Spatial spillover effects of the digital economy on the green total factor productivity of China’s manufacturing industry

The rapid expansion of the digital economy has garnered significant attention because of its potential to drive high-quality advancement in traditional sectors, particularly manufacturing. This study examines the spatial dynamics and potential spatial disparities between the digital economy and green total factor productivity (GTFP) in China’s manufacturing sector. We utilize a novel set of indicators to assess the advancement of the digital economy during Chinese provinces and apply spatial econometric models to investigate its spatial influence on GTFP. The main research content and conclusions of this study are as follows. (1) By employing a novel index system to quantify the digital economy’s advancement level within the manufacturing sector across various provinces in China, and utilizing it as the primary explanatory variable, the index system demonstrates significant efficacy in empirical analysis and is both scientifically robust and methodologically sound. (2) Using the spatial Dubin model, this study analyzes the spatial effects of the digital economy on the GTFP of the manufacturing sector and finds that it has a dominant positive spatial spillover effect on the GTFP of the manufacturing industry nationwide. (3) The results show that the effects of digital economy advancement on GTFP in the manufacturing industry have a positive spatial spillover effect in the eastern and central area, whereas it is negative in the western area. This study extends the applicability of the new economic geography and imperfect competition theories to the digital economy era, thereby contributing to these academic fields. Moreover, it introduces a novel analytical framework for assessing the digital economy’s influence on manufacturing advancement. The findings provide valuable insights and policy recommendations for fostering the development of the digital economy advancement across diverse regions in China.


Introduction
The swift advancements in information technology have catalyzed the digital economy, positioning it as a pivotal engine for global economic expansion (Cheshmehzangi et al 2022, Guo et al 2022, Huang et al 2022, Mubarak and Suomi 2022).In recent years, the accelerated expansion of the digital economy has emerged as a pivotal feature of China's macroeconomic landscape, significantly transforming production organization methods and altering the lifestyles of its populace (Shen andZhang 2022, Wang andSun 2023).The further advancement of the digital economy should receive higher attention at the national level (Qi and Liu 2020, Xian and Wang 2022, Varlamova and Kadochnikova 2023).The economic advancement paradigm in China is transitioning from a rapid to a high-quality model, with the digital economy poised to serve as a key driver of sustainable economic growth during this pivotal historical era (Wang and Cen 2022, Dong and Liu 2023, Su et al 2023, Yin and Zhao 2024a).Undoubtedly, the digital economy is poised to emerge as the primary catalyst in advancing the level of sustainable growth and eco-friendly development within the manufacturing sector (Li et al 2022, Liu et al 2023, Yu et al 2023, Gong and Du 2024).
Several in-depth studies have been conducted on how the digital economy promotes high-quality development in the manufacturing sector.Furthermore, numerous empirical analyses have been performed by the academic community.In these studies, total factor productivity (TFP) and green total factor productivity (GTFP) are commonly used as core explanatory variables in the empirical analysis.The GTFP serves as a more robust metric for assessing the environmental sustainability of the manufacturing industry, as it amalgamates energy utilization, pollution discharges, and industrial economic advancement, thus rendering it extensively utilized in academic research.
Multiple empirical studies have substantiated that the progression of the digital economy exerts a beneficial influence on green development and production efficiency within the manufacturing sector.Analyzing provincial panel data from China, Xia et al (2018), Huang et al (2019) and demonstrates that the digital economy plays a pivotal role in ameliorating resource misallocation, diminishing transaction and distribution expenses, fostering innovation capabilities, and ultimately augmenting manufacturing sector's GTFP.From the perspective of industrial integration, Wang and Li (2024) emphasized the significance of integrating the manufacturing sector with producer services, facilitated by the digital economy, as a pivotal strategy for elevating TFP in manufacturing.This perspective is corroborated by scholars such as Li et al (2022), Huang et al (2022), Guo et al (2022), Su et al (2023), and Gong and Du (2024), who validated these findings at the micro level using data from listed enterprises.Zdražil and Kraftová (2022) explores the impression of the digital economy on productivity from an international perspective and finds that it enhances the economic competitiveness of Europe and China, with China's digital economy substantially surpassing that of European countries.Cheng and Qian (2021) and Li and Su (2023) found that there is a threshold effect in the relationship between digital economy and GTFP, that is, once the advancement of digital economy reaches a certain level, its role in promoting GTFP in manufacturing industry will be more effective.Furthermore, Hao et al (2022) considered external shocks, such as COVID-19, and found that the digital economy can still raise manufacturing industry's GTFP by ameliorating green technology efficiency despite such disruptions.At the regional scale, researchers have scrutinized the provincial variations in digital economy's effect on manufacturing sector's green advancement.Yang and Zeng (2022) utilized the effect of digital economy on TFP between regions by analyzing provincial data from 2011 to 2018 in China, and found that regions with advanced technological infrastructure are more able to take advantage of the advantages of the digital economy.In a similar vein, Hu et al (2022) used 10-year data from 30 provinces in China to examine the spatial association between the digital economy and TFP.Their findings corroborate those of Yang and Zeng (2022), affirming that the digital economy is a crucial role in enhancing TFP.However, the magnitude of its impact varies due to regional disparities.Ma et al (2023) focused on the Yellow River Basin, revealing notable discrepancies in the GTFP of the manufacturing industry among cities, attributed to the difference in resource distribution and the gap in economic aggregate.Additionally, some researchers utilized enterprise-level data to corroborate the findings of the aforementioned studies (Dong et al 2023, Yu et al 2023).
The above research robustly supports the notion that the digital economy is the crucial path to enhancing GTFP within the manufacturing sector.These studies provid both theoretical and empirical evidence that is instrumental for advancing the green advancement of this industry and holds significant referential value.Nevertheless, prior research exhibits certain limitations, which can be primarily categorized into two main aspects.(1) The index systems developed by similar researches to assess the advancement of the manufacturing digital economy primarily reflect the regional digital economy's progress.However, they overlook the specific advancement level of manufacturing within that region.Consequently, the applicability of these index systems requires further validation.(2) While regional-level research on the impression of digital economy advancement on the manufacturing industry's GTFP considers regional heterogeneity, it fails to quantitatively analyze the spatial correlation between the two.This oversight may result in neglecting spatial dependence and spillover effects, thereby diminishing the regional relevance of policy recommendations.
This study can improve these objective shortcomings in previous research to make some marginal contributions to existing similar research.Firstly, this study develops a novel index system that accounts for both provincial disparities in digital economic advancement and the digital economy's impression on the manufacturing sector across different area.This addresses the omission in previous studies that failed to incorporate the manufacturing industry's digital economy advancement level.Consequently, this index system is more comprehensive and enhances existing research.Additionally, by considering both regional and manufacturing development, it provides a more precise representation of the spatial relationship between the manufacturing sector's digital economy advancement and GTFP, offering a new analytical perspective for related studies.Secondly, this study will leverage new economic geography and growth pole theory, employing the spatial Durbin model to conduct spatial econometric analysis on the correlation between the manufacturing sector's digital economy advancement level and GTFP.Furthermore, it will investigate the heterogeneity of this relationship across different area.The empirical analysis aims to elucidate the intrinsic connection and spatial association between the digital economy's advancement and GTFP, providing empirical support and recommendations for regional manufacturing development, environmental protection, and energy utilization.
This study enhances the concepts of New Economic Geography Theory and Growth Pole Theory.New Economic Geography Theory focuses on the spatial connections and interactions of economic activities and highlights regional development disparities.Our spatial measurement and regional heterogeneity analysis deepen the understanding of the digital economy's mechanisms across different area, underlining the importance of spatial dependence and spillover effects in the digital economy era.Additionally, this research offers new empirical support for regional development imbalances within new economic geography.Moreover, it furnishes empirical evidence for the formation and effect of digital economy growth poles, further enriching the theory's connotations and application scenarios.
Section 2 reviews existing research methodologies and proposes hypotheses.Section 3 develops a spatial econometric model, detailing the research metrics and data sources.Section 4 conducts an empirical analysis.Section 5 investigates regional variations in spatial spillover effects across Eastern, Central, and Western China.Section 6 provides policy recommendations.

Literature review and research hypotheses
2.1.Literature review 2.1.1.Index system selection Although there is no unified and authoritative index system for measuring the advancement of digital economy at this stage, the academic practice is more consistent in the selection of some indicators.Commonly selected metrics include the quantity of mobile phone users, mobile Internet users, optical cable length, Internet access ports, software business revenue, and ICT investment, all of which reflect the advancement level of the regional digital economy (Wen and Chen 2020, Zhao et al 2020, Cheng and Qian 2021, Ceng et al 2023, Yin and Zhao 2024b).However, as mentioned in section 1, these indicators only compute the advancement level of the digital economy in a certain area.To reflect the development level of the digital economy in the regional manufacturing industry more comprehensively, relevant indicators of the manufacturing industry must be added to the current indicators.Some researchers' results provide theoretical and methodological support for measuring the digital economy advancement level in the manufacturing sector.Qi and Liu (2020) and Dai (2020) have demonstrated that the essence of the digital economy lies in leveraging digital technologies to generate and exploit data elements.Consequently, the formulation of an index system must take into account the industry's capabilities in data production and utilization.Qing et al (2022) argued that data, as a virtual factor of production, cannot be invested in production links with traditional production management modes; thus, to achieve a digital economy that enables production, enterprises need to constantly improve their information management ability and awareness.Wang (2019) also noted that whether enterprises can realize information management is also an intuitive reflection of whether the industry can carry out digital transition.The research of Xu and Li (2022) is similar to that of the above scholars, and the digital platform, digital industry, and other factors are included in the digital economy index evaluation system they have constructed.Huang et al (2023) synthesized prior academic perspectives and identified pertinent metrics to evaluate the advancement of the digital economy within the manufacturing sector across three key dimensions: data production capacity, data utilization capacity, and information management capacity.Employing this index framework, they conducted an empirical analysis to examine the relationship between the progression of digital economy in manufacturing and GTFP, uncovering significant results.

Spatial correlation between the digital economy and GTFP
Current research lacks extensive analysis on the spatial relevance between the advancement extent of the manufacturing's digital economy and GTFP.However, given that pollution emissions and energy consumption are critical determinants of GTFP (Shi et al 2018, Zhang et al 2022, Mao et al 2023), we can derive research hypotheses and empirical insights from the effects of the digital economy on production output, pollution emissions, and energy consumption.
Research demonstrates that the proliferation of the digital economy exerts a substantial spatial spillover effect on output growth and regional economic advancement.Luo and Zhou (2022) conducted a spatial econometric analysis using provincial data from China, revealing that the digital economy serves as a pivotal driver for regional economic growth, especially pronounced in economically advanced provinces.This finding is corroborated by Hu et al (2022) and Dong and Liu (2023).Additionally, Xu and Li (2023) employed provincial data to regression analyzed the effect of the digital economy on manufacturing innovation output, discovering that it enhances manufacturing innovation with varying degrees of effect across different provinces.
Second, digital economy advancement can effectively reduce regional environmental pollution and energy consumption.Xu et al (2022) employed simultaneous spatial equations and generalized three-stage least squares (GS3SLS) to investigate the correlation between the digital economy and environmental pollution across 287 prefecture-level cities in China from 2008 to 2018.They found that the digital economy reduced environmental pollution through green and innovative advancement impressions and a significant spatial-spillover-effect was also observed.Sun et al (2022), and Wang and Sun(2023) obtained similar results.Chen (2022) analyzed data from 276 Chinese cities to demonstrate that digital economy advancement boosts clean energy use, the study further revealed that advancements in a city's digital economy significantly enhance the proportion of clean energy use in neighboring cities.Zhao et al (2024) demonstrated the inhibitory effect of the digital economy on energy use and highlighted the significance of this effect in achieving high-quality regional economic growth.
Drawing on the aforementioned literature, we propose that the advancement of digital economy within regional manufacturing can enhance output while diminishing energy consumption and pollutant emissions, consequently boosting GTFP.This shows that the regional-manufacturing-sector's digital progression may produce spatial spillover effects on GTFP.Given the distinct variations in resource endowment, economic development, and policy support across different area, these spillover effects are likely to exhibit regional heterogeneity.Following the methodologies of Luo and Zhou (2022) and Hu et al (2022), our research employs a spatial econometric model to examine this hypothesis.

Research hypotheses
2.2.1.Spatial spillover of the digital economy on high-quality manufacturing development Based on the above literature review, we argue that the digital economy progression in the regional manufacturing sector can enhance the GTFP in geographic space and demonstrate spatial spillover effects, which can be supported by new economic geography and growth pole theory.
The principles of new economic geography theory assert that the spatial distribution of economic activities and regional development is uneven, shaped by determinants such as transportation accessibility, economies of scale, and market interactions.The establishment of digital infrastructure has notably decreased information and communication costs, thereby amplifying the economies of scale in manufacturing (Brette and Moriset 2009, Foresman and Luscombe 2017, Zhou et al 2022).This not only enhances the manufacturing development level in specific sectors but also disseminates innovation and productivity gains to adjacent regions through interconnected networks and data transmission (Guo and Jiang 2023, Mikhaylova and Hvaley 2023, Varlamova and Kadochnikova 2023).This spatial spillover effect manifests as technological innovations and knowledge accumulation in central areas that rapidly diffuses to neighboring areas through digital networks, enabling manufacturing industries in these areas to use advanced digital tools and resources to improve their production efficiency and management levels (Wilson 2017, Tang et al 2021).As a result, the digital economy serves as a regional dissemination catalyst that fosters economic integration and enhances high-quality manufacturing development by mitigating information asymmetry and lowering transaction costs (Zixun Yahong 2021).
Growth pole theory, originally proposed by French economist François Perroux in the 1950s, is a regional economic development theory.The core idea is that, within a specific region, some economic activities (growth poles) have strong innovation and investment capabilities that attract various resources and radiate to surrounding areas, thus driving local development and creating spillover effects (Jian 2008).Growth poles generally refer to key industries or business clusters within a region that have advantages in terms of technology, management, and capital accumulation (Chinyamakobvu et al 2018).Much like magnets, these core industries or businesses attract labor, capital, technology, and other resources to the region through forward and backward linkages in the industry chain, thus forming the pivot driving force for regional development (Benedek et al 2022).Growth pole theory offers strategic guidance for governmental regional development planning and industrial layout to some extent, suggesting that the government can support the priority development of certain key industries or regions through investment and legislative means to promote overall economic growth.
Thus, the new economic geography and growth pole theories provide positive theoretical guidance for this study.Both theories recognize that the economic growth of specific growth poles will drive the development of surrounding areas, creating spillover effects (Wei-guan 2015, Wenlong 2012).
In practical terms, the ongoing enhancement of digital infrastructure has substantially lowered the obstacles and expenses linked with data resource-sharing and the transfer of digital technologies.This advancement in the digital economy not only elevates the manufacturing advancement level within a specific area but also propels the high-quality growth of manufacturing in adjacent areas, thereby exhibiting a regional diffusion effect, also known as the spatial spillover effect.Digital infrastructure construction is a prerequisite for achieving data interconnectivity and interoperability, as well as ensuring the circulation and sharing of data elements among areas.First, digital infrastructure construction helps improve the speed and efficiency of digital transmission within and between areas, breaking down information barriers and promoting information exchange and coordination between local and other regional manufacturing industries, thereby raising the level of manufacturing development overall.Second, digital infrastructure construction provides convenient conditions for cross-regional technological innovation and intellectual mobility.Enterprises can engage in remote collaboration and online research and development (R&D) using digital technologies, attract highquality intellectual resources from surrounding areas to participate in local manufacturing development, promote technological innovation and knowledge-sharing, and enhance the quality of manufacturing development.Furthermore, the construction of digital infrastructure can facilitate cross-regional environmental monitoring and management, thereby promoting regional green development and cooperation.Governments and enterprises can use digital technology to monitor environmental conditions in surrounding areas in real time, achieve policy coordination and resource-sharing between areas, and carry out environmental protection and management actions together, thereby promoting regional green production and sustainable development.Thus, the following hypothesis is proposed: Hypothesis 1: The digital economy has a spatial spillover effect on high-quality manufacturing development.

Regional heterogeneity of digital economy spillover the high-quality manufacturing development
The preceding literature review emphasized the regional disparities in the spatial effects of the digital economy on enhancing output, reducing energy use, and lowering pollution emissions.Consequently, we postulate that the spatial influence of digital economy advancement in regional manufacturing on GTFP may also exhibit regional heterogeneity.This perspective can be further elucidated through the frameworks of new economic geography theory and growth pole theories.
The new economic geography theory and growth pole theories both indicate the significant imbalance in economic activities and development levels between areas, suggesting that this imbalance leads to variations in economic structures within areas.
From the viewpoint of the growth pole theory, the digital economy, by creating new growth poles (e.g., hightech parks and innovation centers), can attract and concentrate high-end talent, capital, and information, forming new clusters of economic activity (Albiman and Sulong 2017).These growth poles have become the core concepts for the high-quality advancement of the manufacturing industry, and through the interconnection of industrial chains and the diffusion of innovative results, they produce spatial spillover effects on the surrounding areas.However, owing to differences in infrastructure, human resources, and industrial foundations among areas, this spillover effect exhibits heterogeneity, meaning that areas closer to the growth poles with better foundations can absorb and utilize this technology and knowledge more effectively, thereby achieving high-quality advancement.
From the perspective of new economic geography, the digital economy reduces the spatial cost of information transmission and transactions, thereby intensifying the trend in economic activity concentration (Zhou et al 2022).This concentration affects productivity and innovation capabilities between areas, leading to spatial disparities in the quality of manufacturing development.Specifically, regions that can more effectively utilize digital technologies and integrate broader market and resource networks, such as metropolises and advanced economic belts, will enjoy faster, high-quality development owing to economies of scale and network effects.In contrast, regions with lower development levels and insufficient digitization may face slower development speeds, exacerbating regional heterogeneity (Liu et al 2023).Therefore, the spatial spillover effects of the digital economy are not uniformly distributed but show differences related to regional conditions and the degree of digital economy integration.This viewpoint is also explained by imperfect competition.The theory of imperfect competition focuses on the heterogeneity of different types of firms, suggesting that, owing to inherent differences between firms, they exert varying influences within their respective niche markets.Furthermore, owing to these objective differences, industries respond differently to digital economy advancement (Huang et al 2023).Similarly, each region forms its own niche market, and, owing to differences in regional resource endowments, economic development gaps, and workforce quality, the same industry can have different influences in different areas.Accordingly, the digital economy can have heterogeneous effects on the same industry in different areas.
The theoretical underpinnings and analytical frameworks for examining the interplay between digital economy advancement and regional disparities in high-quality manufacturing are rooted in new economic geography, growth pole theory, and imperfect competition theory (Kim et al 2019).China's vast territory and diverse regional conditions such as geography, history, and policy ensure that the impression of the digital economy on manufacturing advancement will inevitably exhibit regional heterogeneity.
The eastern region of China possesses substantial advantages in the realm of digital-economy-advancement.To begin with, this area boasts a higher level of economic prosperity, a robust industrial foundation, and market strengths that collectively create conducive conditions for the advancement of digital economy.Furthermore, the eastern region's dense population and elevated educational standards provide a rich reservoir of talent essential for digital economic growth.Additionally, Eastern China exhibits a high degree of openness to international markets, facilitating the influx of foreign capital, technology, and managerial expertise, which further accelerates digital economic progress.Concerning infrastructure, this region has historically seen earlier and more substantial investments compared to other areas, resulting in more extensive and sophisticated digital infrastructure coverage, thereby establishing a favorable hardware environment for digital economic activities.Lastly, the governmental policy support in the eastern region is particularly robust, fostering innovation and encouraging the proliferation of the digital economy, thereby amplifying the region's competitive edge.
China's central region is similar to the eastern region.although the overall economy is smaller compared to the east, It also has well-developed digital infrastructure, a large high-quality labor force, and a complete industrial development foundation Thus, the central region has some advantages over the eastern region in terms of land prices and labor costs.Therefore, digital economy development also has tremendous potential in China's central region.
The western region of China experiences lower economic development and a weak industrial foundation, coupled with insufficient technological advancements, resulting in a significant lag in the growth of digital economy compared to the eastern and central areas.Additionally, the region's lower average education level fails to provide the necessary intellectual support for digital economic progress.Remote geography and complex terrain lead to elevated logistics costs, further hampering the advancement of digital infrastructure in the west.Therefore, digital economy advancement in the western region has been relatively slow to date.However, the western region has abundant power and land resources, making it highly suitable for the deployment of largescale digital economy core facilities, such as big data centers, that require high power consumption.This requires the western region to choose a different path of digital economy development from the central and eastern areas, meaning that the impression of digital economy development on manufacturing in the west will differ from that in central and eastern areas.
In summary, the following hypothesis can be proposed: Hypothesis 2: The digital economy has a spatial spillover effect on the high-quality advancement of the manufacturing industry, which exhibits regional heterogeneity.The global Moran's index can explore the spatial autocorrelation relationship of an entire spatial dataset and can be used to determine whether a general association in space exists among all observations within a region.The value of the global Moran's index should be between [−1, 1].A positive value means a positive spatial relevance and a negative value means a negative spatial relevance.The global Moran's index is calculated as follows:

Research design
where N represents the number of samples, which in this study represents 30 provincial administrative units; W ij is the spatial weight matrix; x i and x j are the indicator values of provinces i and j, respectively; and x ̅ is the average value of all indicators.
The local Moran's index is used for identify the overall level of spatial clustering or dispersion within a specific area.The local Moran's index results are generally reported as Moran's scatter plots.Moran scatter plots reveal spatial autocorrelation by comparing the characteristic values of spatial units with the weighted averages of their neighboring units.The first and third quadrants represent spatial clustering, which is the gathering of characteristic values in space, revealing the clustering effect of similarity.The second and fourth quadrants represent spatial heterogeneity, the difference in characteristic values from those of neighboring units, highlighting structural differences in the space of the study object.The local Moran's index is calculated as follows: where Moran I i ¢ represents the local Moran's index of province i, N represents the number of samples, which in this study corresponds to 30 provincial administrative units, W ij is the spatial weight matrix, x i is the indicator value of province i, and x ̅ is the average value of all indicators.

Choice of spatial econometric model
A spatial econometric model was established to test the spatial correlation between the digital economy and high-quality manufacturing development.The formula for the model is as follows: + where gtfp i t , represents the GTFP of the manufacturing sector in province i in year t, measures the level of high- quality manufacturing advancement in that province.ide i t , represents the level of digital economy advancement in the manufacturing industry of province i in year t.W m n , is a spatial weight matrix.b represents the correlation coefficient corresponding to the independent variable.r and q are spatial relevance coefficients, l is the spatial error coefficient, i t , m and i t , e are random error terms, with i t , e following a normal distribution.0 a is the intercept term.
Based on the different values of , r q and l in the model, the following three different spatial econometric models are often used.When r≠0, q≠0, l = 0, the spatial Durbin model (SDM) should be used; when r ≠ 0, q = 0, l = 0, the spatial autoregressive model (SAR) should be used; when r = 0, q = 0, l ≠ 0, the spatial error model (SEM) should be used.In the following sections, an appropriate model is selected to conduct a spatial econometric analysis based on the actual test results.

Core explanatory variables
The core-explanatory-variable in our research is the digital economy advancement level of the manufacturing industry in each province.Previous literature reviews demonstrated that to insure the comprehensiveness of the research findings, the combination of explanatory variables needs to rounded consider the advancement levels of the provincial and manufacturing digital economies.Zhao et al (2020) constructed an index system to evaluate the regional digital economy advancement levels.The index system has easy data acquisition and good research effects and has been extensively used in similar studies in the academic community.Huang et al (2023) built an index system to evaluate the digital economy advancement level in an industry, and this index system has achieved good results in various applications.Therefore, this study integrates these two index systems to build an index system for the advancement level of the regional manufacturing digital economy that meets the research objectives and requirements.The indicator systems used in this study are listed in table 1.The entropy method is an disinterested weight distribution method widely used in multi-attribute decision analysis, with several advantages.First, it does not rely on any subjective judgment but is entirely based on the information distribution of the data itself to determine weights, thereby avoiding the uncertainties and biases brought by subjective weight setting.Second, the entropy method can fully utilize the information of indicators by quantifying the differences and amount of information between indicators, ensuring that the contribution of each indicator is fully considered.Finally, by converting indicators into relative weight values, the entropy method can intuitively compare the strengths and weaknesses of different indicators or evaluation objects, making the results easy to interpret.Therefore, our research uses the entropy method to estimate the level of digital economy advancement in Chinese manufacturing subindustries.

Core explained variable
The core explained variable in our research is the overall GTFP of the manufacturing industry in China's provincial administrative units.
Following the existing literature, the GTFP of provincial manufacturing was determined by SBM-Malmquist model.Compared to the limitations of the traditional super-efficiency DEA-SBM model, the SBM-Malmquist model can capture the dynamic changes in GTFP over time, enabling the analysis of efficiency changes over multiple periods and expanding the depth of related research.
The Malmquist index calculation formula is as follows: Referencing existing studies in the same category, this study selects the stock of material capital, number of industry employees, and total energy consumption as input items.The output of industrial is selected as the desired output item, with chemical oxygen demand and sulfur dioxide emissions as the undesired output items.Table 2 displays all indicator items.The stock of material capital is calculated in section 3, and other data are sourced from the Statistical Yearbook of China, Industrial Statistical Yearbook of China, and Environment Statistical Yearbook of China.

Spatial weight matrix construction
The construction of a spatial weight matrix is a precondition for conducting spatial econometric analysis.The spatial weight matrix is primarily used to express the positional relationships and interaction intensities between spatial units and serves as a key tool for revealing and quantifying the interactions and spatial correlations between geographical entities.By constructing a reasonable spatial weight matrix, spatial econometric models can more effectively capture the autocorrelation of spatial data, thus providing a scientific basis for regional development planning and socioeconomic decision-making.The basic form of the spatial weight matrix W is defined as follows: There are four common types of spatial weight matrices.

Geographic contiguity matrix
A geographic contiguity matrix is constructed based on the contiguity conditions between spatial units.In this matrix, if two spatial units are geographically contiguous, the corresponding relationship is assigned a value of 1; otherwise, it is set to 0. The advantage of this matrix is its simple setup that intuitively reflects the basic contiguity between spatial units, thereby making spatial econometric analysis operations more convenient.However, its deficiencies are also clear.The geographic contiguity matrix does not reflect the specific distances or economic ties between contiguous units.Thus, an economic analysis may result in information loss.Therefore, in research scenarios that require an in-depth exploration of the interactions between spatial units, this may lead to biased conclusions.
In the geographic contiguity matrix, the elements of the matrix indicate whether two corresponding provinces are adjacent, usually denoted by 1 for adjacent provinces and 0 for non-adjacent provinces.The geographic contiguity matrix is created as follows: 0, if province i and province j are not adjacent 1, if province i and province j are adjacent 7 ( ) =

Geographic distance matrix
A geographic distance matrix is formulated based on the actual distances between spatial units.Each element in this matrix signifies the distance between two specific spatial units, often measured using Euclidean distance or other geographic metrics such as road mileage, railway mileage, or travel time.The primary advantage of this matrix is its ability to more precisely represent the intensity of interactions between spatial units, as real-world spatial interactions typically diminish with increasing distance.Consequently, this matrix offers more granular insights for spatial econometric analysis compared to the geographic contiguity matrix.However, the geographic distance matrix has certain limitations.First, its calculation is relatively complex and its construction requires considerable effort.Second, it only accounts for the distance factor, and as transportation develops, the influence of spatial distance on regional development tends to decrease.Thus, when applied to regional economic analysis, the resulting quantifications may incorporate a degree of inaccuracy.
In the geographic distance matrix, the distances between the capital cities of the corresponding provinces are first calculated based on their latitude and longitude; then, the reciprocal is taken.The calculation formula is as follows: where d mn represents the geographic distance between the capital cities of the provinces m and n.

Economic distance matrix
Unlike the geographic contiguity and distance matrices, which are based on geographic spatial concepts, the economic distance matrix considers the economic ties between spatial units.It typically defines the distance between spatial units based on economic indicators.In this matrix, the smaller the economic distance between two spatial units, the closer their economic links, and the higher the corresponding matrix weight.The economic distance matrix can more accurately depict the economic interactions and dependencies between spatial units.Therefore, compared to the geographic contiguity and geographic distance matrices, the economic distance matrix is more suitable for regional economic analysis.However, the economic distance matrix has certain limitations.First, similar to the geographic distance matrix, the economic distance matrix requires a large amount of accurate economic data to construct, which involves extensive calculations and significant workload.Second, economic distance can also change with policy and market changes, implying a strongly dynamic nature.Thus, the economic distance matrix needs to be updated regularly to maintain its accuracy.
Third, the diversity and complexity of economic factors mean that using a single economic distance indicator makes it difficult to cover all economic interactions comprehensively, hence the need to combine multiple indicators to more fully reflect economic distance.
In the Economic distance matrix, the weights are based on the per capita GDP difference between the corresponding provinces.The calculation formula is as follows: where Y mn represents the per capita GDP difference between provinces m and n.

Economic and geographic nested matrix
The economic and geographic nested matrix integrates the advantages of economic and geographic distance matrices, considering the geographical and economic ties between spatial objects.This provides a more comprehensive reflection of the hierarchical and diverse economic connections between spatial units, which is beneficial for revealing the unevenness of regional development and the spatial distribution pattern of economic activities.Thus, economic and geographic nested matrices are often used in spatial econometric research.
Based on the geographic distance and economic distance matrices, each element value from both matrices is recombined using a weight of 0.5 to construct the economic and geographic nested matrix.The calculation formula is as follows: To ensure the rigor of the research, the rationality of the four matrices are tested separately, and the most appropriate matrix for is selected for subsequent research.

Control variables
Based on existing literature, six control variables are selected for the study.Based on the frameworks established by Deng et al (2022) and Ceng et al (2023), the level of industry openness (open) is quantified by the ratio of the primary business revenue generated by foreign enterprises to the total primary business revenue of the industry.Drawing on the works of Hu et al (2022), Wang and Cen (2022), and Wang (2022), we incorporate the industrial technology scale as a control variable, denoted by the logarithm of the industry's current year's R&D expenditures (lrd).Following Peng and Wang (2019), the industrial labor force scale control variable (llab) is introduced, using the logarithmic form of the current year's average industry employment.In line with the research of Lu and Xu (2019), He et al (2022), and Wang et al (2022), the current year's industrial pollution control facility operation costs in logarithmic form are selected to reflect the effect of environmental regulation (hjgz).Drawing on the approaches of.Li and Zhou (2021), Li et al (2022), and Wang and Li (2024), the industrial structure control variable (cyjg) is chosen, represented by the proportion of the secondary industry's output value to the regional gross product.Influenced by the ideas of Peng and Wang (2019), Ceng et al (2023), Liu and Song (2023), and Wang and Li (2024), the government intervention degree control variable (zfgy) is selected, represented by the logarithm of the average fiscal budget of manufacturing enterprises.
The indicators used in the study and their descriptive statistics are shown in table 3. The findings presented in tables 4 and 5 reveal that, irrespective of the type of spatial weight matrix used, Moran's I for the GTFP of China's 30 provincial administrative units is significantly positive at the 10% level for the majority of years from 2011 to 2021.Likewise, for each year within the same period, Moran's I for the digital economy advancement level (ide) of these units is also significantly positive at the 10% level.This indicates a strong positive spatial correlation between the advancement of the digital economy and high-quality manufacturing industry across the provinces, thereby substantiating the use of spatial econometric models in this research., ** , and * denote significance at the 1%, 5%, and 10% levels, respectively.The numbers in parentheses are robust standard errors.The same applies below.

Data description
In addition, the data from tables 4 and 5 demonstrate that the economic geographical nested matrix is the most effective spatial weight matrix.Hence, future research will utilize this matrix as the spatial weight matrix.

Local moran's index
Using Stata 17 software combined with formula (2), the local Moran's index for GTFP and the level of digital economy advancement (ide) of the manufacturing industry in China's 30 provincial administrative units from 2011 to 2021 are calculated.Figures 1 and 2 show the local Moran's indices for manufacturing GTFP and IDE in 2021, respectively.
The analysis presented in figures 1 and 2 reveals that a substantial number of provincial administrative regions display both elevated GTFP and advanced digital economy advancement, predominantly situated in the 1st and 3rd quadrants.This shows a pronounced positive local spatial relevance.Consequently, this justifies the employment of a spatial econometric model in this research.

Spatial econometric models selection
Spatial econometric models include spatial Durbin models (SDM), spatial autoregressive models (SAR), and spatial error models (SEM).Further testing is required to determine which model is suitable for the research content of this study.

LM test
The LM test can report the LM-Error and LM-Lag statistics.When both were significant, the chosen dataset exhibited both spatial error correlation effects and spatial lag correlation effects, suggesting that the SDM should be used for econometric analysis.Table 6 presents the LM test results.All four test results pass at the 1% significance level, indicating the preliminary selection of the SDM for further analysis.

Hausman test
The Hausman test is used to determine whether the model should adopt fixed or random effects.If the Hausman test is significant at the 10% level or the chi 2 value is negative, a fixed-effects model should be used; otherwise, a random-effects model is a better selection.Table 7 presents the Hausman test results.
Table 7 indicates that the dataset selected for this study passed the Hausman test at the 1% level; hence, a fixed-effects SDM was adopted.

Wald test
The Wald test is employed to assess whether SDM reduces to SAR or SEM.If the Wald test is significant at the 10% level, SDM will not collapse into SAR or SEM.Table 8 displays the Wald test outcomes.
Table 8 shows that the dataset chosen for this article passes the Wald test at the 1% significance level, meaning that SDM constructed using this dataset will not collapse into SAR or SEM.Based on the combined results of the three tests above, our research adopts SDM with fixed effects.

Baseline regression results
Using Stata 17 software, a spatial econometric analysis was conducted on the selected dataset using SDM with fixed effects.The baseline regression results are presented in table 9.
The regression outcomes displayed in table 9 illustrate that, upon considering various spatial weight matrices, the coefficient for the variable ide is positive at the 1% significance level, means that spatial factors substantially enhance the GTFP of regional manufacturing, driven by advancements in the digital economy within provincial manufacturing sectors.The spatial effect coefficient W * ide is also positive at the 1% level, means that improvements in the digital economy within provincial manufacturing can positively influence the high-quality advancement of regional manufacturing through geographical spatial mechanisms.This implies that elevating the digital economy advancement level within a province will have a significant and positive spatial spillover effect on manufacturing sector's high-quality advancement in neighboring provinces.This observation can be rationalized by three potential explanations.
(1) The swift exchange of data and digital technology across areas fosters manufacturing sector's high-quality development.First, the rapid flow of a large amount of high-value data helps manufacturing enterprises analyze market demand more accurately, optimize production factor investments, and improve resource utilization efficiency, thereby driving the growth of manufacturing output value.Second, the extensive application of innovative digital technology such as automation and digital twins can significantly ameliorate the accuracy and production capacity of manufacturing processes, reduce manufacturing costs, and promote an overall improvement in manufacturing production efficiency.The synergy between the two improves TFP and realizes green advancement in the manufacturing industry.Subsequently, improved manufacturing output value and production efficiency between areas can lead to the advancement of links along related industrial and supply chains, promoted the formation of industrial clusters in the region, expanded the market share of products inside and outside the region, and formed positive spillover effects across areas.In conclusion, the rapid proliferation of data elements and digital technologies across various regions facilitates the best distribution of production resources, elevates the level of intelligence within the manufacturing sector, and ultimately drives its high-quality advancement at a regional scale, thereby contributing to an overall enhancement in GTFP.
(2) The rapid dissemination of data elements and digital technology across various regions contributes to the reduction of pollution emissions and energy consumption in the interregional manufacturing sector, subsequently enhancing the GTFP of the industry.As the digital economy progresses, technologies such as the Internet and big data enable the optimization of the industrial chain layout, foster information sharing and collaboration between upstream and downstream enterprises, and reduce energy wastage and environmental pollution during the circulation of materials and products.Secondly, digital technology advances the manufacturing sector towards precision and automation, enabling meticulous control of production processes to minimize energy consumption and emissions.In addition, the rapid diffusion of data elements between areas enables manufacturing industries in different areas to realize the optimal allocation of production factors, efficient utilization of resources based on big data analysis, and reduced energy use and pollution output overall.Finally, the extensive implementation of digital technology fosters green manufacturing innovations like process optimization and clean production, promoting the regional dissemination of green technologies and enhancing energy efficiency along with emission reductions in the manufacturing sector.In essence, the swift interregional spread of data elements and digital technology can significantly lower pollution and energy usage in manufacturing by optimizing industrial chain allocation, refining production processes, and encouraging cross-regional resource sharing and green technology advancements, thus achieving an overall enhancement in the industry's GTFP.
(3) Digital economy advancement provides a new path for environmental governance cooperation in the manufacturing sector, which is conducive to the industry's GTFP growth.First, the rapid dissemination of information technology promotes the exchange and learning of manufacturing development models among provinces.The successful experiences and best practices of resource conservation and pollution control in areas with mature manufacturing development can be quickly transmitted to other regions with the help of digital technology, which helps strengthen exchanges and cooperation between provinces and talent flows, thereby generating positive spillover effects and improving the overall green transition of the manufacturing sector.Second, the promotion of digital technology provides new means for cross-regional environmental monitoring, pollution prevention and control, and resource management.Based on the IoT, big-data and other technologies, manufacturing enterprises and regional governments can track and monitor the entire production and operation process, accurately identify pollution sources, effectively control pollution emissions, and improve resource allocation efficiency.Moreover, digital technology can catalyze the innovation and implementation of green technology within the manufacturing sector.It facilitates the dissemination and enhancement of green manufacturing techniques through online collaboration, remote diagnostics, and other digital means.Additionally, big data analytics plays a important role in supporting the research and advancement of green technology.In essence, the advancement of digital economy has created fresh ways to improve environmental governance in manufacturing sector.The spread of information technology among provinces has promoted the learning and replication of good development models.The application of digital methods enhances cross-regional collaborative governance.Green technology innovation has also been digitally enabled, which is conducive to improving an overall improvement in the manufacturing sector's GTFP.
Considering that the economic-geographical nested matrix can more comprehensively reflect the geographic and economic connections between areas, the significance of the control variables based on the spatial econometric results is analyzed in this section, after considering the economic-geographical nested matrix as a spatial weight matrix.
(1) The level of openness (open) and the corresponding spatial effect coefficient W * open are significantly negative at the 5% level, indicating that an increase in the degree of openness reduces the GTFP of manufacturing in neighboring provinces.The reasons for these findings are complex.First, opening up brings intense market competition; thus, to maintain the export competitiveness of their products, neighboring provinces may adopt low-cost production strategies at the expense of the environment.Second, owing to differences in openness between areas, provinces with a high-level of openness often concentrate on a large amount of talent, technology, and investment, leading to regional development imbalances and a lag in the green production technology of neighboring provinces.Third, as provinces with a higher degree of openness tend to more stringent environmental policies, they prefer to retain industries with higher green production levels and transfer high-pollution industries to neighboring provinces with lower environmental standards, triggering a pollution haven effect that severely affects highquality manufacturing development in neighboring provinces.
(2) The level of labor input (llab)'s increasing has a negative effects on high-quality manufacturing advancement.A possible reason for this is that at a certain stage of manufacturing development, the marginal output of labor input gradually decreases, leading to a decline in production efficiency and resource allocation efficiency.Furthermore, excessive labor input may hinder the process of automation and digital transition in manufacturing industries, making it difficult for manufacturing to achieve green production.Simultaneously, overreliance on labor input may also reduce manufacturing enterprises' enthusiasm for technological innovation and digital transition, as investments in these areas often cost more than increasing the number of laborers, none of which are conducive to high-quality manufacturing advancement.
The corresponding spatial effect coefficient, W * llab, is significantly negative, suggesting that increased labor input in a province's manufacturing sector diminishes the GTFP of manufacturing industries in adjacent provinces.One plausible rationale for this phenomenon is that a rise in the labor force within a province's manufacturing industry often reflects improved wage conditions, which can attract labor from neighboring provinces, resulting in a brain drain.As high-caliber labor, crucial for advancing green technology and enhancing productivity, migrates in substantial numbers, the neighboring provinces experience a decline in the human capital needed for the green advancement of their manufacturing sectors.Consequently, this adversely impressions the manufacturing industrie's high-quality advancement in those areas.
(3) Government intervention (zfgy) and its corresponding spatial effect coefficient W * zfgy are positive at the 10% level, suggesting that government intervention in manufacturing industry of a province also promotes the high-quality advancement of the manufacturing industry in neighboring provinces.When a provincial government department implements effective policy measures, these measures are often viewed as best practices and subsequently adopted by neighboring provinces, which significantly fosters the high-quality advancement of the manufacturing sector in that area.Conversely, when a provincial government introduces specific incentive policies aimed at maintaining the competitiveness of its industry, other provinces tend to enhance their support for their respective industries as well.This competitive dynamic further accelerates the manufacturing sector's high-quality advancement during multiple provinces.

Robustness testing 4.4.1. Replacing the spatial weight matrix
The baseline regression employs four distinct matrices: the geographic adjacency matrix, the geographic distance matrix, the economic distance matrix, and an economic-geographic nested matrix.Examination of the spatial correlation between provincial high-quality manufacturing advancement and the digital economy level within the manufacturing sector indicates that the coefficients of the core explanatory variables are positive at the 1% significance level across all matrices.This consistency confirms the robustness of the study's conclusions.

Replacing the core explanatory variable
Following Zhao et al (2020), the China Provincial Digital Economy Composite Development Index (pide) was constructed to replace the core explanatory variable (ide) in this study.Table 10 shows the spatial econometric regression results after replacing the core explanatory variables.
Upon replacing the core-explanatory variable, the coefficient of the principal variable, pide, as well as the associated spatial effect coefficient, W * pide, consistently exhibit positive at the 1% significance level.This finding reinforces the robustness of the study's results, demonstrating that the main conclusion remains valid even with different core explanatory variables.Specifically, the improvement in the manufacturing pide level and the interregional pide spillover effect can effectively enhance GTFP within the manufacturing sector.The of these findings not only substantiates the validity of the research methodology and the reliability of the conclusions but also underscores the pivotal role of interregional pide spillovers in advancing GTFP in regional manufacturing.Furthermore, this provides strong empirical evidence for leveraging the advancement of the digital economy to encourage the green transition and progress of regional manufacturing industries.

Excluding the years affected by COVID-19
Following the approach of Huang et al (2023), and considering the potential effects of the COVID-19 pandemic, the data for 2020 and 2021 were excluded, and spatial econometric calculations were performed again.The results are shown in table 11.
Excluding the year impacted by the COVID-19 pandemic, the core variable coefficient (IDE) and its corresponding spatial effect coefficient (W * ide) remain positive at the 5% significance level, finding further corroborates the robustness of our study's results.It demonstrates that the principal conclusion of this research holds true even when the disruptive effects of the COVID-19 pandemic are removed.Enhancing IDE levels within the manufacturing industry, along with the interregional spillover effects of IDE, continues to effectively drive improvements in GTFP in the manufacturing sector.The robustness test outcomes not only bolster the reliability of our conclusions but also underscore the rigor of our research methodology.Given the substantial  (2021).Using SDM, the total effects are disaggregated into direct and indirect effects.The direct effect quantifies the influence of a province's independent variable on its own dependent variable, while the indirect effect, often termed spatial spillover effect, captures the effect of variations in the independent variables of neighboring provinces on the dependent variables of the focal province.The results of this decomposition are detailed in table 12.
In table 12, the coefficient for the indicator ide is positive at the 1% level, means that enhancing the digital economy within one province's manufacturing sector facilitates its high-quality advancement.Furthermore, the coefficient for the indicator lrd is positive at the 10% level, implying that technological investment is also a crucial driver of high-quality advancement in the manufacturing industry of a province.These results align with the conclusions drawn in section 5, reinforcing the validity and scientific rigor of the previous research.
The indirect effect coefficients of the indicators ide and zfgy are significantly positive at the 1% and 10% levels, respectively, indicating the presence of positive spatial spillover effects for the level of digital economy advancement and degree of government intervention in manufacturing.Thus, the improvement of the digital economy advancement level in the manufacturing industry of a province and the increase in government intervention will both enhance the high-quality advancement level of the manufacturing industries in neighboring provinces.The indirect effect coefficient of the indicator llab is significantly negative at the 1% level, suggesting that an increase in the manufacturing workforce in a province will lead to a reduction in the GTFP of neighboring provinces' manufacturing industries.These conclusions are also consistent with the results reported in section 3, verifying the robustness of the conclusions of this study.

Discussion
Due to factors such as resource endowment, economic policies, cultural environment, and geographic location, the levels of digital economy advancement and high-quality manufacturing sector advancement exhibit substantial regional disparities across China.To examine the spatial heterogeneity of digital economy's influence on the high-quality advancement of the manufacturing sector, this section categorizes China's provincial administrative units into three principal areas: East, Central, and West.
5.1.Regional heterogeneity results and analysis Regional heterogeneity is tested using economic, geographical, nested matrices and spatial Durbin models.Table 13 presents the spatial econometric results for China's eastern, central, and western areas.
The econometric results in table 13 indicate significant heterogeneity in the high-quality advancement of manufacturing and its digital economy level during different areas.The specific analysis is as follows.
(1) The correlation coefficient of IDE, the principal explanatory variable, is sensibly positive in the eastern and central area, means that digital economy advancement in the manufacturing industry has notably enhanced the overall high-quality advancement in these areas.The findings in table 9 reveal that the IDE coefficient for the eastern and central area surpasses the national average, underscoring their critical role in driving high-quality manufacturing in China.From the vantage point of resource endowment, the eastern coastal area and select central areas of China possess the majority of the nation's advanced production inputs.These include superior energy resources, state-of-the-art logistics hubs, and centers for R&D and innovation, which collectively form a solid foundation for the digital transition and high-quality advancement of the local manufacturing sector.Conversely, the western region faces a relative scarcity of natural resources and infrastructure, resulting in lagging manufacturing development.Regarding market openness, the eastern coastal and central area have historically been the most economically open in China, characterized by substantial foreign trade and a high level of foreign capital inflow, facilitating better integration of their manufacturing industries into the global value chain and enhancing competitiveness through digital technology.In contrast, the western region has experienced delayed economic opening, with low market openness and insufficient external impetus for digital advancement in the manufacturing sector.From the standpoint of talent flow, the eastern and central area, with their strong economic advancement and high quality of life, continue to attract high-end talent, providing essential support for the digital transition of the local manufacturing industry.However, the western region, hampered by slower economic advancement and a relative shortage of high-quality labor, faces significant challenges in the digital advancement of its manufacturing sector.In summary, the eastern and central area exhibit significant advantages in key areas such as resource endowment, market liberalization, and talent mobility.These advantages form a robust foundation for digital progress and the high-quality transition of the local manufacturing sector.This allows digital economy to significantly contribute to the high-quality advancement of the manufacturing sector.Conversely, the western region lacks in these aspects, which limits the role of digital economy in enhancing high-quality advancement of its local manufacturing.
(2) The spatial effect coefficient W * ide corresponding to ide reflects regional heterogeneity.The W * ide coefficients of the eastern and western areas are positive at the 1% level.Combined with the IDE indirect effect coefficient reported in table 13, these findings show that in the eastern and central area experience a positive spatial spillover effect on the advancement of digital economy in manufacturing sector, and the spatial spillover effect in the central area is stronger than that in the eastern region.From the perspective of resource endowment, the eastern area has abundant natural resources, an industrial base, and innovative elements that provide good basic conditions for digital transition of the manufacturing sector.Although the resource conditions in the central region are relatively weak, they can quickly improve the digital economy of the manufacturing industry by learning and imitating the successful experience of the eastern region as well as introducing advanced technology and talent from the eastern region, thus producing a stronger positive spillover effect.In contrast, the resource endowment of the western region is relatively weak, and coupled with the lack of infrastructure and talent reserves, the digitalization process of its manufacturing industry is greatly restricted but shows a negative spillover effect.From the standpoint of market liberalization, the eastern coastal area boast the most advanced economies and exhibit a high level of openness.This environment is favorable for the manufacturing sector in these areas to seamlessly integrate into the global value chain and fully leverage the cutting-edge technology and management practices of multinational corporations.Although the central region has a relatively lower degree of market openness, it can markedly enhance the digital transition of its manufacturing sector by actively adopting and internalizing the advancement paradigms of the eastern region.Conversely, the western area has experienced a considerable lag in opening up, with limited introduction of advanced technology and management expertise.This lag impedes the manufacturing sector in the west from reaping the benefits of digital economy advancements.From a talent mobility perspective, the eastern region, with its robust economic foundation and advanced urbanization, is well-positioned to attract high-caliber talent, thereby providing essential human capital for the digital transition of its manufacturing sector.While central region faces a relative scarcity of talent reserves, it can still leverage its proximity and interactions with the eastern region to benefit from talent inflows, facilitating the diffusion of manufacturing digitalization across areas.
Conversely, the western region, hindered by lagging economic advancement and severe brain drain, faces significant challenges in attracting talent, which has become a critical bottleneck in the digital transition of its manufacturing sector.
In summary, the eastern and central area have better resource conditions, higher market openness, and stronger talent attraction, which provide favorable support for the regional spillover effect of manufacturing digital economy advancement in these areas.The relative shortage in the western region has a more obvious negative spillover effect on digital transition process of manufacturing sector.

Comprehensive analysis
One of the primary conclusions of this research is that the digital economy exerts a spatial spillover effect on the high-quality advancement of the manufacturing sector, aligning with prior studies (Deng et al 2022, Ji et al 2023, Zou et al 2024).This finding substantiates the validity, scientific rigor, and persuasiveness of the index system and research methodology employed in this study.Additionally, recent trends indicate that fostering the digital economy within key manufacturing areas has catalyzed high-quality growth across a broader geographical area, thereby affirming the efficacy of China's current policy measures (Ma andZhu 2022, Li et al 2023).
The heterogeneity analysis conducted in our research shows that the spatial spillover effect of the digital economy on high-quality advancement of the manufacturing sector is sensibly in eastern and central area of China.These findings are similar to existing studies (Ma and Zhu 2022, Li et al 2023, Zou et al 2024).
In contrast to the conclusions drawn by Deng et al (2022), this research contends that the spatial spillover effect in western area is negative.This discrepancy may arise because their analytical framework evaluates digital economy growth at a regional level rather than focusing specifically on the manufacturing sector.As a result, Deng et al (2022) effectively investigated the impression of regional digital economic advancement on the manufacturing sector, which diverges from the focal point of this study.There is a temporal lag in the influence of regional digital economic advancements on the digital advancement within the local manufacturing sector.Hence, the digital economic advancement level within the manufacturing industry is lower than the overall regional digital economic advancement level, particularly in western area.This implies that the methodology employed by Deng et al (2022) overestimates the effect of the digital economy on the high-quality advancement of the manufacturing sector in western area of China, leading to divergent conclusions in our analysis.

Conclusion and policy recommendations 6.1. Conclusion
Drawing on panel data from 30 provinces (including autonomous areas and municipalities directly governed by the central government) in China from 2011 to 2021, this study employs a novel index system to evaluate the advancement level of the digital economy in the manufacturing sector across each province.Utilizing a SDM, we investigate the spatial effects of regional manufacturing digital economy advancement on GTFP and assess its regional heterogeneity.This study enriches the internal mechanism between the digital economy and green advancement of the manufacturing sector and provides a basis for formulating effective regional advancement policies.Three main conclusions can be drawn from this study.
First, the IDE of the manufacturing digital economy and its spatial spillover effect have a dominant positive effect on the manufacturing sector's GTFP.This means that the digital transition of the manufacturing sector cannot only enhance the GTFP in this region but also drive the improvement of GTFP in neighboring areas through spillover effect between areas.
Second, analyzing regional disparities, the IDE coefficient for the manufacturing sector and its spatial effect coefficient are notably positive in the eastern and central area.This suggests that the advancement of digital economy in these areas is pivotal in boosting GTFP.Conversely, the IDE coefficient for the western region is not dominant, and the spatial effect coefficient is notably negative, suggesting that digital advancements in the manufacturing sector in the western area have a limited effect on boosting GTFP and may even exert negative spillover effects.
Third, further analysis shows that the eastern and central area have advantages in resource endowment, market openness, and talent attraction, thereby providing a solid foundation for the digital transition and highquality advancement of the manufacturing industry, which is also an important reason for their more positive spatial effect.The relative inadequacy of the western region limits its ability to benefit from the advancement of digital economy.

Policy recommendations
Drawing on the aforementioned conclusions, this study advances tailored policy recommendations for various regions in China, predicated on their unique economic characteristics.
The advancement of China's digital economy within the manufacturing sector and its regional spillover effects play a crucial role in improving the GTFP of the manufacturing sector.To leverage the digital economy's supportive role in fostering high-quality, green advancement within this sector, several measures need to be undertaken.First, it is essential to further intensify the integration and advancement of the digital economy with the manufacturing sector, facilitate the digital transition of manufacturing industries, and encourage the exchange and dissemination of digital technologies and management practices across different areas.Second, we should continue to strengthen the support of scientific and technological innovation, increase investment in the research and advancement of digital technology in the manufacturing industry, and encourage cross-regional industry university research collaborative innovation.Third, we should improve the regional collaborative governance mechanism, improve the cross-regional environmental monitoring system, and strengthen regional exchanges and cooperation in green manufacturing technology, experience, and practices.Considering the significant differences in key factors such as resource endowment, market openness, and talent attraction in different areas, differentiated policies and measures need to be formulated according to local conditions.
The eastern region's strategic geographical advantage, advanced economic growth, comprehensive infrastructure, and abundant human resources provide a solid groundwork for the digital transition and sustainable advancement of the manufacturing sector.To harness these strengths, the eastern region should concentrate on several key initiatives.Firstly, it is essential to strengthen and expand the leading sectors of the digital economy, promoting deeper integration with the manufacturing industry.Secondly, there must be expanded capital outlay in technological innovation, coupled with the acceleration of cutting-edge digital technologies' dissemination to the central and western area.Thirdly, exploiting the strategic advantages of regional international exchanges is crucial to establish a resilient platform for digital economy collaboration.Lastly, continuous talent cultivation and acquisition must be prioritized to ensure the adequate supply of essential human capital for the nationwide digital transition of the manufacturing sector.
In comparison, despite the existing disparities in economic advancement, infrastructure, and human resources in the central region, it also possesses distinct advancement potential and advantages.Firstly, the central region should fortify the foundation for the advancement of the local digital economy and expedite the integration of digital technology with traditional industries.Secondly, it is imperative for this region to enhance scientific and technological innovation, actively assimilate advanced technology and management practices from the eastern area, and effectively bridge the gap with eastern area.Lastly, the regional strengths must be fully leveraged to establish a platform for regional digital economic cooperation and transition, thereby fostering the integration of eastern and western elements.
Despite encountering challenges such as underdeveloped economic conditions and a scarcity of high-caliber labor, the western region's rich natural resources provide a solid foundation for implementing distinct digital economy advancement strategies.Initially, the western region should leverage its abundant energy resources to aggressively cultivate green and low-carbon data industry clusters.Additionally, it should proactively accommodate the relocation of digital industries from the eastern and central area, fostering the aggregation of digital economy growth factors in regional central cities, ultimately establishing a digital economy stronghold.

Research prospects
Because of objective factors, such as significant differences in the statistical system, caliber, and content among provincial administrative regions, our research fails to survey the advancement level of digital economy in different manufacturing industries at the provincial level.Therefore, this study also fails to explore the impression of the digital economy on industry heterogeneity of the manufacturing industry's GTFP in each province, which affects the integrity of the study to a certain extent.
The constraints are predominantly observable in the following dimensions.Firstly, the inconsistencies in statistical metrics and measurement benchmarks among provinces impede the collection of comprehensive and dependable data on digital economy's advancement within the manufacturing sector, thus limiting the research's detail.Secondly, even when pertinent data are available, significant disparities in the structural composition and advancemental phases of the manufacturing sector during provinces complicate the accurate depiction of the heterogeneity in the effect of various industry characteristics on the digital economy.Lastly, this study assesses digital economy's effect on the aggregate green advancement of the manufacturing sector from a national standpoint but doesn't investigate the mechanisms at the industry-specific level.
Therefore, with the acquisition of more comprehensive datasets in subsequent studies, it becomes feasible to undertake more detailed and extensive analyses at the provincial and municipal levels.This would facilitate a focused investigation into the varying effects of digital economy on GTFP across diverse manufacturing industries.Such an approach not only enriches theoretical understanding but also offers a more valuable reference for targeted policy formulation.Concurrently, we can delve deeper into the specific pathways and industry characteristics of the digital-advance within the manufacturing sector, thereby providing a more holistic insight for advancing the green and high-quality-develop-level of the manufacturing sector.

3. 1 .
Spatial econometric model selection 3.1.1.Moran's index calculation method Whether an indicator data pass the spatial correlation test is an important prerequisite for conducting spatial econometrics.Currently, the academic community commonly uses Moran's I index to verify spatial correlations.Moran's index include global Moran's index and local Moran's index.

Figure 2 .
Figure 2. Local Moran's Map for Manufacturing IDE in 2021.

Table 1 .
Evaluation indicator system for digital economy development level in industry.Percentage of firms employing electronic procurement, sales, and inventory control systems Percentage of firms implementing electronic production and manufacturing systems Percentage of firms adopting electronic logistics and distribution systems Percentage of firms using electronic customer relationship management systems Percentage of firms deploying electronic human resources management systems

Table 2 .
List of indicators for measuring GTFP category of indicator.
Leveraging Stata 17 software in conjunction with formula (1), we computed Moran's global index of GTFP and the digital economy advancement level (IDE) for the manufacturing sector across 30 provincial administrative units in China from 2011 to 2021.Table4presents the global Moran's index of GTFP derived from four distinct spatial weight matrices, while table 5 illustrates the global Moran's index of IDE, also calculated using the same four types of spatial weight matrices.
To ensure comparability over time, all price-related indicators are converted based on the corresponding price indices, with 1990 as the base year.Missing values are calculated using the annual average growth rate.For noncensus year missing data, data from the census year are used to replace all data sources from the Statistical Yearbook of China, Industrial Statistical Yearbook of China, Science and Technology Statistical Yearbook of China, Fixed Asset Investment Statistical Yearbook of China and Economic Census Yearbook of China.

Table 3 .
Descriptive statistics of the variables.

Table 5 .
Global moran's index for overall manufacturing ide.

Table 11 .
Xiang and Sun (2020)luding COVID-19.COVID-19 pandemic on manufacturing output and environmental performance, excluding the pandemic year provides a more accurate reflection of the intrinsic trends in manufacturing industry's greendevelopment under typical conditions.These robustness test results validate the soundness of our theoretical framework and empirical model design, substantiating their efficacy in capturing the critical mechanisms underpinning sustainable development in the manufacturing industry.4.5.Spatial impact effect decomposition of the digital economy and high-quality manufacturing industry developmentTo further investigate the spatial spillover effects of digital economy development within China's manufacturing sector during various provinces, this study employs the methodologies ofXiang and Sun (2020)and Li and Zhou

Table 13 .
Spatial econometric results of different regions in China.