, and smart city construction, while accelerating progress towards building a strong manufacturing nation. Digital industrialization and industrial digitalization should be advanced in a coordinated manner, promoting the in-depth integration of the digital economy with the real economy, and closely monitoring the trends of technological and industrial revolutions. Strategic support should focus on emerging and future industries, such as algorithms, computing power, and new energy. The “AI+” model should be utilized to empower traditional sectors, and agglomeration development should be leveraged to achieve comprehensive industrial transformation and upgrading, thereby enhancing the nation's core competitiveness through the advancement of NQPF.