Internet Infrastructure Construction and Digital Productive Forces: Empirical Evidence from China

Internet Infrastructure Construction and Digital Productive Forces: Empirical Evidence from China | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Internet Infrastructure Construction and Digital Productive Forces: Empirical Evidence from China Zhiliang Yang, Juan Li, Jinfeng Long, Jialing Zhao, Junhong Du This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5814647/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Internet infrastructure construction is an important condition to promote the development of digital productivity, and an important guarantee to promote the digital economy as a new driving force for economic growth. This paper analyzes the impact of internet infrastructure development on digital productivity using 2011–2019 prefecture-level city panel data and a quasi-natural experiment on the "Broadband China" pilot policy. The study concludes that internet infrastructure development significantly promotes the development of digital productivity, and the result passes several robustness tests. The promotion effect of internet infrastructure construction on digital productivity has significant heterogeneity among regions, between cities of different administrative levels, and between cities in urban agglomerations and non-urban agglomerations. Meanwhile, the mechanism analysis finds that internet infrastructure development affects digital productivity development through four ways: attracting the concentration of highly skilled personnel, improving the level of marketization, stimulating the city's innovation vitality, and growing the science and technology service industry. Business and commerce/Information systems and information technology Social science/Economics Internet infrastructure digital productivity broadband China double difference Figures Figure 1 Figure 2 Figure 3 Figure 4 1 Introduction The new productive forces generated by the fourth technological revolution result from continuous evolution and innovation based on traditional productive forces. These forces have undergone a fundamental qualitative transformation by applying advanced and emerging technologies, serving as a critical driving force for contemporary economic development and social progress. The formation of digital productivity is primarily reflected in two key dimensions: at the micro level, it manifests in the integration of digital technology and digital elements with other factors of production; at the macro level, it is characterized by the convergence of the digital economy with the real economy (Dunn, 2021). This integration facilitates a qualitative leap in productivity to a new level. However, the development of digital technology and the establishment of digital productivity rely heavily on internet infrastructure as the foundational support, providing the essential means of production. Consequently, strengthening the construction of internet infrastructure and ensuring its compatibility with the requirements of digital productivity are of great significance in accelerating the formation and advancement of digital productivity. Digital productivity refers to the productivity generated through the innovation and application of digital technologies. It encompasses digital workers, digital labor materials, and digital labor objects. Among these, internet infrastructure is classified as a digital means of labor. However, as the foundational material condition for the development of the digital economy, internet infrastructure is intricately coupled with digital workers and digital labor objects, providing essential impetus for the advancement of digital productivity. Notably, since the 1990s, the Chinese government has actively initiated the construction of communication infrastructure networks. This effort has evolved, progressing through two distinct phases: the establishment of Internet and mobile communication facilities during the first decade of the 21st century, and the subsequent construction of internet infrastructure after 2010, characterized by the deployment of 4G and 5G networks (Guo and Liu, 2020). To meet the growing demand for high-speed, stable, and wide-coverage broadband networks essential for economic and social development, the Chinese government launched the "Broadband China" strategy in 2013. As part of this initiative, the government designated 39 pilot cities for the "Broadband China" project in 2014, 2015, and 2016, and has since continued to build and enhance broadband internet infrastructure across the country. Driven by this strategy, the Chinese government has accelerated the transformation and upgrading of broadband infrastructure, leading to rapid growth in user numbers, a significant increase in household broadband penetration, and the swift expansion of broadband applications across various economic and social sectors. Notably, since entering the new era, the development and widespread application of internet infrastructure have provided a strong foundation for the rapid growth of the digital economy, driven primarily by the mobile Internet, and the dynamic potential of digital productivity has gradually become evident. To what extent has China’s long-standing and expanding internet infrastructure development contributed to the growth of digital productivity, and what are the underlying mechanisms? Both researchers and policymakers need to examine the impact of internet infrastructure development on digital productivity, particularly to clarify the mechanisms through which this infrastructure influences digital productivity. Such an understanding holds significant practical value for the continued advancement of internet infrastructure in the future. In response to this need, this paper constructs a quasi-natural experiment based on the "Broadband China" pilot policy. It employs a multi-period Difference-in-Differences (DID) method to assess the impact of internet infrastructure development on digital productivity. The study also analyzes the heterogeneity of the "Broadband China" pilot policy’s effects on digital productivity from the perspectives of region, city administrative level, and city cluster. Furthermore, it investigates the primary mechanisms through which internet infrastructure affects the development of digital productivity, focusing on four key aspects: attracting the concentration of highly skilled talent, enhancing marketization levels, stimulating urban innovation, and expanding the scientific and technological service industry. The goal is to provide theoretical and practical insights into the development of digital productivity within China’s policy framework. Compared to the existing literature, the contribution of this paper is mainly in the following points: First, this paper provides an in-depth analysis of the impact of Internet infrastructure development on digital productivity, examining the heterogeneity across regions, cities with different administrative levels, and urban agglomerations versus non-urban agglomerations. The analysis reveals that the promotion of digital productivity varies by region, and offers explanations for these disparities. Second, drawing from Marx's productivity theory, this paper defines digital productivity as an integrated system comprising digital workers, digital labor materials, and digital labor objects. It then calculates digital productivity in the Marxian sense and analyzes the critical role of internet infrastructure in enhancing digital productivity using the econometric Difference-in-Differences (DID) model. The application of Marxian productivity theory in empirical research within the digital economy is a novel approach. Third, the paper explores the mechanisms through which internet infrastructure influences digital productivity from four key dimensions: attracting highly skilled talent, improving marketization, stimulating urban innovation, and expanding the science and technology service industry. This multi-dimensional analysis not only elucidates the internal logic of internet infrastructure's impact on digital productivity but also provides a more detailed foundation for related policy development. 2 Literature review and research hypotheses 2.1 Literature review The rapid spread of fixed and mobile broadband has led to an increasing substitution between economic activities, giving rise to the "productivity puzzle"—the phenomenon of real productivity being underestimated (Coyle, 2019). The digitization of the agricultural sector, for instance, can facilitate technological advancements in agriculture, thereby boosting agricultural productivity. Similarly, the digital transformation of companies can promote Environmental, Social, and Governance (ESG) practices, which in turn enhances their productivity (Li, 2024). Pan et al. (2022) study explores labor force changes in the digital era from the Marxist theory of productivity, emphasizing that digital tools and technologies have profoundly impacted the division of labor. Digital technologies play a critical role in driving innovation and economic growth, particularly by improving labor efficiency and capital utilization. These technologies significantly enhance firm productivity by enabling automation and facilitating data sharing. They also streamline workflows, improve operational efficiency, and promote the sharing and dissemination of knowledge, thereby enhancing innovation capacity (Gaglio et al., 2022). Moreover, the adoption of digital technologies by firms can increase total factor productivity (Nucci et al., 2023). In sum, digital transformation not only fosters innovation in small manufacturing firms but also contributes to overall productivity improvements. Most of the studies on internet infrastructure development have examined the economic and social impacts of digital infrastructure development based on the quasi-natural experiment of Broadband China. Zhang and Fu (2021) and Hou and Liu (2023) argue that the "Broadband China" policy significantly promotes the level of urban innovation and that the driving effect is stronger in the eastern region, where large-scale cities are located. On this basis, Yu and He (2023) further investigated the effect of the "Broadband China" policy on the improvement of urban green innovation level. Some scholars analyze the effect of the "Broadband China" policy on the level of green innovation in cities. Some scholars analyze the impact of the "Broadband China" policy on industrial development from the meso level. Guo et al. (2024) found that the "Broadband China" policy can significantly promote the rationalization of industrial structure by reducing information asymmetry and improving transaction efficiency. Some scholars have also looked at this issue from a micro perspective. Some scholars have also explained that the "Broadband China" policy promotes corporate innovation from a micro perspective and alleviates financing constraints, and alleviate financing constraints (Sun and Li, 2022; Zheng, 2023). internet infrastructure can foster technological innovation and alleviate financing constraints. It enhances the optimization of factor allocation, enables economies of scale, and, consequently, increases total factor productivity (Tang and Zhao, 2023). Research on the relationship between internet infrastructure development and digital productivity has gained significant attention in the context of the digital economy. Data is widely regarded as a core factor of production in the development of digital productivity (Dong, 2024; He and Chang, 2021). However, the value generated by data elements lies not in the data itself, but in the integration and activation of other production factors (Feng, 2022). Under the "Broadband China" strategy, the development of internet infrastructure has provided a foundational platform for data collection, storage, processing, and analysis. In particular, high-speed Internet connections and powerful cloud computing platforms have enhanced the capacity to process massive datasets. This enables data to be efficiently integrated into other production factors, thus playing an active role in various economic activities. It facilitates the aggregation of dispersed production factors into substantial production resources (He and Chang, 2021). thereby effectively promoting the growth of digital productivity. Similarly, algorithms and computational power—emerging as new production tools under digital productivity—can only derive meaningful insights from ever-expanding datasets when processed by increasingly powerful algorithms and computational capacity (Zhang, 2023). With improvements in internet infrastructure, particularly in 5G and cloud computing technologies, the application of algorithms and computational power is expanding. This results in larger-scale datasets, enabling more complex data analysis and pattern recognition. Consequently, this accelerates the transformation of data into information and knowledge, making data-driven decision-making more accurate and efficient, and contributing significantly to the flourishing of digital productivity. In summary, the existing literature has explored the issues related to new productivity from many angles, but there are relatively few studies on how to develop digital productivity, in particular, there is little literature exploring the theoretical mechanisms and empirical evidence of the relationship between internet infrastructure development and digital productivity. Given this, this paper explains the connotation of digital productivity from the perspective of Marx's production theory, takes the "Broadband China" pilot as a quasi-natural experimental scenario, and adopts the DID method to assess the policy effect of internet infrastructure construction on the development of digital productivity, and promotes the gathering of highly skilled talents, improves the degree of marketization, stimulates urban innovation vitality, and strengthens the science and technology service industry. It also analyzes the impact mechanism of internet infrastructure construction on digital productivity from four aspects: promoting the gathering of highly skilled talents, improving the degree of marketization, stimulating urban innovation, and expanding the science and technology service industry. 2.2 Theoretical analysis and research hypothesis 2.2.1 The meaning of digital productivity According to the fundamental logic of Marx's theory of productivity, productivity is the productive capacity generated through the interaction and integration of workers, means of labor, and objects of labor. The distinction between digital productivity and general productivity lies in the former's immense potential to generate new value through the use of digital technologies. Digital productivity is characterized by its focus on high-tech, digitization, and intelligence in the context of new industrialization. It emphasizes breakthrough technological innovations, the iterative development of disruptive products, and the cultivation of future-oriented industries, with a particular focus on fostering a robust and sustained productive capacity in the real economy, including the manufacturing sector. As the digital economy has become a key driver of economic growth for the Chinese government, data, algorithms, and computational power have emerged as new factors of productivity. In this framework, data is regarded as being on par with or even surpassing traditional production factors in its importance (Men, 2024). Digital productivity has emerged as one of the key areas for future progress in productivity. It represents a new form of productivity within the digital realm. From the perspective of Marx's theory, digital productivity consists of digital laborers, digital labor materials, and digital labor objects. Digital laborers primarily include practitioners from the digital service industry, while digital labor materials encompass both tangible resources, such as the Internet, and intangible assets, such as patents for digital technologies. Digital labor objects comprise digital enterprises and related digital businesses. With the ongoing expansion of the digital economy, technologies such as artificial intelligence, the Internet of Things, big data, and blockchain will become central to the formation and development of digital productivity. The advancement of these technologies is heavily reliant on the support of internet infrastructure, with data transmission, storage, and computation playing a crucial role in enabling the transformation of digital technologies into digital productivity. Moreover, the development of digital productivity is also accompanied by evolving digital production relations. Key aspects of these relations include the property rights associated with digital assets, the distribution of digital value, and organizational forms such as loose coupling, virtual agglomeration, and network linkages. These elements are critical factors influencing the development of digital productivity in the future. 2.2.2 Internet infrastructure development and digital productivity The development of digital productivity requires the formation and integration of digital workers, digital means of labor, and digital objects of labor, often driven by significant exogenous factors, such as internet infrastructure construction policies initiated by government agencies. In promoting the digital economy, government departments have invested substantial financial resources into the construction of internet infrastructure, particularly under national strategies like "Broadband China." This has triggered a nationwide surge in internet infrastructure development. The ongoing expansion of internet infrastructure has facilitated the creation of digital workers, digital labor resources, and digital labor objects, thereby providing the foundational conditions for the growth of digital productivity. First, internet infrastructure construction plays a key role in cultivating digital laborers. As government agencies promote the development of internet infrastructure, they can directly generate relevant job opportunities through construction projects, train and develop skilled technicians and workers, and increase labor demand within enterprises (Sun and Guo, 2021). Additionally, internet infrastructure development encourages higher education institutions, research institutes, and related enterprises to train digital professionals across various fields such as R&D, application, and promotion, in line with policy directives. This process gradually builds and expands a large-scale digital workforce. Secondly, internet infrastructure construction provides essential digital labor materials. Digital labor means can generally be categorized into tangible and intangible types, with internet infrastructure construction primarily offering tangible digital labor means, such as broadband Internet ports, information communication base stations, fiber optic networks, big data computing facilities, and cloud computing platforms. These infrastructures ensure the smooth transmission of information, data storage, data computation, and network connectivity, enabling data elements to integrate with traditional production factors and be utilized in production processes. Furthermore, internet infrastructure development also fosters the advancement of digital technology research, digital finance, and other digital service sectors, leading to the creation of digital patents, digital financial products, and other intangible digital labor materials. These innovations provide crucial technical and capital support for the growth of digital productivity. Finally, internet infrastructure construction gives rise to digital labor objects such as digital enterprises and various digital businesses. Generally speaking, certain businesses in internet infrastructure construction need to be undertaken by specialized digital enterprises, and the intermediate products and end products produced by various links of digital enterprises are direct digital labor objects. At the same time, telecommunications and postal services built on internet infrastructure, as well as other digital industries and the demand for financial and commercial services resulting from the construction of internet infrastructure, can become numerous digital labor objects (Guo et al., 2020). Therefore, internet infrastructure construction can promote the development of digital productivity by facilitating the formation and integration of digital workers, digital labor materials, and digital labor objects. Based on this, this paper proposes the first research hypothesis. Hypothesis 1: internet infrastructure development can significantly contribute to digital productivity development. 2.2.3 Mechanisms by which internet infrastructure development affects digital productivity This paper describes the mechanism of internet infrastructure development for digital productivity development from four aspects: internet infrastructure promotes the concentration of highly skilled personnel, improves the degree of marketization, stimulates the vitality of urban innovation, and strengthens the science and technology service industry. As a national strategic initiative and key industrial policy promoted by the government, internet infrastructure construction tends to have multiple policy objectives, and there are often multiple ways for the policy to play a role. internet infrastructure construction is essentially a channel and platform for the transmission of information to society, aiming to improve the efficiency of information transmission, reduce information costs, and promote market expansion and inter-subjective synergy. At the same time, the construction of internet infrastructure will also bring about the in-depth use of a large number of digital devices as well as extensive knowledge sharing and spillover, in particular, technological innovation triggered by digitization has become an important driving factor in the development of digital productivity. Specifically: First, internet infrastructure promotes the clustering of highly skilled talent. Highly skilled workers are the driving force of the knowledge economy and are essential for the development of digital productivity. Well-developed internet infrastructure facilitates the dissemination, diffusion, and sharing of knowledge, which, in turn, attracts the concentration of highly skilled talent, particularly entrepreneurial talent. This clustering can occur both in physical spaces and through virtual networks, with the latter made possible by digital platforms. When internet infrastructure fosters the concentration of skilled workers, it increases the likelihood of digital technological innovation and iteration, thereby enhancing innovation efficiency. This, undoubtedly, serves as a vital source of momentum for the advancement of digital productivity. Second, internet infrastructure increases the degree of marketization. Acemoglu (2002) argues that the degree of marketization plays a decisive role in the factor bias of scientific and technological progress. With robust internet infrastructure, market information can circulate rapidly, significantly reducing communication costs between producers and consumers, thereby facilitating more efficient market transactions and behavioral coordination. As a result, internet infrastructure contributes to enhancing the degree of marketization. An increased degree of marketization improves the efficiency of optimal factor allocation, particularly by promoting the rapid movement and concentration of digital factors. The swift flow of data can be more effectively integrated with other production factors, while the agglomeration of data factors also fosters technological innovation (Liu et al., 2023a). Notably, the growth of e-commerce and its derivative industries, driven by digital payment and digital finance, allows for more efficient integration of digital workers, digital labor materials, and digital labor objects, thus advancing the development of digital productivity. Once again, it stimulates the city's innovation vitality. As mentioned earlier, cyberinfrastructure contributes to the agglomeration of innovative talents and knowledge overflow (He and Guo, 2023), which is the main way to enhance urban innovation capacity and activate urban innovation vitality. In addition, internet infrastructure can both promote the digital enhancement of urban innovation platforms and accelerate the realization of digital transformation of traditional industries, generating new business forms and new models, thus forming a better innovation ecology and enabling urban innovation subjects to produce more innovation results. At the same time, the inclusion of data elements can also promote the diffusion of enterprise technology (Xue et al., 2020), promote enterprises to expand the innovation boundary and develop new technologies (Shen et al., 2023) and help enterprises realize continuous innovation, which is also an important way for internet infrastructure construction to stimulate urban innovation vitality. Finally, internet infrastructure contributes to the growth of the science and technology service industry. This industry is fundamental to the development of science and technology, as well as to the advancement of high-tech industries where technology is the core production factor. The professional and technical services it provides significantly enhance the added value of industries and the technological content of products (Qian and Cai, 2023). The construction of internet infrastructure creates better physical conditions and conducive environments for technology consulting, R&D services, information technology services, and education and training, enabling more efficient utilization of scientific and technological resources. It also provides a better environment for research and innovation for scientific and technological workers. In particular, the growing level of intelligence in the science and technology service industry helps improve service efficiency, saving substantial amounts of scientific resources and the time of technology workers. This, without a doubt, acts as a crucial driver in advancing digital productivity. Hypothesis 2: internet infrastructure development has a significant effect on the development of digital productivity by promoting the pooling of highly skilled people. Hypothesis 3: internet infrastructure development has a significant effect on digital productivity development through increased marketization. Hypothesis 4: internet infrastructure development has a significant effect on digital productivity development by stimulating urban innovation. Hypothesis 5: Cyberinfrastructure development has a significant impact on digital productivity development through the growth of the science and technology services sector. 3 Introduction to the empirical methodology and data 3.1 Modeling The "Broadband China" pilot policy, utilized in this paper, is commonly considered a "quasi-natural experiment." The Difference-in-Differences (DID) model is a widely applied econometric technique that offers significant advantages when analyzing panel data, particularly in terms of controlling for individual heterogeneity and time trends. This enables more precise estimation of causal relationships between variables and has become an established method for evaluating the effects of policy interventions. Consequently, this paper constructs a quasi-natural experiment based on the "Broadband China" pilot program and employs the DID model for empirical analysis. Given that the list of pilot cities for the "Broadband China" policy was released in batches in 2014, 2015, and 2016, the paper applies a multi-period DID model to assess the policy's impact. The cities selected as pilot locations are designated as the treatment group, while those not selected serve as the control group, with the control group coded as 0. By comparing the difference in digital productivity between the treatment and control groups, this analysis allows for the evaluation of the policy's effect on the development of the digital economy. The specific modeling is presented in Eq. ( 1 ): $$\:Dignq{p}_{it}={\alpha\:}_{0}+{\alpha\:}_{1}DID+{\alpha\:}_{2}Contro{l}_{it}+{\varphi\:}_{i}+{\gamma\:}_{t}+{\epsilon\:}_{it}$$ 1 (1) In Eq. ( 1 ), the explained variable \(\:Dignq{p}_{it}\) represents the city's digital productivity, the subscript i represents the city to which it belongs, and t represents the year, and \(\:DID\) is the regional variable of whether it is selected as a pilot city at the policy point in time; \(\:Contro{l}_{it}\) is the control variable; \(\:{\varphi\:}_{i}\) for city fixed effects; \(\:{\gamma\:}_{t}\) is the Time fixed effect; \(\:{\epsilon\:}_{it}\) is the randomized disturbance term. (1) The coefficients of \(\:DID\) is the coefficient of \(\:{\alpha\:}_{1}\) is the double-difference estimator, which can measure the impact of the "Broadband China" pilot policy on digital productivity, and is the estimator that this paper focuses on, i.e., if the "Broadband China" pilot policy is conducive to promoting digital productivity, the coefficient is significantly positive. \(\:{\alpha\:}_{1}\) That is, if the "Broadband China" pilot policy is conducive to promoting digital productivity, the coefficient is significantly positive. Conversely, if the "Broadband China" pilot policy is not conducive to the promotion of digital productivity, the coefficient is significantly negative. \(\:{\alpha\:}_{1}\) is significantly negative. 3.2 Variable selection 3.2.1 Explained variables: Digital productivity ( \(\:Dignq\) ) Considering that digital productivity is a comprehensive indicator and consists of multiple indicators, we draws on the theoretical results of scholars such as Xu et al. ( 2024 ), and adopts the Entropy Method to measured the comprehensive index of digital productivity of different cities in each year from 2011 to 2019. And since each indicator in this paper is positively influenced, the raw data of each three-level indicator is standardized according to the way (2): $$\:{\text{z}}_{ij}=\frac{{\mathbf{x}}_{ij}-\text{m}\text{i}\text{n}\left({\mathbf{x}}_{ij}\right)}{\text{m}\text{a}\text{x}\left({\mathbf{x}}_{ij}\right)-\text{m}\text{i}\text{n}\left({\mathbf{x}}_{ij}\right)}$$ 2 Where (2) in the equation \(\:{\mathbf{x}}_{ij}\) is the original value of each basic indicator, which represents the specific value of the jth indicator of the ith city, and \(\:{\text{z}}_{ij}\) is the result after the standardization of indicator j . In addition, after the standardization process, it is necessary to calculate the information entropy and weight of specific indicators, which is calculated as follows: $$\:{\text{E}}_{\text{j}}=-\frac{1}{\text{l}\text{n}\left(\text{n}\right)}\sum\:_{\text{i}=1}^{\text{n}}\left(\frac{{\text{z}}_{ij}}{\sum\:_{\text{i}=1}^{\text{n}}{\text{z}}_{ij}}\text{l}\text{n}\frac{{\text{z}}_{ij}}{\sum\:_{\text{i}=1}^{\text{n}}{\text{z}}_{ij}}\right)$$ 3 $$\:{\omega\:}_{j}=\frac{\left(1-{E}_{j}\right)}{\sum\:_{j=1}^{m}\left(1-{E}_{j}\right)}$$ 4 where equations ( 3 ) and ( 4 ) calculate the information entropy E ij of indicator j and weights respectively \(\:{\omega\:}_{j}\) , n is the number of sample cities, m denotes the number of indicators, and finally the composite index of digital productivity is calculated and its expression is as follows: $$\:{\text{D}\text{i}\text{g}\text{n}\text{q}\text{p}}_{i1}=\sum\:_{j=1}^{m}{\text{z}}_{ij}\times\:{{\omega\:}}_{\text{j}}$$ 5 Table 1 Indicator system for digital productivity Level 1 indicators Secondary indicators Tertiary indicators Indicator measurement modalities Indicator properties Digital Worker Number of digital workers Digital industry practitioners Total information transmission, computer, software personnel (10,000) + Digital labor information Physical means of production Regional Internet coverage International Internet users (million) + Cell phone penetration rate Number of cell phone subscribers (million) + Intangible means of production Level of digital finance Digital Financial Inclusion Composite Index + Number of digital technology inventions Natural logarithm of patents for digital inventions in the current year + Digital Labor Objects digital enterprise Number of digital businesses Artificial Intelligence Enterprises (number) + Total telecommunication services Natural logarithm of total telecommunications operations + digital business Total postal operations Natural logarithm of total postal operations + 3.2.2 Explanatory variables: Internet infrastructure development The explanatory variable in this paper is internet infrastructure construction, which is represented by the interaction term DID between the "Broadband China" policy pilot treatment variable and the policy point-in-time variable, which takes the value of 1 if the city is selected as a pilot city after the policy point-in-time, and the value of 0 if the city is not selected as a pilot city after the policy point-in-time. 3.2.3 Control variables In this paper, the level of economic development, the level of openness to the outside world, the extent of the service sector, the development of industrialization, the expenditure on education, and the level of financial development, which may have an impact on the explanatory variables, are chosen as control variables. The variables are defined in the following way Table 2 shown: Table 2 Definition of the main variables Variable classification variable name measurement method explanatory variable Digital productivity Measured by the entropy method Core explanatory variables DID Whether city i is a pilot area for the "broadband policy" strategy in period t : yes = 1, no = 0 Mechanism variables highly skilled person Number of employees in scientific and technical services and geological surveying (10,000 persons) Marketization index Marketization index Urban Innovation Index Urban Innovation Index Science and technology services industry Number of enterprises belonging to the scientific research and technological services industry (10,000) Select Variable Aggregate index score China Digital Innovation Index control variable Level of economic development Natural logarithm of real per capita GDP Egypt's open-door policy towards the outside world Natural logarithm of the amount of foreign investment actually utilized in the year, in tens of thousands of dollars Level of services Ratio of value added of tertiary industry in 10,000 yuan to GDP in 10,000 yuan Industrialized development Ratio of value added of secondary industry in 10,000 yuan to gross regional product in 10,000 yuan Expenditure on education Ratio of education expenditures of $ 10,000,000 to expenditures of $ 10,000,000 in the general budget of local finances Level of financial development Balance of deposits in financial institutions at the end of the year, million yuan / Gross regional product, million yuan 3.3 Descriptive statistics of variables Table 3 reports the results of descriptive statistics for each variable. The mean value of digital productivity is 0.574, while the maximum and minimum values are 12.87 as well as -14.77, respectively, indicating that digital productivity remains highly variable across different cities in the country. Table 3 Results of descriptive statistics of variables variable name Number of observations average value (statistics) standard deviation minimum value maximum values Digital productivity 2153 0.182 1.598 -14.77 12.87 DID 2153 0.242 0.429 0 1 highly skilled person 2153 1.547 4.787 0.0110 71.72 Marketization index 2111 11.70 2.216 4.960 19.16 Urban Innovation Index 2153 0.241 0.964 0.000113 19.63 Science and technology services industry 2153 0.171 0.540 0.00170 7.602 stock index (statistics) 2153 56.62 27.39 0.298 100 Expenditure on education 2153 0.177 0.0396 0.0357 0.356 Industrialized development 2152 47.16 10.22 11.70 89.34 Level of services 2152 41.92 10.06 10.15 83.52 Level of economic development 2152 10.76 0.566 8.773 13.06 Egypt's open-door policy towards the outside world 2102 10.25 1.842 1.099 14.94 Level of financial development 2152 1.470 0.683 0.371 8.871 3.4 Data presentation The empirical study in this paper selects the panel data of prefecture-level cities from 2011 to 2019, which contains 251 samples, of which the city sample data are from China Urban Statistical Yearbook, China Science and Technology Statistical Yearbook, and Digital Finance Research Center of Peking University. The list of pilot cities is from the website of the Ministry of Industry and Information Technology. This paper also fixes some of the missing values present in the data using linear interpolation. 4 Empirical results 4.1 Benchmark regression results Table 4 reports the results of the estimation of internet infrastructure development on digital productivity. The control variables are gradually incorporated into the model, one by one, through stepwise regression, while individual (city) fixed effects and Time fixed effects are also controlled for in order to more accurately estimate the net effect of the "Broadband China" pilot policy on digital productivity. The regression result of introducing the multiplicative term in column (1) shows that the regression coefficient of DID on digital productivity is 0.0166 (significantly positive at the 1% level), which shows that internet infrastructure construction can significantly promote the development of digital productivity. Considering that the economic development characteristics of prefecture-level cities may affect the development of digital productivity to a greater or lesser extent, and there is a certain relationship with whether or not the sample of prefecture-level cities has been selected by the pilot program of the "Broadband China" policy, Columns (2) to (7) gradually control for the economic development characteristics of the prefecture-level city level. The regression results of columns (2) to (7) show that the regression coefficient of digital productivity fluctuates slightly between 0.0160 and 0.0174 during the process of gradually adding control variables, but the regression result is still significantly positive at the 1% level. It indicates that the addition of control variables can to a certain extent exclude the influence of other potential factors on the benchmark regression, thus making the results of the benchmark regression more stable and accurate. The above regression results indicate that internet infrastructure construction can significantly promote the development of digital productivity under the promotion of the "Broadband China" pilot policy, which is in line with hypothesis H1. Table 4 Estimated results of internet infrastructure development on digital productivity Variables M (1) (2) (3) (4) (5) (6) (7) DID 0.0166 *** (0.0047) 0.0160 *** (0.0046) 0.0162 *** (0.0046) 0.0162 *** (0.0046) 0.0173 *** (0.0046) 0.0174 *** (0.0044) 0.0164 *** (0.0044) Expenditure on education – 0.3416 *** (0.0759) 0.3524 *** (0.0760) 0.3533 *** (0.0762) 0.3166 *** (0.0752) 0.2171 *** (0.0725) 0.2109 *** (0.0724) Industrialized development – – 0.0008 ** (0.0004) 0.0010 (0.0009) −0.0034 *** (0.0011) −0.0038 *** (0.0010) −0.0040 *** (0.0010) Level of services – – – 0.0002 (0.0011) −0.0034 *** (0.0011) −0.0041 *** (0.0011) −0.0041 *** (0.0011) Level of economic development – – – – 0.0826 *** (0.0110) 0.0870 *** (0.0106) 0.0758 *** (0.0116) Egypt's open-door policy towards the outside world – – – – – −0.0015 (0.0015) −0.0018 (0.0015) Level of financial development – – – – – – −0.0164 ** (0.0067) Constant 0.1773 *** (0.0016) 0.1169 *** (0.0135) 0.0755 *** (0.0229) 0.0593 (0.0883) −0.4666 *** (0.1116) −0.4210 *** (0.1078) −0.2645 ** (0.1252) Individual fixed effect Yes Yes Yes Yes Yes Yes Yes Time fixed effect Yes Yes Yes Yes Yes Yes Yes N 2152 2152 2150 2150 2150 2099 2099 R 2 0.9990 0.9990 0.9990 0.9990 0.9990 0.9992 0.9992 Notes: * p < 0.1 denote the significance level of 10%. ** p < 0.05 denote the significance level of 5%. *** p < 0. 01 denote the significance level of 1%. The numbers in parentheses are the standard errors. 4.2 Robustness tests 4.2.1 Parallel trend test When assessing the timeliness of a policy using the double-difference method, a parallel trend test needs to be satisfied. That is, in the "Broadband China" pilot policy, the treatment and control groups have similar trends in digital productivity before the implementation of the policy. Therefore, this paper draws on Beck et al. ( 2010 ) and Fang and Zhao ( 2021 ) to conduct a balanced trend test using event analysis. In this paper, one dummy variable is set for each year before the implementation of the "Broadband China" pilot policy and interacted with the dummy variables of the experimental group, and then the core explanatory variable DID is added to the regression together with the study of the effect of these four interaction terms on digital productivity. The regression results are shown in Fig. 2 , in which the coefficients of the dummy variables interacted with the experimental group in the years before the year of policy implementation are insignificant, but the results of DID as the core explanatory variable in the figure show significant positive. So to a certain extent, it can be proved that the model satisfies the parallel trend test. 4.2.2 Indented processing samples In order to eliminate the influence of extreme outliers on the benchmark regression results, this study truncates and shrinks the upper and lower 1% of the study sample and re-runs the regression analysis. The results are shown in Column (1) of Table 5 . After removing outliers, the coefficient estimates of the "Broadband China" pilot policy pass the test at the 1% significant level, which is consistent with the baseline estimates. This further validates the reliability and robustness of the study findings. 4.2.3 PSM-DID method test In this study, propensity score matching (PSM) was used to cope with selectivity bias and endogeneity. PSM allows for the transformation of multidimensional covariates into one-dimensional propensity matching scores in the first place, and then matching based on these scores ensures that there is no significant difference between the treated and control groups after matching. Thus, it helps to reduce the bias due to self-selection and makes the research results more credible and interpretable. In this paper, GDP, urban household population, and financial level are used as covariates to match the propensity scores of the cities selected as the pilot cities of Broadband China, and the selection bias value of propensity score matching is within 10%, which indicates that this paper is suitable for propensity score matching. In addition, in order to further illustrate that this paper is suitable for propensity score matching, after propensity score matching, this paper further presents the histograms of the treatment group and control group (see Fig. 3 ), which shows that the distribution of propensity scores of the treatment group and the control group after matching has a large overlap interval, and the propensity score is mostly concentrated in the vicinity of 0.1. Therefore, it is finally judged that it is suitable to use propensity score matching in this paper. As shown in column (2) of Table 5 , the results of using DID estimation after near-neighbor matching in caliper are shown. The estimation results show that the "Broadband China" pilot policy can promote the development of digital productivity, and the regression results after propensity score matching are similar to the baseline regression results in many aspects, which means that the model is robust and reliable. 4.2.4 Instrumental variable method The endogeneity problem caused by selection bias can be mitigated to some extent by shrinking the top and bottom 1% in the baseline regression, but the "Broadband China" pilot policy is still unavoidably affected by many unobservable factors. For this reason, this paper uses as instrumental variables the interaction term between the degree of terrain relief and the time dummy variable of whether or not the "Broadband China" pilot policy has been implemented. As shown in column (3) of Table 5 , the regression results show that the "Broadband China" pilot policy promotes the development of digital productivity still holds and the regression results are significant at the 1% level. In addition, the table shows that the LM statistic of the instrumental variable has a P-value of 0.0000, which significantly rejects the original hypothesis; and the F-statistic is larger than the critical value of Stock-Yogo's weak identification test at the 10% level. Therefore, it is reasonable to choose the interaction term of the time dummy variable between the degree of terrain relief and whether or not to start the implementation of the "Broadband China" pilot policy as the instrumental variable. Table 5 Robustness test of the impact of internet infrastructure development on digital productivity Explained variable: Digital productivity Winsor2 (1) PSM-DID (2) Instrumental variable (3) DID 0.0159 *** (0.0044) 0.0130 *** (0.0043) 0.0958 *** (0.0088) Expenditure on education 0.2691 *** (0.0765) 0.1397 * (0.0727) 0.1854 ** (0.0785) Industrialized development −0.0037 *** (0.0011) −0.0049 *** (0.0011) −0.0031 *** (0.0011) Level of services −0.0042 *** (0.0011) −0.0057 *** (0.0012) −0.0032 *** (0.0012 ) Level of economic development 0.0796 *** (0.0130) 0.0716 *** (0.0116) 0.0929 *** (0.0127) Egypt’s open-door policy towards the outside world −0.0018 (0.0017) −0.0015 (0.0015) −0.0034 ** (0.0017) Level of financial development −0.0154 * (0.0079) −0.0171 *** (0.0065) −0.0057 (0.0073) Constant −0.3170 ** (0.1391) −0.0938 (0.1296) – Anderson canon. corr. LM statistic – – 535.063 [0.0000] Cragg-Donald Wald F statistic – – 747.167 [16.38] Individual fixed effect Yes Yes Yes Time fixed effect Yes Yes Yes N 2099 2001 2090 R 2 0.9976 0.993 0.572 Notes: * p < 0.1 denote the significance level of 10%. ** p < 0.05 denote the significance level of 5%. *** p < 0. 01 denote the significance level of 1%. The numbers in parentheses are the standard errors. 4.2.5 Placebo test To ensure that the results of the benchmark regression are not due to some other unobservable or omitted variables, this paper further constructs a placebo test. This is done by randomizing the treatment groups, conducting 1000 random samples of the variables in the treatment groups, obtaining 1000 corresponding regression coefficients and p-values, and plotting their kernel density distributions and p-value distributions. Based on the distribution of kernel density estimates of 1000 randomized experiments (see Fig. 3 ), it is found that the corresponding estimates of regression coefficients are around the 0 point and very close to the standard normal distribution, and the majority of the P-values are greater than 0.1, indicating that the majority of the regression results are not significant, and thus the original hypothesis is not valid, which indicates that the results of the benchmark regression results obtained in the previous paper passed the placebo test, and that the The promotion effect of the "Broadband China" pilot policy on the development of digital productivity is not caused by other unobservable factors. 4.2.6 Goodman-Bacon decomposition Since the treatment effect of TWFE regression in the estimation process of DID model can have heterogeneous treatment effect (HTE) at different treatment times or between different treatment groups, which leads to "bad treatment groups", thus leading to possible bias in the estimation of DID parameters in the traditional multi-period DID model, and the literature is not clear on this issue. For example, Zhang et al. ( 2024 ) and Baker et al. ( 2022 ). have thoroughly discussed the bias problem of multi-temporal double difference models with two-way fixed (TWFE) effects using Goodman-Bacon decomposition. Therefore, this paper draws on this literature as well as the Goodman-Bacon ( 2021 ) approach, utilizes the Goodman-Bacon decomposition to test the robustness of the impact of internet infrastructure development on digital productivity. In conducting the Goodman-Bacon decomposition, this paper further treats the sample data as a strongly balanced panel from 2011 to 2019. Referring to He and Wang ( 2024 ) study, the decomposition results reported in Table 6 and Fig. 4 are obtained. From the results, it can be seen that the share of Late_v_Early is only 6.61%, thus further proving that the benchmark regression results in this paper are robust. Table 6 Goodman-Bacon decomposition weighting table Beta Total Weight Early_v_Late -0.0008504615 0.0122276324 Late_v_Early -0.0013131396 0.0203793867 Early_v_Late -0.0051221242 0.0244552648 Late_v_Early 0.0123147555 0.0326070173 Early_v_Late -0.0065626237 0.0132190616 Late_v_Early 0.0111245615 0.0132190616 Never_v_timing 0.0181979939 0.8838925755 4.2.7 Heckman two-step estimation From the perspective of the interaction logic between the "Broadband China" pilot policy and digital productivity, it can be concluded that there is actually an endogenous problem caused by sample selectivity bias. The outstanding level of digital innovation of a city is more likely to be selected as a pilot city for the "Broadband China" policy by government departments, and these endogenous problems will lead to biased estimation results. Therefore, this paper adopts Heckman’s ( 1979 ) two-stage regression method to test whether the results are biased. This paper adopts Heckman’s ( 1979 ) two-stage regression method to test whether there is an endogeneity problem due to sample selection. In addition, this paper introduces the aggregate index score as a selection variable, and in order to satisfy the Heckman two-step estimation, extreme values are excluded, and the dependent variable is truncated with upper and lower 1% before the Heckman two-step estimation is carried out (the results are shown in columns (1) and (2) of Table 7 ). From the regression results, the inverse Mills ratio in column (2) of Table 7 is significantly positive at the 5% level, i.e., it indicates that there is some degree of sample selection bias problem in the original equation. However, the core explanatory variables are still significantly positive in the Heckman two-step estimation results, which indicates that the results of the benchmark regression are reliable when the sample selection bias problem is considered. 4.2.8 Exclusion of special cities The "Broadband China" pilot policy is a governmental policy for internet infrastructure construction, which has obvious geographical characteristics and may be influenced by urban characteristics. There are not only large cities with unique and representative economic status like Beijing, Chongqing, and Shanghai, but also provincial capitals with important political, cultural, and economic status, and will these cities with important responsibilities and functions and special distribution of resources also have an impact on digital productivity regarding internet infrastructure construction? In order to more accurately assess the impact of internet infrastructure construction on digital productivity under the "Broadband China" pilot policy, this paper excludes municipalities and provincial capitals from the original full sample, and then conducts a regression on this basis. The final regression results in column (3) of Table 7 show that after excluding the samples of municipalities and provincial capitals, the "Broadband China" pilot policy still significantly improves the level of digital productivity, which further proves that the conclusions of this paper are robust. Table 7 Robustness test Explained Variables: Digital productivity The Heckman Two-Step Excluding provincial capitals DML (1) (2) (3) (4) did 0.1045** (0.0418) 0.6839*** (0.2129) 0.0106*** (0.0040) 0.2017** (0.0904) Digital Innovation Index - -0.0737*** (0.0137) - - inverse Mills ratio - 0.4083** (0.1890) - - Expenditure on education 0.2960 (0.4755) -17.2038*** (2.7562) 0.1370** (0.0623) 0.2783 (1.1021) Industrialized development 0.0091** (0.0038) -0.1197*** (0.0398) -0.0020** (0.0009) -0.0006 (0.0097) Level of services 0.0097** (0.0047) -0.0967** (0.0442) -0.0026*** (0.0009) 0.0035 (0.0115) Level of economic development -0.1998*** (0.0519) 0.6818** (0.3282) 0.0478*** (0.0103) 0.0315 (0.1242) Egypt's open-door policy towards the outside world 0.0111 (0.0104) 0.0995* (0.0572) -0.0017 (0.0013) -0.0337 (0.0259) Level of financial development -0.0683* (0.0367) -0.0639 (0.2093) -0.0255*** (0.0070) -0.0944 (0.0807) Constant 1.4092*** (0.4236) 12.7107*** (3.5220) -0.0882 (0.1118) 0.1679 (0.9139) Individual fixed effect YES YES YES - Time fixed effect YES YES YES - N 2102 2102 1849 2153 R2 - - 0.9995 0.002 4.2.9 Tests of dual machine learning methods (DML) Since the DID model estimation relies on a strict parallel trend assumption, i.e., it is assumed that the difference between the control and treatment groups remains constant over time in the absence of treatment benefits. However, the parallel trend assumption of the DID model is considered to be too stringent and can have an impact on the consistency of the estimation results. In contrast, the dual machine learning (DML) approach proposed by Chernozhukov et al. ( 2018 ) is able to make causal inferences without relying on this overly harsh assumption, and therefore has some advantages over the DID model. Therefore, in this paper, the DML method is used for robustness testing. First, it is necessary to construct a partial linear regression model, which is similar to a semiparametric regression model without specifying the functional form of the characteristic variables, and the partial linear model is as follows: $$\:{\text{D}\text{i}\text{g}\text{n}\text{q}\text{p}}_{\text{i}\text{t}+1}={{\theta\:}}_{0}DID+\text{g}\left({\text{X}}_{\text{i}\text{t}}\right)+{\text{U}}_{\text{i}\text{t}}，\text{E}\left({\text{U}}_{\text{i}\text{t}}\mid\:{\text{X}}_{\text{i}\text{t}},\text{D}\text{I}\text{D}\right)=0$$ 6 $$\:DID=\text{m}\left({\text{X}}_{\text{i}\text{t}}\right)+{\text{V}}_{\text{i}\text{t}}，\text{E}\left({\text{V}}_{\text{i}\text{t}}\mid\:{\text{X}}_{\text{i}\text{t}}\right)=0$$ 7 wherein the \(\:{\text{D}\text{i}\text{g}\text{n}\text{q}\text{p}}_{\text{i}\text{t}+1}、DID\) has the same meaning as above, and \(\:{\text{X}}_{\text{i}\text{t}}\) denotes the high-dimensional feature variables, and \(\:\text{g}\left({\text{X}}_{\text{i}\text{t}}\right)\text{和}\text{m}\left({\text{X}}_{\text{i}\text{t}}\right)\) denotes two functions on the feature variables (control variables), the specific function form is unknown and needs to be estimated by machine learning. \(\:{\text{U}}_{\text{i}\text{t}}\) and \(\:{\text{V}}_{\text{i}\text{t}}\) are error terms with conditional mean 0. In the process of performing dual machine learning estimation, this paper adopts the random forest method to split the total study sample into two parts: the main sample N-n and the auxiliary sample n. The main sample is used to estimate \(\:{{\theta\:}}_{0}\) and the auxiliary sample is used to estimate \(\:\text{g}\left({\text{X}}_{\text{i}\text{t}}\right)\) . Machine learning estimation of Eq. ( 8 ) is performed by introducing the Neyman orthogonal function to counteract the bias arising from the bias introduced in the first step of estimating Eq. ( 7 ) with machine learning. Here the \(\:{\text{V}}_{\text{i}\text{t}}\) viewed as an instrumental variable for DID, with \(\:{\text{V}}_{\text{i}\text{t}}\) Replacing the DID for the \(\:{\text{D}\text{i}\text{g}\text{n}\text{q}\text{p}}_{\text{i}\text{t}+1}\) regression, an unbiased coefficient estimate is obtained \(\:{\stackrel{ˇ}{{\theta\:}}}_{0}\) : $$\:{\stackrel{ˇ}{{\theta\:}}}_{0}={\left(\frac{1}{\text{n}}\sum\:_{\text{i}\in\:\text{I},\text{t}\in\:\text{T}}{\widehat{\text{V}}}_{\text{i}\text{t}}\text{D}\text{I}\text{D}\right)}^{-1}\frac{1}{\text{n}}\sum\:_{\text{i}\in\:\text{I},\text{t}\in\:\text{T}}{\widehat{\text{V}}}_{\text{i}\text{t}}\left({\text{D}\text{i}\text{g}\text{n}\text{q}\text{p}}_{\text{i}\text{t}+1}-\widehat{\text{g}}\left({\text{X}}_{\text{i}\text{t}}\right)\right)$$ 8 Column (4) of Table 7 reports the estimation results of the DML methodology, which shows that the estimated coefficients of DID are significant at the 5% level, indicating that the baseline regression results in this paper are not affected by the strict parallel trend assumption, and so the baseline regression results are robust. 4.3 Heterogeneity analysis 4.3.1 Regional heterogeneity In this paper, from the regional perspective, we will set regional dummy variables, take the values of the three types of samples in the west, central and east, and generate the interaction term with did, and then use the interaction term to conduct a regression. The estimation results, as shown in column (1) of Table 8 , show that there is significant heterogeneity in the promotion effect of internet infrastructure construction on digital productivity in the East, Central and West. Therefore, it can be concluded that under the pilot policy of "Broadband China", internet infrastructure construction can promote the development of digital productivity in the western region, and the benefit of digital productivity in the eastern region is not obvious. 4.3.2 Heterogeneity of city administrative levels Since important economic resources of the Chinese government are mainly allocated from top to bottom according to the administrative level, cities with higher administrative levels tend to receive more resources. The administrative levels of Chinese government cities, from highest to lowest, are municipalities, sub-provincial cities, planned cities, and ordinary prefectures, with sub-provincial cities including provincial capitals and planned cities (Feng and Li, 2023 ). In this paper, we distinguish the study sample into high-level cities (including municipalities, separately listed cities, and provincial capitals) and low-level cities (including ordinary prefecture-level cities), generate administrative level dummy variables, and generate interaction terms with did, and then regress the benchmark model using the interaction. The analysis results in Column (2) of Table 8 show that internet infrastructure development promotes digital productivity in high-administrative-level cities more significantly than in low-administrative-level cities. The reason for this is that high-level cities have greater financial autonomy and are able to invest more resources in digital productivity development (Jiang et al., 2018 ), at the same time, high-level cities can attract more high-quality talents and high-tech industries (Ge et al., 2024 ) and the scale effect of internet infrastructure construction is stronger. While low administrative level cities have relative disadvantages in these aspects, so internet infrastructure construction has a relatively weaker role in promoting the development of digital productivity in low administrative level cities. 4.3.3 Heterogeneity of urban agglomerations The report of the twentieth Party Congress emphasized the need to "build a coordinated development pattern of large, medium-sized and small cities based on city clusters and metropolitan areas". City clusters are an important form of regional economic cooperation and integrated development for the Chinese Government; through the radiation-driven central cities, multiple cities complement each other's strengths and integrate their markets, generating economies of scale and spillover effects in the allocation of factors. In fact, the important role of city clusters is that it strengthens industrial integration, knowledge spillover, factor flow, and sharing of facilities and services within the city clusters from the perspective of the overall coordinated development of the regional economy (Dai and Yang, 2023 ). In terms of digital productivity development, there may be an advantage for cities in a city cluster over those that are not. So, is there such a difference? In this paper, based on the list of 19 city clusters and the cities included in the national "13th Five-Year Plan", we distinguish the research sample into city clusters and non-city clusters and generate dummy variables, and then conduct regression analysis by using the interaction term between did and dummy variables, and the results are shown in column (3) of Table 8 . The results show that for cities that are in urban agglomerations, the impact of internet infrastructure development on digital productivity is significantly different from that of cities that are not in urban agglomerations. The reason for this situation may be that the geospatial agglomeration of city clusters can bring economies of scale and also superimpose the virtual agglomeration of the digital economy (Liu et al., 2023b ). The radiation-driven and "grouping" development among cities can play the role of internet infrastructure construction, which brings significant advantages for the development of digital productivity. Table 8 Results of heterogeneity analysis Explained variables: Digital productivity East, center, and west (2) Municipal administrative level (1) City cluster (3) Quyu_did 0.0427 *** (0.0032) Shenghui_did 0.0475 *** (0.0071) Chengshiqun_did 0.0242 *** (0.0049) Expenditure on education 0.1382 ** (0.0697) 0.1914 *** (0.0719) 0.2073 *** (0.0722) Industrialized development −0.0030 *** (0.0010) −0.0038 *** (0.0010) −0.0042 *** (0.0010) Level of services −0.0028 *** (0.0011) −0.0038 *** (0.0011) −0.0043 *** (0.0011) Level of economic development 0.0817 *** (0.0111) 0.0730 *** (0.0114) 0.0759 *** (0.0115) Egypt’s open-door policy towards the outside world −0.0018 (0.0015) −0.0024 (0.0015) −0.0021 (0.0015) Level of financial development −0.0146 ** (0.0064) −0.0204 *** (0.0066) −0.0180 *** (0.0066) Constant −0.4226 *** (0.1203) −0.2407 * (0.1234) −0.2432 * (0.1241) Individual fixed effect Yes Yes Yes Time fixed effect Yes Yes Yes N 2099 2099 2099 R 2 0.9992 0.9992 0.9992 Year FE Yes Yes Yes Id FE Yes Yes Yes Notes: * p < 0.1 denote the significance level of 10%. ** p < 0.05 denote the significance level of 5%. *** p < 0. 01 denote the significance level of 1%. The numbers in parentheses are the standard errors. 5 Mechanism of action analysis The previous paper has confirmed that internet infrastructure construction contributes to the development of digital productivity, and according to the inferences obtained from theoretical analysis, data infrastructure construction may promote the development of digital productivity by attracting the concentration of high-skilled talents, improving the degree of marketization, stimulating the vitality of urban innovation, and growing the scientific and technological service industry, so this paper will further develop the study of these mechanisms by combining the characteristics of internet infrastructure. 5.1 Internet infrastructure attracts concentration of highly skilled personnel In order to test the mechanism impact of internet infrastructure on digital productivity, this paper invokes research technology and other personnel as a new variable, and the regression results, as shown in Table 9 , columns (1) and (2), show that the internet infrastructure can significantly increase the urban high-skilled talent agglomeration, and at the same time, high-skilled personnel through the internet infrastructure can continue to innovate, optimize the technology and improve the digital capabilities, injecting new enterprise and industrial development Power. The continuous improvement of urban internet infrastructure construction makes it easier for science and technology practitioners, highly educated and highly skilled talents to access digital technology services, which can help them improve efficiency in specific scientific research, innovation and entrepreneurship, and production and operation (Guo et al., 2020 ), especially in the digital economy to get more boosts, thus promoting the development of digital productivity. 5.2 Internet infrastructure contributes to increased marketization In this paper, we refer to the calculation method of Fan et al. on marketization index ( Fan et al., 2003 ), which calculates the marketization index of prefecture-level cities to measure the level of regional marketization. Increased marketization can stimulate competition among enterprises and promote continuous innovation. Provide broader space and opportunities, promote enterprises to increase R&D investment, optimize the allocation of resources, so that a more reasonable flow of resources, to a certain extent, to break the "information cocoon" in order to improve the efficiency of the flow of factors of production and efficiency of utilization, which is one of the important driving forces for the continuous development of digital productivity. This paper uses the marketization index of each prefecture-level city to maintain the balance, consistency and completeness of the sample to ensure the validity and reliability of the research results. Its regression results, as shown in Table 9 , column (3) and column (4), reveal that the study finds that the development of internet infrastructure significantly increases the degree of marketization, and that the degree of marketization also significantly improves digital productivity, which proves that the internet infrastructure helps to improve the market dynamics and promote digital productivity. Table 9 Mechanism test of highly skilled person and marketization index Explained Variables: highly skilled person Digital productivity Marketization index Digital productivity (1) (2) (3) (4) DID 0.4998*** (0.0750) - 0.0542* (0.0318) - highly skilled person - 0.0097*** (0.0013) - - Marketization index - - - 0.0104*** (0.0032) Expenditure on education 1.7387 (1.2427) 0.1978*** (0.0717) 0.0807 (0.5223) 0.2026*** (0.0711) Industrialized development -0.0662*** (0.0178) -0.0035*** (0.0010) -0.0142* (0.0075) -0.0035*** (0.0010) Level of services -0.0958*** (0.0191) -0.0033*** (0.0011) -0.0122 (0.0080) -0.0034*** (0.0011) Level of economic development 0.7184*** (0.1987) 0.0663*** (0.0115) -0.0321 (0.0838) 0.0660*** (0.0114) Egypt's open-door policy towards the outside world 0.0668** (0.0261) -0.0022 (0.0015) -0.0217** (0.0109) -0.0018 (0.0015) Level of financial development 0.1501 (0.1145) -0.0194*** (0.0066) -0.0422 (0.0488) -0.0215*** (0.0066) Constant -0.3600 (2.1485) -0.2211* (0.1230) 13.5035*** (0.9024) -0.3216** (0.1297) Individual fixed effect YES YES YES YES Time fixed effect YES YES YES YES N 2099 2099 2063 2063 R 2 0.9723 0.9992 0.9769 0.9992 t statistics in parentheses * p < 0.1, ** p < 0.05, *** p < 0.01 5.3 Cyberinfrastructure effectively stimulates urban innovation Innovation is one of the key elements of modern economic development. It is no coincidence that urban innovation is still true for digital productivity, as it promotes the development of the digital economy and productivity through technological innovation, industrial upgrading, talent attraction and other aspects. Urban innovation and digital productivity complement each other, realizing the "symbiotic effect" and jointly promoting the sustainable development and competitiveness of urban economy. Columns (1) and (2) of Table 10 show the results of the urban innovation path. The results show that the promotion effects of the "Broadband China" pilot policy on the urban innovation index and the urban innovation index on digital productivity are both significant at the 1% level, suggesting that cities with better internet infrastructure can stimulate urban innovation and thus improve the development of digital productivity. 5.4 Cyberinfrastructure can grow the science and technology services industry Innovation is the core of scientific and technological progress and the first driving force leading social development. In the context of the innovation-driven strategy and in the face of the double superposition of the globalization of innovation and the era of service economy, the science and technology service industry has become one of the most active industries in the current global layout of the whole chain around innovation and entrepreneurship. In order to promote the rapid transformation of scientific and technological achievements into real-life productivity, policies have been introduced to promote the development of science and technology service industry, and a variety of new forms, new models and new industries have constantly emerged in the science and technology service industry, which has become a hotspot for the development of new economy. At the same time, digital productivity is a contemporary advanced productive force spawned by revolutionary breakthroughs in technology, innovative allocation of production factors, and deep transformation and upgrading of industries. This makes the deep cross-fertilization of science and technology service industry and digital productivity, and the estimation results, as shown in Table 10 Column (3) Column (4), indicate that the internet infrastructure significantly enhances the total amount of science and technology service industry at the level of 1%, while the development of science and technology service industry can provide enterprises with more digital technology and solutions to help them improve productivity, optimize management and promote innovation, etc., thus promoting the enhancement of digital productivity, and the results of the estimation results are further shown in Table 10 Column (4). 10 Column (4) The estimation results further show that the science and technology service industry can significantly promote the development of digital productivity at the 1% level. This also indicates that internet infrastructure can effectively contribute to digital productivity. Table 10 Mechanism test of urban innovation index and science and technology services explanatory variable Urban Innovation Index Digital productivity Science and technology services Digital productivity (1) (2) (3) (4) DID 0.2397*** (0.0409) - 0.1528*** (0.0203) - Urban Innovation Index - 0.0225*** (0.0024) - - Science and technology services - - - 0.0229*** (0.0049) Expenditure on education 1.2605* (0.6780) 0.1862*** (0.0711) 0.3340 (0.3362) 0.2076*** (0.0723) Industrialized development -0.0387*** (0.0097) -0.0032*** (0.0010) -0.0162*** (0.0048) -0.0038*** (0.0010) Level of services -0.0627*** (0.0104) -0.0028*** (0.0011) -0.0247*** (0.0052) -0.0037*** (0.0011) Level of economic development 0.2355** (0.1084) 0.0681*** (0.0113) 0.0751 (0.0538) 0.0713*** (0.0115) Egypt's open-door policy towards the outside world 0.0457*** (0.0142) -0.0026* (0.0015) 0.0227*** (0.0071) -0.0021 (0.0015) Level of financial development 0.1006 (0.0625) -0.0201*** (0.0065) 0.0019 (0.0310) -0.0182*** (0.0066) Constant 1.2672 (1.1722) -0.2550** (0.1220) 0.8319 (0.5813) -0.2390* (0.1242) Individual fixed effect YES YES YES YES Time fixed effect YES YES YES YES N 2099 2099 2099 2099 R 2 0.7964 0.9992 0.8405 0.9992 6 Conclusions and policy implications The digital economy has emerged as a powerful force, driving economic growth and becoming a "new engine" of development. This growth is fundamentally reflected in the advancement of digital productivity, with the construction of internet infrastructure serving as a crucial foundation for fostering digital productivity. This paper uses the "Broadband China" pilot policy as a quasi-natural experiment and employs panel data from prefecture-level cities between 2011 and 2019 to empirically examine the impact of internet infrastructure development on digital productivity. The findings indicate that the development of internet infrastructure significantly promotes digital productivity, and the results remain robust after various robustness checks, including PSM-DID, parallel trend tests, sensitivity tests, exclusion of special cities, Goodman-Bacon decomposition, instrumental variable analysis, and double machine learning techniques. The heterogeneity analysis reveals that the impact of internet infrastructure development on digital productivity varies significantly across regions, cities of different administrative levels, and urban versus non-urban agglomerations. Furthermore, the mechanism analysis identifies four key channels through which internet infrastructure construction influences digital productivity: attracting the concentration of highly skilled talent, improving marketization, stimulating urban innovation, and fostering the growth of the science and technology service industry. Based on the above conclusions, the policy implications of this paper are as follows: internet infrastructure is important for the development of digital productivity, based on the new characteristics and new needs of the Chinese government's urban development, on the one hand, we should continue to steadily promote the "Broadband China" strategy, increase the construction of internet infrastructure, and give full play to the positive effect of internet infrastructure construction on digital workers, digital labor means, and digital labor objects. On the one hand, we should continue to steadily push forward the "Broadband China" strategy, increase the construction of internet infrastructure, and give full play to the positive effects of internet infrastructure construction on digital workers, digital labor materials and digital labor objects. On the other hand, according to the need to develop new productivity according to local conditions, in the process of internet infrastructure construction, we should focus on mending the shortcomings and strengthening the weaknesses, combining the differences of different regions, relying on the level of the existing internet infrastructure construction according to the local actual situation and practical needs, further attracting highly skilled talents, optimizing the business environment, increasing investment in innovation, and developing the scientific and technological service industry, so as to provide support for the continuous promotion of the development of digital productivity. Declarations Author Contribution Author Contributions Statement：Z. Y. conceptualized the research, developed the methodology, wrote the main manuscript, conducted the empirical analysis and prepared the data visualization. J. L. and J. 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Manag World 40(1):196–222.https://link.cnki.net/doi/10.19744/j.cnki.11-1235/f.2024.0010 Zheng Y (2023) The mechanism of digital infrastructure construction on corporate innovation: an empirical examination based on the quasi-natural experiment of "Broadband China" strategy pilot. J Cent Univ Finance Econ (4):90–104. https://link.cnki.net/doi/10.19681/j.cnki.jcufe.2023.04.008 Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-5814647","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":405066378,"identity":"e2868be5-1529-44a1-8a81-251e200419c6","order_by":0,"name":"Zhiliang Yang","email":"","orcid":"","institution":"Northwest Normal University","correspondingAuthor":false,"prefix":"","firstName":"Zhiliang","middleName":"","lastName":"Yang","suffix":""},{"id":405066379,"identity":"96ed997d-d7b4-446b-895d-27ef3bc61f47","order_by":1,"name":"Juan Li","email":"","orcid":"","institution":"Northwest Normal 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1","display":"","copyAsset":false,"role":"figure","size":52398,"visible":true,"origin":"","legend":"\u003cp\u003eMechanisms of the impact of internet infrastructure development on digital productive forces\u003c/p\u003e","description":"","filename":"1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5814647/v1/f984c5cd12570806721e6828.jpg"},{"id":74522858,"identity":"ab4375a8-0e5d-446b-ad9f-671fb903ac2d","added_by":"auto","created_at":"2025-01-23 06:11:07","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":35626,"visible":true,"origin":"","legend":"\u003cp\u003eParallel trend test\u003c/p\u003e","description":"","filename":"2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5814647/v1/d9ef7314a2de2ec4109448b9.jpg"},{"id":74522862,"identity":"5c18b72b-0a3c-4534-90e6-47ba07adf0ca","added_by":"auto","created_at":"2025-01-23 06:11:08","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":47922,"visible":true,"origin":"","legend":"\u003cp\u003ePlacebo test\u003c/p\u003e","description":"","filename":"3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5814647/v1/874199a81afaf2caf2f083c8.jpg"},{"id":74522867,"identity":"cf812347-f82b-40be-acf0-f1dea7ebeddf","added_by":"auto","created_at":"2025-01-23 06:11:08","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":34717,"visible":true,"origin":"","legend":"\u003cp\u003eGoodman-Bacon decomposition results\u003c/p\u003e","description":"","filename":"4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5814647/v1/ff7a57012b47b2973e5ad8b5.jpg"},{"id":80236903,"identity":"59432745-f5a2-40f3-ba29-ae97579b51b6","added_by":"auto","created_at":"2025-04-09 14:02:02","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2099521,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5814647/v1/6ea8bdba-1173-4df2-9c4b-4e203f255414.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Internet Infrastructure Construction and Digital Productive Forces: Empirical Evidence from China","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003eThe new productive forces generated by the fourth technological revolution result from continuous evolution and innovation based on traditional productive forces. These forces have undergone a fundamental qualitative transformation by applying advanced and emerging technologies, serving as a critical driving force for contemporary economic development and social progress. The formation of digital productivity is primarily reflected in two key dimensions: at the micro level, it manifests in the integration of digital technology and digital elements with other factors of production; at the macro level, it is characterized by the convergence of the digital economy with the real economy (Dunn, 2021). This integration facilitates a qualitative leap in productivity to a new level. However, the development of digital technology and the establishment of digital productivity rely heavily on internet infrastructure as the foundational support, providing the essential means of production. Consequently, strengthening the construction of internet infrastructure and ensuring its compatibility with the requirements of digital productivity are of great significance in accelerating the formation and advancement of digital productivity.\u003c/p\u003e\n\u003cp\u003eDigital productivity refers to the productivity generated through the innovation and application of digital technologies. It encompasses digital workers, digital labor materials, and digital labor objects. Among these, internet infrastructure is classified as a digital means of labor. However, as the foundational material condition for the development of the digital economy, internet infrastructure is intricately coupled with digital workers and digital labor objects, providing essential impetus for the advancement of digital productivity. Notably, since the 1990s, the Chinese government has actively initiated the construction of communication infrastructure networks. This effort has evolved, progressing through two distinct phases: the establishment of Internet and mobile communication facilities during the first decade of the 21st century, and the subsequent construction of internet infrastructure after 2010, characterized by the deployment of 4G and 5G networks (Guo and Liu, 2020).\u003c/p\u003e\n\u003cp\u003eTo meet the growing demand for high-speed, stable, and wide-coverage broadband networks essential for economic and social development, the Chinese government launched the \u0026quot;Broadband China\u0026quot; strategy in 2013. As part of this initiative, the government designated 39 pilot cities for the \u0026quot;Broadband China\u0026quot; project in 2014, 2015, and 2016, and has since continued to build and enhance broadband internet infrastructure across the country. Driven by this strategy, the Chinese government has accelerated the transformation and upgrading of broadband infrastructure, leading to rapid growth in user numbers, a significant increase in household broadband penetration, and the swift expansion of broadband applications across various economic and social sectors. Notably, since entering the new era, the development and widespread application of internet infrastructure have provided a strong foundation for the rapid growth of the digital economy, driven primarily by the mobile Internet, and the dynamic potential of digital productivity has gradually become evident.\u003c/p\u003e\n\u003cp\u003eTo what extent has China\u0026rsquo;s long-standing and expanding internet infrastructure development contributed to the growth of digital productivity, and what are the underlying mechanisms? Both researchers and policymakers need to examine the impact of internet infrastructure development on digital productivity, particularly to clarify the mechanisms through which this infrastructure influences digital productivity. Such an understanding holds significant practical value for the continued advancement of internet infrastructure in the future. In response to this need, this paper constructs a quasi-natural experiment based on the \u0026quot;Broadband China\u0026quot; pilot policy. It employs a multi-period Difference-in-Differences (DID) method to assess the impact of internet infrastructure development on digital productivity. The study also analyzes the heterogeneity of the \u0026quot;Broadband China\u0026quot; pilot policy\u0026rsquo;s effects on digital productivity from the perspectives of region, city administrative level, and city cluster. Furthermore, it investigates the primary mechanisms through which internet infrastructure affects the development of digital productivity, focusing on four key aspects: attracting the concentration of highly skilled talent, enhancing marketization levels, stimulating urban innovation, and expanding the scientific and technological service industry. The goal is to provide theoretical and practical insights into the development of digital productivity within China\u0026rsquo;s policy framework.\u003c/p\u003e\n\u003cp\u003eCompared to the existing literature, the contribution of this paper is mainly in the following points:\u003c/p\u003e\n\u003cp\u003eFirst, this paper provides an in-depth analysis of the impact of Internet infrastructure development on digital productivity, examining the heterogeneity across regions, cities with different administrative levels, and urban agglomerations versus non-urban agglomerations. The analysis reveals that the promotion of digital productivity varies by region, and offers explanations for these disparities. Second, drawing from Marx\u0026apos;s productivity theory, this paper defines digital productivity as an integrated system comprising digital workers, digital labor materials, and digital labor objects. It then calculates digital productivity in the Marxian sense and analyzes the critical role of internet infrastructure in enhancing digital productivity using the econometric Difference-in-Differences (DID) model. The application of Marxian productivity theory in empirical research within the digital economy is a novel approach. Third, the paper explores the mechanisms through which internet infrastructure influences digital productivity from four key dimensions: attracting highly skilled talent, improving marketization, stimulating urban innovation, and expanding the science and technology service industry. This multi-dimensional analysis not only elucidates the internal logic of internet infrastructure\u0026apos;s impact on digital productivity but also provides a more detailed foundation for related policy development.\u003c/p\u003e"},{"header":"2 Literature review and research hypotheses","content":"\u003cp\u003e\u003cstrong\u003e\u003cem\u003e2.1 Literature review\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe rapid spread of fixed and mobile broadband has led to an increasing substitution between economic activities, giving rise to the \"productivity puzzle\"—the phenomenon of real productivity being underestimated (Coyle, 2019). The digitization of the agricultural sector, for instance, can facilitate technological advancements in agriculture, thereby boosting agricultural productivity. Similarly, the digital transformation of companies can promote Environmental, Social, and Governance (ESG) practices, which in turn enhances their productivity (Li, 2024). Pan et al. (2022) study explores labor force changes in the digital era from the Marxist theory of productivity, emphasizing that digital tools and technologies have profoundly impacted the division of labor. Digital technologies play a critical role in driving innovation and economic growth, particularly by improving labor efficiency and capital utilization. These technologies significantly enhance firm productivity by enabling automation and facilitating data sharing. They also streamline workflows, improve operational efficiency, and promote the sharing and dissemination of knowledge, thereby enhancing innovation capacity (Gaglio et al., 2022). Moreover, the adoption of digital technologies by firms can increase total factor productivity (Nucci et al., 2023). In sum, digital transformation not only fosters innovation in small manufacturing firms but also contributes to overall productivity improvements.\u003c/p\u003e\n\u003cp\u003eMost of the studies on internet infrastructure development have examined the economic and social impacts of digital infrastructure development based on the quasi-natural experiment of Broadband China. Zhang and Fu (2021) and Hou and Liu (2023) argue that the \"Broadband China\" policy significantly promotes the level of urban innovation and that the driving effect is stronger in the eastern region, where large-scale cities are located. On this basis, Yu and He (2023) further investigated the effect of the \"Broadband China\" policy on the improvement of urban green innovation level. Some scholars analyze the effect of the \"Broadband China\" policy on the level of green innovation in cities. Some scholars analyze the impact of the \"Broadband China\" policy on industrial development from the meso level. Guo et al. (2024) found that the \"Broadband China\" policy can significantly promote the rationalization of industrial structure by reducing information asymmetry and improving transaction efficiency. Some scholars have also looked at this issue from a micro perspective. Some scholars have also explained that the \"Broadband China\" policy promotes corporate innovation from a micro perspective \u0026nbsp;and alleviates financing constraints, and alleviate financing constraints (Sun and Li, 2022; Zheng, 2023). internet infrastructure can foster technological innovation and alleviate financing constraints. It enhances the optimization of factor allocation, enables economies of scale, and, consequently, increases total factor productivity (Tang and Zhao, 2023).\u003c/p\u003e\n\u003cp\u003eResearch on the relationship between internet infrastructure development and digital productivity has gained significant attention in the context of the digital economy. Data is widely regarded as a core factor of production in the development of digital productivity (Dong, 2024; He and Chang, 2021). However, the value generated by data elements lies not in the data itself, but in the integration and activation of other production factors (Feng, 2022). Under the \"Broadband China\" strategy, the development of internet infrastructure has provided a foundational platform for data collection, storage, processing, and analysis. In particular, high-speed Internet connections and powerful cloud computing platforms have enhanced the capacity to process massive datasets. This enables data to be efficiently integrated into other production factors, thus playing an active role in various economic activities. It facilitates the aggregation of dispersed production factors into substantial production resources (He and Chang, 2021). thereby effectively promoting the growth of digital productivity. Similarly, algorithms and computational power—emerging as new production tools under digital productivity—can only derive meaningful insights from ever-expanding datasets when processed by increasingly powerful algorithms and computational capacity (Zhang, 2023). With improvements in internet infrastructure, particularly in 5G and cloud computing technologies, the application of algorithms and computational power is expanding. This results in larger-scale datasets, enabling more complex data analysis and pattern recognition. Consequently, this accelerates the transformation of data into information and knowledge, making data-driven decision-making more accurate and efficient, and contributing significantly to the flourishing of digital productivity.\u003c/p\u003e\n\u003cp\u003eIn summary, the existing literature has explored the issues related to new productivity from many angles, but there are relatively few studies on how to develop digital productivity, in particular, there is little literature exploring the theoretical mechanisms and empirical evidence of the relationship between internet infrastructure development and digital productivity. Given this, this paper explains the connotation of digital productivity from the perspective of Marx's production theory, takes the \"Broadband China\" pilot as a quasi-natural experimental scenario, and adopts the DID method to assess the policy effect of internet infrastructure construction on the development of digital productivity, and promotes the gathering of highly skilled talents, improves the degree of marketization, stimulates urban innovation vitality, and strengthens the science and technology service industry. It also analyzes the impact mechanism of internet infrastructure construction on digital productivity from four aspects: promoting the gathering of highly skilled talents, improving the degree of marketization, stimulating urban innovation, and expanding the science and technology service industry.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003e2.2 Theoretical analysis and research hypothesis\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cem\u003e2.2.1 The meaning of digital productivity\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003eAccording to the fundamental logic of Marx's theory of productivity, productivity is the productive capacity generated through the interaction and integration of workers, means of labor, and objects of labor. The distinction between digital productivity and general productivity lies in the former's immense potential to generate new value through the use of digital technologies. Digital productivity is characterized by its focus on high-tech, digitization, and intelligence in the context of new industrialization. It emphasizes breakthrough technological innovations, the iterative development of disruptive products, and the cultivation of future-oriented industries, with a particular focus on fostering a robust and sustained productive capacity in the real economy, including the manufacturing sector. As the digital economy has become a key driver of economic growth for the Chinese government, data, algorithms, and computational power have emerged as new factors of productivity. In this framework, data is regarded as being on par with or even surpassing traditional production factors in its importance (Men, 2024).\u003c/p\u003e\n\u003cp\u003eDigital productivity has emerged as one of the key areas for future progress in productivity. It represents a new form of productivity within the digital realm. From the perspective of Marx's theory, digital productivity consists of digital laborers, digital labor materials, and digital labor objects. Digital laborers primarily include practitioners from the digital service industry, while digital labor materials encompass both tangible resources, such as the Internet, and intangible assets, such as patents for digital technologies. Digital labor objects comprise digital enterprises and related digital businesses. With the ongoing expansion of the digital economy, technologies such as artificial intelligence, the Internet of Things, big data, and blockchain will become central to the formation and development of digital productivity. The advancement of these technologies is heavily reliant on the support of internet infrastructure, with data transmission, storage, and computation playing a crucial role in enabling the transformation of digital technologies into digital productivity. Moreover, the development of digital productivity is also accompanied by evolving digital production relations. Key aspects of these relations include the property rights associated with digital assets, the distribution of digital value, and organizational forms such as loose coupling, virtual agglomeration, and network linkages. These elements are critical factors influencing the development of digital productivity in the future.\u003c/p\u003e\n\u003cp\u003e\u003cem\u003e2.2.2 Internet infrastructure development and digital productivity\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003eThe development of digital productivity requires the formation and integration of digital workers, digital means of labor, and digital objects of labor, often driven by significant exogenous factors, such as internet infrastructure construction policies initiated by government agencies. In promoting the digital economy, government departments have invested substantial financial resources into the construction of internet infrastructure, particularly under national strategies like \"Broadband China.\" This has triggered a nationwide surge in internet infrastructure development. The ongoing expansion of internet infrastructure has facilitated the creation of digital workers, digital labor resources, and digital labor objects, thereby providing the foundational conditions for the growth of digital productivity.\u003c/p\u003e\n\u003cp\u003eFirst, internet infrastructure construction plays a key role in cultivating digital laborers. As government agencies promote the development of internet infrastructure, they can directly generate relevant job opportunities through construction projects, train and develop skilled technicians and workers, and increase labor demand within enterprises (Sun and Guo, 2021). Additionally, internet infrastructure development encourages higher education institutions, research institutes, and related enterprises to train digital professionals across various fields such as R\u0026amp;D, application, and promotion, in line with policy directives. This process gradually builds and expands a large-scale digital workforce.\u003c/p\u003e\n\u003cp\u003eSecondly, internet infrastructure construction provides essential digital labor materials. Digital labor means can generally be categorized into tangible and intangible types, with internet infrastructure construction primarily offering tangible digital labor means, such as broadband Internet ports, information communication base stations, fiber optic networks, big data computing facilities, and cloud computing platforms. These infrastructures ensure the smooth transmission of information, data storage, data computation, and network connectivity, enabling data elements to integrate with traditional production factors and be utilized in production processes. Furthermore, internet infrastructure development also fosters the advancement of digital technology research, digital finance, and other digital service sectors, leading to the creation of digital patents, digital financial products, and other intangible digital labor materials. These innovations provide crucial technical and capital support for the growth of digital productivity.\u003c/p\u003e\n\u003cp\u003eFinally, internet infrastructure construction gives rise to digital labor objects such as digital enterprises and various digital businesses. Generally speaking, certain businesses in internet infrastructure construction need to be undertaken by specialized digital enterprises, and the intermediate products and end products produced by various links of digital enterprises are direct digital labor objects. At the same time, telecommunications and postal services built on internet infrastructure, as well as other digital industries and the demand for financial and commercial services resulting from the construction of internet infrastructure, can become numerous digital labor objects (Guo et al., 2020). Therefore, internet infrastructure construction can promote the development of digital productivity by facilitating the formation and integration of digital workers, digital labor materials, and digital labor objects. Based on this, this paper proposes the first research hypothesis.\u003c/p\u003e\n\u003cp\u003eHypothesis 1: internet infrastructure development can significantly contribute to digital productivity development.\u003c/p\u003e\n\u003cp\u003e\u003cem\u003e2.2.3 Mechanisms by which internet infrastructure development affects digital productivity\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003eThis paper describes the mechanism of internet infrastructure development for digital productivity development from four aspects: internet infrastructure promotes the concentration of highly skilled personnel, improves the degree of marketization, stimulates the vitality of urban innovation, and strengthens the science and technology service industry. As a national strategic initiative and key industrial policy promoted by the government, internet infrastructure construction tends to have multiple policy objectives, and there are often multiple ways for the policy to play a role. internet infrastructure construction is essentially a channel and platform for the transmission of information to society, aiming to improve the efficiency of information transmission, reduce information costs, and promote market expansion and inter-subjective synergy. At the same time, the construction of internet infrastructure will also bring about the in-depth use of a large number of digital devices as well as extensive knowledge sharing and spillover, in particular, technological innovation triggered by digitization has become an important driving factor in the development of digital productivity. Specifically:\u003c/p\u003e\n\u003cp\u003eFirst, internet infrastructure promotes the clustering of highly skilled talent. Highly skilled workers are the driving force of the knowledge economy and are essential for the development of digital productivity. Well-developed internet infrastructure facilitates the dissemination, diffusion, and sharing of knowledge, which, in turn, attracts the concentration of highly skilled talent, particularly entrepreneurial talent. This clustering can occur both in physical spaces and through virtual networks, with the latter made possible by digital platforms. When internet infrastructure fosters the concentration of skilled workers, it increases the likelihood of digital technological innovation and iteration, thereby enhancing innovation efficiency. This, undoubtedly, serves as a vital source of momentum for the advancement of digital productivity.\u003c/p\u003e\n\u003cp\u003eSecond, internet infrastructure increases the degree of marketization. Acemoglu (2002) argues that the degree of marketization plays a decisive role in the factor bias of scientific and technological progress. With robust internet infrastructure, market information can circulate rapidly, significantly reducing communication costs between producers and consumers, thereby facilitating more efficient market transactions and behavioral coordination. As a result, internet infrastructure contributes to enhancing the degree of marketization. An increased degree of marketization improves the efficiency of optimal factor allocation, particularly by promoting the rapid movement and concentration of digital factors. The swift flow of data can be more effectively integrated with other production factors, while the agglomeration of data factors also fosters technological innovation (Liu et al., 2023a). Notably, the growth of e-commerce and its derivative industries, driven by digital payment and digital finance, allows for more efficient integration of digital workers, digital labor materials, and digital labor objects, thus advancing the development of digital productivity.\u003c/p\u003e\n\u003cp\u003eOnce again, it stimulates the city's innovation vitality. As mentioned earlier, cyberinfrastructure contributes to the agglomeration of innovative talents and knowledge overflow (He and Guo, 2023), which is the main way to enhance urban innovation capacity and activate urban innovation vitality. In addition, internet infrastructure can both promote the digital enhancement of urban innovation platforms and accelerate the realization of digital transformation of traditional industries, generating new business forms and new models, thus forming a better innovation ecology and enabling urban innovation subjects to produce more innovation results. At the same time, the inclusion of data elements can also promote the diffusion of enterprise technology (Xue et al., 2020), promote enterprises to expand the innovation boundary and develop new technologies (Shen et al., 2023) and help enterprises realize continuous innovation, which is also an important way for internet infrastructure construction to stimulate urban innovation vitality.\u003c/p\u003e\n\u003cp\u003eFinally, internet infrastructure contributes to the growth of the science and technology service industry. This industry is fundamental to the development of science and technology, as well as to the advancement of high-tech industries where technology is the core production factor. The professional and technical services it provides significantly enhance the added value of industries and the technological content of products (Qian and Cai, 2023). The construction of internet infrastructure creates better physical conditions and conducive environments for technology consulting, R\u0026amp;D services, information technology services, and education and training, enabling more efficient utilization of scientific and technological resources. It also provides a better environment for research and innovation for scientific and technological workers. In particular, the growing level of intelligence in the science and technology service industry helps improve service efficiency, saving substantial amounts of scientific resources and the time of technology workers. This, without a doubt, acts as a crucial driver in advancing digital productivity.\u003c/p\u003e\n\u003cp\u003eHypothesis 2: internet infrastructure development has a significant effect on the development of digital productivity by promoting the pooling of highly skilled people.\u003c/p\u003e\n\u003cp\u003eHypothesis 3: internet infrastructure development has a significant effect on digital productivity development through increased marketization.\u003c/p\u003e\n\u003cp\u003eHypothesis 4: internet infrastructure development has a significant effect on digital productivity development by stimulating urban innovation.\u003c/p\u003e\n\u003cp\u003eHypothesis 5: Cyberinfrastructure development has a significant impact on digital productivity development through the growth of the science and technology services sector.\u003c/p\u003e"},{"header":"3 Introduction to the empirical methodology and data","content":"\u003cdiv id=\"Sec2\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Modeling\u003c/h2\u003e \u003cp\u003eThe \"Broadband China\" pilot policy, utilized in this paper, is commonly considered a \"quasi-natural experiment.\" The Difference-in-Differences (DID) model is a widely applied econometric technique that offers significant advantages when analyzing panel data, particularly in terms of controlling for individual heterogeneity and time trends. This enables more precise estimation of causal relationships between variables and has become an established method for evaluating the effects of policy interventions. Consequently, this paper constructs a quasi-natural experiment based on the \"Broadband China\" pilot program and employs the DID model for empirical analysis. Given that the list of pilot cities for the \"Broadband China\" policy was released in batches in 2014, 2015, and 2016, the paper applies a multi-period DID model to assess the policy's impact. The cities selected as pilot locations are designated as the treatment group, while those not selected serve as the control group, with the control group coded as 0. By comparing the difference in digital productivity between the treatment and control groups, this analysis allows for the evaluation of the policy's effect on the development of the digital economy. The specific modeling is presented in Eq.\u0026nbsp;(\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e):\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:Dignq{p}_{it}={\\alpha\\:}_{0}+{\\alpha\\:}_{1}DID+{\\alpha\\:}_{2}Contro{l}_{it}+{\\varphi\\:}_{i}+{\\gamma\\:}_{t}+{\\epsilon\\:}_{it}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e(1) In Eq.\u0026nbsp;(\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e), the explained variable\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:Dignq{p}_{it}\\)\u003c/span\u003e\u003c/span\u003erepresents the city's digital productivity, the subscript \u003cem\u003ei\u003c/em\u003e represents the city to which it belongs, and \u003cem\u003et\u003c/em\u003e represents the year, and\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:DID\\)\u003c/span\u003e\u003c/span\u003e is the regional variable of whether it is selected as a pilot city at the policy point in time;\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:Contro{l}_{it}\\)\u003c/span\u003e\u003c/span\u003e is the control variable; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varphi\\:}_{i}\\)\u003c/span\u003e\u003c/span\u003e for city fixed effects;\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\gamma\\:}_{t}\\)\u003c/span\u003e\u003c/span\u003e is the Time fixed effect; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\epsilon\\:}_{it}\\)\u003c/span\u003e\u003c/span\u003e is the randomized disturbance term. (1) The coefficients of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:DID\\)\u003c/span\u003e\u003c/span\u003e is the coefficient of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\alpha\\:}_{1}\\)\u003c/span\u003e\u003c/span\u003e is the double-difference estimator, which can measure the impact of the \"Broadband China\" pilot policy on digital productivity, and is the estimator that this paper focuses on, i.e., if the \"Broadband China\" pilot policy is conducive to promoting digital productivity, the coefficient is significantly positive.\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\alpha\\:}_{1}\\)\u003c/span\u003e\u003c/span\u003e That is, if the \"Broadband China\" pilot policy is conducive to promoting digital productivity, the coefficient is significantly positive. Conversely, if the \"Broadband China\" pilot policy is not conducive to the promotion of digital productivity, the coefficient is significantly negative. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\alpha\\:}_{1}\\)\u003c/span\u003e\u003c/span\u003e is significantly negative.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Variable selection\u003c/h2\u003e \u003cdiv id=\"Sec4\" class=\"Section3\"\u003e \u003ch2\u003e3.2.1 Explained variables: Digital productivity (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:Dignq\\)\u003c/span\u003e\u003c/span\u003e)\u003c/h2\u003e \u003cp\u003eConsidering that digital productivity is a comprehensive indicator and consists of multiple indicators, we draws on the theoretical results of scholars such as Xu et al. (\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2024\u003c/span\u003e), and adopts the Entropy Method to measured the comprehensive index of digital productivity of different cities in each year from 2011 to 2019. And since each indicator in this paper is positively influenced, the raw data of each three-level indicator is standardized according to the way (2):\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:{\\text{z}}_{ij}=\\frac{{\\mathbf{x}}_{ij}-\\text{m}\\text{i}\\text{n}\\left({\\mathbf{x}}_{ij}\\right)}{\\text{m}\\text{a}\\text{x}\\left({\\mathbf{x}}_{ij}\\right)-\\text{m}\\text{i}\\text{n}\\left({\\mathbf{x}}_{ij}\\right)}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere (2) in the equation \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\mathbf{x}}_{ij}\\)\u003c/span\u003e\u003c/span\u003e is the original value of each basic indicator, which represents the specific value of the \u003cem\u003ejth\u003c/em\u003e indicator of the \u003cem\u003eith\u003c/em\u003e city, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{z}}_{ij}\\)\u003c/span\u003e\u003c/span\u003e is the result after the standardization of indicator \u003cem\u003ej\u003c/em\u003e. In addition, after the standardization process, it is necessary to calculate the information entropy and weight of specific indicators, which is calculated as follows:\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:{\\text{E}}_{\\text{j}}=-\\frac{1}{\\text{l}\\text{n}\\left(\\text{n}\\right)}\\sum\\:_{\\text{i}=1}^{\\text{n}}\\left(\\frac{{\\text{z}}_{ij}}{\\sum\\:_{\\text{i}=1}^{\\text{n}}{\\text{z}}_{ij}}\\text{l}\\text{n}\\frac{{\\text{z}}_{ij}}{\\sum\\:_{\\text{i}=1}^{\\text{n}}{\\text{z}}_{ij}}\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\:{\\omega\\:}_{j}=\\frac{\\left(1-{E}_{j}\\right)}{\\sum\\:_{j=1}^{m}\\left(1-{E}_{j}\\right)}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere equations (\u003cspan refid=\"Equ3\" class=\"InternalRef\"\u003e3\u003c/span\u003e) and (\u003cspan refid=\"Equ4\" class=\"InternalRef\"\u003e4\u003c/span\u003e) calculate the information entropy \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003eij\u003c/em\u003e\u003c/sub\u003e of indicator \u003cem\u003ej\u003c/em\u003e and weights respectively\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\omega\\:}_{j}\\)\u003c/span\u003e\u003c/span\u003e, \u003cem\u003en\u003c/em\u003e is the number of sample cities, \u003cem\u003em\u003c/em\u003e denotes the number of indicators, and finally the composite index of digital productivity is calculated and its expression is as follows:\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$$\\:{\\text{D}\\text{i}\\text{g}\\text{n}\\text{q}\\text{p}}_{i1}=\\sum\\:_{j=1}^{m}{\\text{z}}_{ij}\\times\\:{{\\omega\\:}}_{\\text{j}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eIndicator system for digital productivity\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel 1 indicators\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSecondary indicators\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTertiary indicators\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eIndicator measurement modalities\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eIndicator properties\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDigital Worker\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNumber of digital workers\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eDigital industry practitioners\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eTotal information transmission, computer, software personnel (10,000)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e+\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003eDigital labor information\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003ePhysical means of production\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eRegional Internet coverage\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eInternational Internet users (million)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e+\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCell phone penetration rate\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eNumber of cell phone subscribers (million)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e+\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eIntangible means of production\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eLevel of digital finance\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eDigital Financial Inclusion Composite Index\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e+\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eNumber of digital technology inventions\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eNatural logarithm of patents for digital inventions in the current year\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e+\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eDigital Labor Objects\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003edigital enterprise\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eNumber of digital businesses\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eArtificial Intelligence Enterprises (number)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e+\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTotal telecommunication services\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eNatural logarithm of total telecommunications operations\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e+\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003edigital business\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTotal postal operations\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eNatural logarithm of total postal operations\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e+\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section3\"\u003e \u003ch2\u003e3.2.2 Explanatory variables: Internet infrastructure development\u003c/h2\u003e \u003cp\u003eThe explanatory variable in this paper is internet infrastructure construction, which is represented by the interaction term DID between the \"Broadband China\" policy pilot treatment variable and the policy point-in-time variable, which takes the value of 1 if the city is selected as a pilot city after the policy point-in-time, and the value of 0 if the city is not selected as a pilot city after the policy point-in-time.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section3\"\u003e \u003ch2\u003e3.2.3 Control variables\u003c/h2\u003e \u003cp\u003eIn this paper, the level of economic development, the level of openness to the outside world, the extent of the service sector, the development of industrialization, the expenditure on education, and the level of financial development, which may have an impact on the explanatory variables, are chosen as control variables. The variables are defined in the following way Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e shown:\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eDefinition of the main variables\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eVariable classification\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003evariable name\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003emeasurement method\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eexplanatory variable\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDigital productivity\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMeasured by the entropy method\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCore explanatory variables\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDID\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eWhether city \u003cem\u003ei\u003c/em\u003e is a pilot area for the \"broadband policy\" strategy in period \u003cem\u003et\u003c/em\u003e: yes\u0026thinsp;=\u0026thinsp;1, no\u0026thinsp;=\u0026thinsp;0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003eMechanism variables\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ehighly skilled person\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eNumber of employees in scientific and technical services and geological surveying (10,000 persons)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMarketization index\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMarketization index\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eUrban Innovation Index\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eUrban Innovation Index\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eScience and technology services industry\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eNumber of enterprises belonging to the scientific research and technological services industry (10,000)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSelect Variable\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAggregate index score\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eChina Digital Innovation Index\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"5\" rowspan=\"6\"\u003e \u003cp\u003econtrol variable\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLevel of economic development\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eNatural logarithm of real per capita GDP\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eEgypt's open-door policy towards the outside world\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eNatural logarithm of the amount of foreign investment actually utilized in the year, in tens of thousands of dollars\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLevel of services\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eRatio of value added of tertiary industry in 10,000 yuan to GDP in 10,000 yuan\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eIndustrialized development\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eRatio of value added of secondary industry in 10,000 yuan to gross regional product in 10,000 yuan\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eExpenditure on education\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eRatio of education expenditures of \u003cspan\u003e$\u003c/span\u003e10,000,000 to expenditures of \u003cspan\u003e$\u003c/span\u003e10,000,000 in the general budget of local finances\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLevel of financial development\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBalance of deposits in financial institutions at the end of the year, million yuan / Gross regional product, million yuan\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e3.3 Descriptive statistics of variables\u003c/h2\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e reports the results of descriptive statistics for each variable. The mean value of digital productivity is 0.574, while the maximum and minimum values are 12.87 as well as -14.77, respectively, indicating that digital productivity remains highly variable across different cities in the country.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eResults of descriptive statistics of variables\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003evariable name\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNumber of observations\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eaverage value\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e(statistics) standard deviation\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eminimum value\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003emaximum values\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDigital productivity\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2153\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.182\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.598\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-14.77\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e12.87\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDID\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2153\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.242\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.429\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ehighly skilled person\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2153\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.547\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e4.787\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0110\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e71.72\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMarketization index\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2111\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e11.70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e2.216\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e4.960\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e19.16\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eUrban Innovation Index\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2153\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.241\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.964\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.000113\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e19.63\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eScience and technology services industry\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2153\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.171\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.540\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.00170\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e7.602\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003estock index (statistics)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2153\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e56.62\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e27.39\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.298\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eExpenditure on education\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2153\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.177\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0396\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0357\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.356\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eIndustrialized development\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2152\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e47.16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e10.22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e11.70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e89.34\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel of services\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2152\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e41.92\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e10.06\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e10.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e83.52\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel of economic development\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2152\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e10.76\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.566\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e8.773\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e13.06\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEgypt's open-door policy towards the outside world\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2102\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e10.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.842\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.099\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e14.94\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel of financial development\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2152\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.470\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.683\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.371\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e8.871\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e3.4 Data presentation\u003c/h2\u003e \u003cp\u003eThe empirical study in this paper selects the panel data of prefecture-level cities from 2011 to 2019, which contains 251 samples, of which the city sample data are from China Urban Statistical Yearbook, China Science and Technology Statistical Yearbook, and Digital Finance Research Center of Peking University. The list of pilot cities is from the website of the Ministry of Industry and Information Technology. This paper also fixes some of the missing values present in the data using linear interpolation.\u003c/p\u003e \u003c/div\u003e"},{"header":"4 Empirical results","content":"\u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e4.1 Benchmark regression results\u003c/h2\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e reports the results of the estimation of internet infrastructure development on digital productivity. The control variables are gradually incorporated into the model, one by one, through stepwise regression, while individual (city) fixed effects and Time fixed effects are also controlled for in order to more accurately estimate the net effect of the \"Broadband China\" pilot policy on digital productivity. The regression result of introducing the multiplicative term in column (1) shows that the regression coefficient of DID on digital productivity is 0.0166 (significantly positive at the 1% level), which shows that internet infrastructure construction can significantly promote the development of digital productivity. Considering that the economic development characteristics of prefecture-level cities may affect the development of digital productivity to a greater or lesser extent, and there is a certain relationship with whether or not the sample of prefecture-level cities has been selected by the pilot program of the \"Broadband China\" policy, Columns (2) to (7) gradually control for the economic development characteristics of the prefecture-level city level. The regression results of columns (2) to (7) show that the regression coefficient of digital productivity fluctuates slightly between 0.0160 and 0.0174 during the process of gradually adding control variables, but the regression result is still significantly positive at the 1% level. It indicates that the addition of control variables can to a certain extent exclude the influence of other potential factors on the benchmark regression, thus making the results of the benchmark regression more stable and accurate. The above regression results indicate that internet infrastructure construction can significantly promote the development of digital productivity under the promotion of the \"Broadband China\" pilot policy, which is in line with hypothesis H1.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eEstimated results of internet infrastructure development on digital productivity\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"8\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eVariables\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"7\" nameend=\"c8\" namest=\"c2\"\u003e \u003cp\u003eM\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(1)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e(2)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e(3)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e(4)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e(5)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e(6)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e(7)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDID\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.0166\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e(0.0047)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0160\u003csup\u003e***\u003c/sup\u003e (0.0046)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0162\u003csup\u003e***\u003c/sup\u003e (0.0046)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0162\u003csup\u003e***\u003c/sup\u003e (0.0046)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.0173\u003csup\u003e***\u003c/sup\u003e (0.0046)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.0174\u003csup\u003e***\u003c/sup\u003e (0.0044)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.0164\u003csup\u003e***\u003c/sup\u003e (0.0044)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eExpenditure on education\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026ndash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.3416\u003csup\u003e***\u003c/sup\u003e (0.0759)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.3524\u003csup\u003e***\u003c/sup\u003e (0.0760)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.3533\u003csup\u003e***\u003c/sup\u003e (0.0762)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.3166\u003csup\u003e***\u003c/sup\u003e (0.0752)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.2171\u003csup\u003e***\u003c/sup\u003e (0.0725)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.2109\u003csup\u003e***\u003c/sup\u003e (0.0724)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eIndustrialized development\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026ndash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026ndash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0008\u003csup\u003e**\u003c/sup\u003e (0.0004)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0010 (0.0009)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u0026minus;0.0034\u003csup\u003e***\u003c/sup\u003e (0.0011)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u0026minus;0.0038\u003csup\u003e***\u003c/sup\u003e (0.0010)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u0026minus;0.0040\u003csup\u003e***\u003c/sup\u003e (0.0010)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel of services\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026ndash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026ndash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026ndash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0002 (0.0011)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u0026minus;0.0034\u003csup\u003e***\u003c/sup\u003e (0.0011)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u0026minus;0.0041\u003csup\u003e***\u003c/sup\u003e (0.0011)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u0026minus;0.0041\u003csup\u003e***\u003c/sup\u003e (0.0011)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel of economic\u003c/p\u003e \u003cp\u003edevelopment\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026ndash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026ndash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026ndash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u0026ndash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.0826\u003csup\u003e***\u003c/sup\u003e (0.0110)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.0870\u003csup\u003e***\u003c/sup\u003e (0.0106)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.0758\u003csup\u003e***\u003c/sup\u003e (0.0116)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEgypt's open-door policy\u003c/p\u003e \u003cp\u003etowards the outside world\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026ndash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026ndash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026ndash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u0026ndash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u0026ndash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u0026minus;0.0015 (0.0015)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u0026minus;0.0018 (0.0015)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel of financial\u003c/p\u003e \u003cp\u003edevelopment\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026ndash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026ndash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026ndash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u0026ndash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u0026ndash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u0026ndash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u0026minus;0.0164\u003csup\u003e**\u003c/sup\u003e (0.0067)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eConstant\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.1773\u003csup\u003e***\u003c/sup\u003e (0.0016)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.1169\u003csup\u003e***\u003c/sup\u003e (0.0135)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0755\u003csup\u003e***\u003c/sup\u003e (0.0229)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0593\u003c/p\u003e \u003cp\u003e(0.0883)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u0026minus;0.4666\u003csup\u003e***\u003c/sup\u003e (0.1116)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u0026minus;0.4210\u003csup\u003e***\u003c/sup\u003e (0.1078)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u0026minus;0.2645\u003csup\u003e**\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e(0.1252)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eIndividual fixed effect\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTime fixed effect\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2152\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2152\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2150\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2150\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2150\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e2099\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e2099\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.9990\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.9990\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.9990\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.9990\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.9990\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.9992\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.9992\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"8\"\u003eNotes:\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003csup\u003e*\u003c/sup\u003e p\u0026thinsp;\u0026lt;\u0026thinsp;0.1 denote the significance level of 10%.\u003c/p\u003e \u003cp\u003e \u003csup\u003e**\u003c/sup\u003e p\u0026thinsp;\u0026lt;\u0026thinsp;0.05 denote the significance level of 5%.\u003c/p\u003e \u003cp\u003e \u003csup\u003e***\u003c/sup\u003e p\u0026thinsp;\u0026lt;\u0026thinsp;0. 01 denote the significance level of 1%.\u003c/p\u003e \u003cp\u003eThe numbers in parentheses are the standard errors.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e4.2 Robustness tests\u003c/h2\u003e \u003cdiv id=\"Sec12\" class=\"Section3\"\u003e \u003ch2\u003e4.2.1 Parallel trend test\u003c/h2\u003e \u003cp\u003eWhen assessing the timeliness of a policy using the double-difference method, a parallel trend test needs to be satisfied. That is, in the \"Broadband China\" pilot policy, the treatment and control groups have similar trends in digital productivity before the implementation of the policy. Therefore, this paper draws on Beck et al. (\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2010\u003c/span\u003e) and Fang and Zhao (\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) to conduct a balanced trend test using event analysis. In this paper, one dummy variable is set for each year before the implementation of the \"Broadband China\" pilot policy and interacted with the dummy variables of the experimental group, and then the core explanatory variable DID is added to the regression together with the study of the effect of these four interaction terms on digital productivity. The regression results are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, in which the coefficients of the dummy variables interacted with the experimental group in the years before the year of policy implementation are insignificant, but the results of DID as the core explanatory variable in the figure show significant positive. So to a certain extent, it can be proved that the model satisfies the parallel trend test.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section3\"\u003e \u003ch2\u003e4.2.2 Indented processing samples\u003c/h2\u003e \u003cp\u003eIn order to eliminate the influence of extreme outliers on the benchmark regression results, this study truncates and shrinks the upper and lower 1% of the study sample and re-runs the regression analysis. The results are shown in Column (1) of Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. After removing outliers, the coefficient estimates of the \"Broadband China\" pilot policy pass the test at the 1% significant level, which is consistent with the baseline estimates. This further validates the reliability and robustness of the study findings.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section3\"\u003e \u003ch2\u003e4.2.3 PSM-DID method test\u003c/h2\u003e \u003cp\u003eIn this study, propensity score matching (PSM) was used to cope with selectivity bias and endogeneity. PSM allows for the transformation of multidimensional covariates into one-dimensional propensity matching scores in the first place, and then matching based on these scores ensures that there is no significant difference between the treated and control groups after matching. Thus, it helps to reduce the bias due to self-selection and makes the research results more credible and interpretable. In this paper, GDP, urban household population, and financial level are used as covariates to match the propensity scores of the cities selected as the pilot cities of Broadband China, and the selection bias value of propensity score matching is within 10%, which indicates that this paper is suitable for propensity score matching. In addition, in order to further illustrate that this paper is suitable for propensity score matching, after propensity score matching, this paper further presents the histograms of the treatment group and control group (see Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e), which shows that the distribution of propensity scores of the treatment group and the control group after matching has a large overlap interval, and the propensity score is mostly concentrated in the vicinity of 0.1. Therefore, it is finally judged that it is suitable to use propensity score matching in this paper. As shown in column (2) of Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e, the results of using DID estimation after near-neighbor matching in caliper are shown. The estimation results show that the \"Broadband China\" pilot policy can promote the development of digital productivity, and the regression results after propensity score matching are similar to the baseline regression results in many aspects, which means that the model is robust and reliable.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec15\" class=\"Section3\"\u003e \u003ch2\u003e4.2.4 Instrumental variable method\u003c/h2\u003e \u003cp\u003eThe endogeneity problem caused by selection bias can be mitigated to some extent by shrinking the top and bottom 1% in the baseline regression, but the \"Broadband China\" pilot policy is still unavoidably affected by many unobservable factors. For this reason, this paper uses as instrumental variables the interaction term between the degree of terrain relief and the time dummy variable of whether or not the \"Broadband China\" pilot policy has been implemented. As shown in column (3) of Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e, the regression results show that the \"Broadband China\" pilot policy promotes the development of digital productivity still holds and the regression results are significant at the 1% level. In addition, the table shows that the LM statistic of the instrumental variable has a P-value of 0.0000, which significantly rejects the original hypothesis; and the F-statistic is larger than the critical value of Stock-Yogo's weak identification test at the 10% level. Therefore, it is reasonable to choose the interaction term of the time dummy variable between the degree of terrain relief and whether or not to start the implementation of the \"Broadband China\" pilot policy as the instrumental variable.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eRobustness test of the impact of internet infrastructure development on digital productivity\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eExplained variable: Digital\u003c/p\u003e \u003cp\u003eproductivity\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWinsor2\u003c/p\u003e \u003cp\u003e(1)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePSM-DID\u003c/p\u003e \u003cp\u003e(2)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eInstrumental variable\u003c/p\u003e \u003cp\u003e(3)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDID\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.0159\u003csup\u003e***\u003c/sup\u003e (0.0044)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0130\u003csup\u003e***\u003c/sup\u003e (0.0043)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0958\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e(0.0088)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eExpenditure on education\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.2691\u003csup\u003e***\u003c/sup\u003e (0.0765)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.1397\u003csup\u003e*\u003c/sup\u003e (0.0727)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.1854\u003csup\u003e**\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e(0.0785)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eIndustrialized development\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026minus;0.0037\u003csup\u003e***\u003c/sup\u003e (0.0011)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026minus;0.0049\u003csup\u003e***\u003c/sup\u003e (0.0011)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026minus;0.0031\u003csup\u003e***\u003c/sup\u003e (0.0011)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel of services\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026minus;0.0042\u003csup\u003e***\u003c/sup\u003e (0.0011)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026minus;0.0057\u003csup\u003e***\u003c/sup\u003e (0.0012)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026minus;0.0032\u003csup\u003e***\u003c/sup\u003e (0.0012\u003csup\u003e)\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel of economic development\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.0796\u003csup\u003e***\u003c/sup\u003e (0.0130)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0716\u003csup\u003e***\u003c/sup\u003e (0.0116)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0929\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e(0.0127)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEgypt\u0026rsquo;s open-door policy towards the outside world\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026minus;0.0018 (0.0017)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026minus;0.0015 (0.0015)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026minus;0.0034\u003csup\u003e**\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e(0.0017)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel of financial development\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026minus;0.0154\u003csup\u003e*\u003c/sup\u003e (0.0079)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026minus;0.0171\u003csup\u003e***\u003c/sup\u003e (0.0065)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026minus;0.0057\u003c/p\u003e \u003cp\u003e(0.0073)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eConstant\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026minus;0.3170\u003csup\u003e**\u003c/sup\u003e (0.1391)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026minus;0.0938 (0.1296)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026ndash;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAnderson canon. corr. LM statistic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026ndash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026ndash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e535.063\u003c/p\u003e \u003cp\u003e[0.0000]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCragg-Donald Wald F statistic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026ndash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026ndash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e747.167\u003c/p\u003e \u003cp\u003e[16.38]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eIndividual fixed effect\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTime fixed effect\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2099\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2090\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.9976\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.993\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.572\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"4\"\u003eNotes:\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003csup\u003e*\u003c/sup\u003e p\u0026thinsp;\u0026lt;\u0026thinsp;0.1 denote the significance level of 10%.\u003c/p\u003e \u003cp\u003e \u003csup\u003e**\u003c/sup\u003e p\u0026thinsp;\u0026lt;\u0026thinsp;0.05 denote the significance level of 5%.\u003c/p\u003e \u003cp\u003e \u003csup\u003e***\u003c/sup\u003e p\u0026thinsp;\u0026lt;\u0026thinsp;0. 01 denote the significance level of 1%.\u003c/p\u003e \u003cp\u003eThe numbers in parentheses are the standard errors.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec16\" class=\"Section3\"\u003e \u003ch2\u003e4.2.5 Placebo test\u003c/h2\u003e \u003cp\u003eTo ensure that the results of the benchmark regression are not due to some other unobservable or omitted variables, this paper further constructs a placebo test. This is done by randomizing the treatment groups, conducting 1000 random samples of the variables in the treatment groups, obtaining 1000 corresponding regression coefficients and p-values, and plotting their kernel density distributions and p-value distributions. Based on the distribution of kernel density estimates of 1000 randomized experiments (see Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e), it is found that the corresponding estimates of regression coefficients are around the 0 point and very close to the standard normal distribution, and the majority of the P-values are greater than 0.1, indicating that the majority of the regression results are not significant, and thus the original hypothesis is not valid, which indicates that the results of the benchmark regression results obtained in the previous paper passed the placebo test, and that the The promotion effect of the \"Broadband China\" pilot policy on the development of digital productivity is not caused by other unobservable factors.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec17\" class=\"Section3\"\u003e \u003ch2\u003e4.2.6 Goodman-Bacon decomposition\u003c/h2\u003e \u003cp\u003eSince the treatment effect of TWFE regression in the estimation process of DID model can have heterogeneous treatment effect (HTE) at different treatment times or between different treatment groups, which leads to \"bad treatment groups\", thus leading to possible bias in the estimation of DID parameters in the traditional multi-period DID model, and the literature is not clear on this issue. For example, Zhang et al. (\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2024\u003c/span\u003e) and Baker et al. (\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). have thoroughly discussed the bias problem of multi-temporal double difference models with two-way fixed (TWFE) effects using Goodman-Bacon decomposition. Therefore, this paper draws on this literature as well as the Goodman-Bacon (\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) approach, utilizes the Goodman-Bacon decomposition to test the robustness of the impact of internet infrastructure development on digital productivity. In conducting the Goodman-Bacon decomposition, this paper further treats the sample data as a strongly balanced panel from 2011 to 2019. Referring to He and Wang (\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2024\u003c/span\u003e) study, the decomposition results reported in Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e are obtained. From the results, it can be seen that the share of Late_v_Early is only 6.61%, thus further proving that the benchmark regression results in this paper are robust.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eGoodman-Bacon decomposition weighting table\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBeta\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTotal Weight\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEarly_v_Late\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-0.0008504615\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0122276324\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLate_v_Early\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-0.0013131396\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0203793867\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEarly_v_Late\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-0.0051221242\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0244552648\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLate_v_Early\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.0123147555\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0326070173\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEarly_v_Late\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-0.0065626237\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0132190616\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLate_v_Early\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.0111245615\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0132190616\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNever_v_timing\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.0181979939\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.8838925755\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec18\" class=\"Section3\"\u003e \u003ch2\u003e4.2.7 Heckman two-step estimation\u003c/h2\u003e \u003cp\u003eFrom the perspective of the interaction logic between the \"Broadband China\" pilot policy and digital productivity, it can be concluded that there is actually an endogenous problem caused by sample selectivity bias. The outstanding level of digital innovation of a city is more likely to be selected as a pilot city for the \"Broadband China\" policy by government departments, and these endogenous problems will lead to biased estimation results. Therefore, this paper adopts Heckman\u0026rsquo;s (\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e1979\u003c/span\u003e) two-stage regression method to test whether the results are biased. This paper adopts Heckman\u0026rsquo;s (\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e1979\u003c/span\u003e) two-stage regression method to test whether there is an endogeneity problem due to sample selection. In addition, this paper introduces the aggregate index score as a selection variable, and in order to satisfy the Heckman two-step estimation, extreme values are excluded, and the dependent variable is truncated with upper and lower 1% before the Heckman two-step estimation is carried out (the results are shown in columns (1) and (2) of Table\u0026nbsp;\u003cspan refid=\"Tab7\" class=\"InternalRef\"\u003e7\u003c/span\u003e). From the regression results, the inverse Mills ratio in column (2) of Table\u0026nbsp;\u003cspan refid=\"Tab7\" class=\"InternalRef\"\u003e7\u003c/span\u003e is significantly positive at the 5% level, i.e., it indicates that there is some degree of sample selection bias problem in the original equation. However, the core explanatory variables are still significantly positive in the Heckman two-step estimation results, which indicates that the results of the benchmark regression are reliable when the sample selection bias problem is considered.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec19\" class=\"Section3\"\u003e \u003ch2\u003e4.2.8 Exclusion of special cities\u003c/h2\u003e \u003cp\u003eThe \"Broadband China\" pilot policy is a governmental policy for internet infrastructure construction, which has obvious geographical characteristics and may be influenced by urban characteristics. There are not only large cities with unique and representative economic status like Beijing, Chongqing, and Shanghai, but also provincial capitals with important political, cultural, and economic status, and will these cities with important responsibilities and functions and special distribution of resources also have an impact on digital productivity regarding internet infrastructure construction? In order to more accurately assess the impact of internet infrastructure construction on digital productivity under the \"Broadband China\" pilot policy, this paper excludes municipalities and provincial capitals from the original full sample, and then conducts a regression on this basis. The final regression results in column (3) of Table\u0026nbsp;\u003cspan refid=\"Tab7\" class=\"InternalRef\"\u003e7\u003c/span\u003e show that after excluding the samples of municipalities and provincial capitals, the \"Broadband China\" pilot policy still significantly improves the level of digital productivity, which further proves that the conclusions of this paper are robust.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab7\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 7\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eRobustness test\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eExplained Variables:\u003c/p\u003e \u003cp\u003eDigital productivity\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003eThe Heckman Two-Step\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eExcluding provincial capitals\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eDML\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(1)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e(2)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e(3)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e(4)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003edid\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.1045**\u003c/p\u003e \u003cp\u003e(0.0418)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.6839***\u003c/p\u003e \u003cp\u003e(0.2129)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0106***\u003c/p\u003e \u003cp\u003e(0.0040)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.2017**\u003c/p\u003e \u003cp\u003e(0.0904)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDigital Innovation Index\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-0.0737***\u003c/p\u003e \u003cp\u003e(0.0137)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003einverse Mills ratio\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.4083**\u003c/p\u003e \u003cp\u003e(0.1890)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eExpenditure on education\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.2960\u003c/p\u003e \u003cp\u003e(0.4755)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-17.2038***\u003c/p\u003e \u003cp\u003e(2.7562)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.1370**\u003c/p\u003e \u003cp\u003e(0.0623)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.2783\u003c/p\u003e \u003cp\u003e(1.1021)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eIndustrialized development\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.0091**\u003c/p\u003e \u003cp\u003e(0.0038)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-0.1197***\u003c/p\u003e \u003cp\u003e(0.0398)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-0.0020**\u003c/p\u003e \u003cp\u003e(0.0009)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-0.0006\u003c/p\u003e \u003cp\u003e(0.0097)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel of services\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.0097**\u003c/p\u003e \u003cp\u003e(0.0047)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-0.0967**\u003c/p\u003e \u003cp\u003e(0.0442)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-0.0026***\u003c/p\u003e \u003cp\u003e(0.0009)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0035\u003c/p\u003e \u003cp\u003e(0.0115)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel of economic development\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-0.1998***\u003c/p\u003e \u003cp\u003e(0.0519)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.6818**\u003c/p\u003e \u003cp\u003e(0.3282)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0478***\u003c/p\u003e \u003cp\u003e(0.0103)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0315\u003c/p\u003e \u003cp\u003e(0.1242)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEgypt's open-door policy towards the outside world\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.0111\u003c/p\u003e \u003cp\u003e(0.0104)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0995*\u003c/p\u003e \u003cp\u003e(0.0572)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-0.0017\u003c/p\u003e \u003cp\u003e(0.0013)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-0.0337\u003c/p\u003e \u003cp\u003e(0.0259)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel of financial development\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-0.0683*\u003c/p\u003e \u003cp\u003e(0.0367)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-0.0639\u003c/p\u003e \u003cp\u003e(0.2093)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-0.0255***\u003c/p\u003e \u003cp\u003e(0.0070)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-0.0944\u003c/p\u003e \u003cp\u003e(0.0807)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eConstant\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.4092***\u003c/p\u003e \u003cp\u003e(0.4236)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e12.7107***\u003c/p\u003e \u003cp\u003e(3.5220)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-0.0882\u003c/p\u003e \u003cp\u003e(0.1118)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.1679\u003c/p\u003e \u003cp\u003e(0.9139)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eIndividual fixed effect\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYES\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eYES\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eYES\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTime fixed effect\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYES\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eYES\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eYES\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2102\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2102\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1849\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2153\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eR2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.9995\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.002\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec20\" class=\"Section3\"\u003e \u003ch2\u003e4.2.9 Tests of dual machine learning methods (DML)\u003c/h2\u003e \u003cp\u003eSince the DID model estimation relies on a strict parallel trend assumption, i.e., it is assumed that the difference between the control and treatment groups remains constant over time in the absence of treatment benefits. However, the parallel trend assumption of the DID model is considered to be too stringent and can have an impact on the consistency of the estimation results. In contrast, the dual machine learning (DML) approach proposed by Chernozhukov et al. (\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2018\u003c/span\u003e) is able to make causal inferences without relying on this overly harsh assumption, and therefore has some advantages over the DID model. Therefore, in this paper, the DML method is used for robustness testing. First, it is necessary to construct a partial linear regression model, which is similar to a semiparametric regression model without specifying the functional form of the characteristic variables, and the partial linear model is as follows:\u003cdiv id=\"Equ6\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ6\" name=\"EquationSource\"\u003e\n$$\\:{\\text{D}\\text{i}\\text{g}\\text{n}\\text{q}\\text{p}}_{\\text{i}\\text{t}+1}={{\\theta\\:}}_{0}DID+\\text{g}\\left({\\text{X}}_{\\text{i}\\text{t}}\\right)+{\\text{U}}_{\\text{i}\\text{t}}，\\text{E}\\left({\\text{U}}_{\\text{i}\\text{t}}\\mid\\:{\\text{X}}_{\\text{i}\\text{t}},\\text{D}\\text{I}\\text{D}\\right)=0$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e6\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ7\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ7\" name=\"EquationSource\"\u003e\n$$\\:DID=\\text{m}\\left({\\text{X}}_{\\text{i}\\text{t}}\\right)+{\\text{V}}_{\\text{i}\\text{t}}，\\text{E}\\left({\\text{V}}_{\\text{i}\\text{t}}\\mid\\:{\\text{X}}_{\\text{i}\\text{t}}\\right)=0$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e7\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewherein the\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{D}\\text{i}\\text{g}\\text{n}\\text{q}\\text{p}}_{\\text{i}\\text{t}+1}、DID\\)\u003c/span\u003e\u003c/span\u003e has the same meaning as above, and\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{X}}_{\\text{i}\\text{t}}\\)\u003c/span\u003e\u003c/span\u003e denotes the high-dimensional feature variables, and\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{g}\\left({\\text{X}}_{\\text{i}\\text{t}}\\right)\\text{和}\\text{m}\\left({\\text{X}}_{\\text{i}\\text{t}}\\right)\\)\u003c/span\u003e\u003c/span\u003e denotes two functions on the feature variables (control variables), the specific function form is unknown and needs to be estimated by machine learning.\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{U}}_{\\text{i}\\text{t}}\\)\u003c/span\u003e\u003c/span\u003e and\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{V}}_{\\text{i}\\text{t}}\\)\u003c/span\u003e\u003c/span\u003e are error terms with conditional mean 0. In the process of performing dual machine learning estimation, this paper adopts the random forest method to split the total study sample into two parts: the main sample N-n and the auxiliary sample n. The main sample is used to estimate\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{{\\theta\\:}}_{0}\\)\u003c/span\u003e\u003c/span\u003e and the auxiliary sample is used to estimate \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{g}\\left({\\text{X}}_{\\text{i}\\text{t}}\\right)\\)\u003c/span\u003e\u003c/span\u003e. Machine learning estimation of Eq.\u0026nbsp;(\u003cspan refid=\"Equ8\" class=\"InternalRef\"\u003e8\u003c/span\u003e) is performed by introducing the Neyman orthogonal function to counteract the bias arising from the bias introduced in the first step of estimating Eq.\u0026nbsp;(\u003cspan refid=\"Equ7\" class=\"InternalRef\"\u003e7\u003c/span\u003e) with machine learning. Here the\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{V}}_{\\text{i}\\text{t}}\\)\u003c/span\u003e\u003c/span\u003e viewed as an instrumental variable for DID, with\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{V}}_{\\text{i}\\text{t}}\\)\u003c/span\u003e\u003c/span\u003e Replacing the DID for the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{D}\\text{i}\\text{g}\\text{n}\\text{q}\\text{p}}_{\\text{i}\\text{t}+1}\\)\u003c/span\u003e\u003c/span\u003e regression, an unbiased coefficient estimate is obtained \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\stackrel{ˇ}{{\\theta\\:}}}_{0}\\)\u003c/span\u003e\u003c/span\u003e:\u003cdiv id=\"Equ8\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ8\" name=\"EquationSource\"\u003e\n$$\\:{\\stackrel{ˇ}{{\\theta\\:}}}_{0}={\\left(\\frac{1}{\\text{n}}\\sum\\:_{\\text{i}\\in\\:\\text{I},\\text{t}\\in\\:\\text{T}}{\\widehat{\\text{V}}}_{\\text{i}\\text{t}}\\text{D}\\text{I}\\text{D}\\right)}^{-1}\\frac{1}{\\text{n}}\\sum\\:_{\\text{i}\\in\\:\\text{I},\\text{t}\\in\\:\\text{T}}{\\widehat{\\text{V}}}_{\\text{i}\\text{t}}\\left({\\text{D}\\text{i}\\text{g}\\text{n}\\text{q}\\text{p}}_{\\text{i}\\text{t}+1}-\\widehat{\\text{g}}\\left({\\text{X}}_{\\text{i}\\text{t}}\\right)\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e8\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eColumn (4) of Table\u0026nbsp;\u003cspan refid=\"Tab7\" class=\"InternalRef\"\u003e7\u003c/span\u003e reports the estimation results of the DML methodology, which shows that the estimated coefficients of DID are significant at the 5% level, indicating that the baseline regression results in this paper are not affected by the strict parallel trend assumption, and so the baseline regression results are robust.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec21\" class=\"Section2\"\u003e \u003ch2\u003e4.3 Heterogeneity analysis\u003c/h2\u003e \u003cdiv id=\"Sec22\" class=\"Section3\"\u003e \u003ch2\u003e4.3.1 Regional heterogeneity\u003c/h2\u003e \u003cp\u003eIn this paper, from the regional perspective, we will set regional dummy variables, take the values of the three types of samples in the west, central and east, and generate the interaction term with did, and then use the interaction term to conduct a regression. The estimation results, as shown in column (1) of Table\u0026nbsp;\u003cspan refid=\"Tab8\" class=\"InternalRef\"\u003e8\u003c/span\u003e, show that there is significant heterogeneity in the promotion effect of internet infrastructure construction on digital productivity in the East, Central and West. Therefore, it can be concluded that under the pilot policy of \"Broadband China\", internet infrastructure construction can promote the development of digital productivity in the western region, and the benefit of digital productivity in the eastern region is not obvious.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec23\" class=\"Section3\"\u003e \u003ch2\u003e4.3.2 Heterogeneity of city administrative levels\u003c/h2\u003e \u003cp\u003eSince important economic resources of the Chinese government are mainly allocated from top to bottom according to the administrative level, cities with higher administrative levels tend to receive more resources. The administrative levels of Chinese government cities, from highest to lowest, are municipalities, sub-provincial cities, planned cities, and ordinary prefectures, with sub-provincial cities including provincial capitals and planned cities (Feng and Li, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). In this paper, we distinguish the study sample into high-level cities (including municipalities, separately listed cities, and provincial capitals) and low-level cities (including ordinary prefecture-level cities), generate administrative level dummy variables, and generate interaction terms with did, and then regress the benchmark model using the interaction. The analysis results in Column (2) of Table\u0026nbsp;\u003cspan refid=\"Tab8\" class=\"InternalRef\"\u003e8\u003c/span\u003e show that internet infrastructure development promotes digital productivity in high-administrative-level cities more significantly than in low-administrative-level cities. The reason for this is that high-level cities have greater financial autonomy and are able to invest more resources in digital productivity development (Jiang et al., \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2018\u003c/span\u003e), at the same time, high-level cities can attract more high-quality talents and high-tech industries (Ge et al., \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2024\u003c/span\u003e) and the scale effect of internet infrastructure construction is stronger. While low administrative level cities have relative disadvantages in these aspects, so internet infrastructure construction has a relatively weaker role in promoting the development of digital productivity in low administrative level cities.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec24\" class=\"Section3\"\u003e \u003ch2\u003e4.3.3 Heterogeneity of urban agglomerations\u003c/h2\u003e \u003cp\u003eThe report of the twentieth Party Congress emphasized the need to \"build a coordinated development pattern of large, medium-sized and small cities based on city clusters and metropolitan areas\". City clusters are an important form of regional economic cooperation and integrated development for the Chinese Government; through the radiation-driven central cities, multiple cities complement each other's strengths and integrate their markets, generating economies of scale and spillover effects in the allocation of factors. In fact, the important role of city clusters is that it strengthens industrial integration, knowledge spillover, factor flow, and sharing of facilities and services within the city clusters from the perspective of the overall coordinated development of the regional economy (Dai and Yang, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). In terms of digital productivity development, there may be an advantage for cities in a city cluster over those that are not. So, is there such a difference? In this paper, based on the list of 19 city clusters and the cities included in the national \"13th Five-Year Plan\", we distinguish the research sample into city clusters and non-city clusters and generate dummy variables, and then conduct regression analysis by using the interaction term between did and dummy variables, and the results are shown in column (3) of Table\u0026nbsp;\u003cspan refid=\"Tab8\" class=\"InternalRef\"\u003e8\u003c/span\u003e. The results show that for cities that are in urban agglomerations, the impact of internet infrastructure development on digital productivity is significantly different from that of cities that are not in urban agglomerations. The reason for this situation may be that the geospatial agglomeration of city clusters can bring economies of scale and also superimpose the virtual agglomeration of the digital economy (Liu et al., \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2023b\u003c/span\u003e). The radiation-driven and \"grouping\" development among cities can play the role of internet infrastructure construction, which brings significant advantages for the development of digital productivity.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab8\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 8\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eResults of heterogeneity analysis\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eExplained variables: Digital\u003c/p\u003e \u003cp\u003eproductivity\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eEast, center,\u003c/p\u003e \u003cp\u003eand west\u003c/p\u003e \u003cp\u003e(2)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMunicipal administrative level\u003c/p\u003e \u003cp\u003e(1)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eCity cluster\u003c/p\u003e \u003cp\u003e(3)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eQuyu_did\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.0427\u003csup\u003e***\u003c/sup\u003e (0.0032)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eShenghui_did\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0475\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e(0.0071)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eChengshiqun_did\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0242\u003csup\u003e***\u003c/sup\u003e (0.0049)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eExpenditure on education\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.1382\u003csup\u003e**\u003c/sup\u003e (0.0697)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.1914\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e(0.0719)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.2073\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e(0.0722)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eIndustrialized development\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026minus;0.0030\u003csup\u003e***\u003c/sup\u003e (0.0010)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026minus;0.0038\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e(0.0010)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026minus;0.0042\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e(0.0010)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel of services\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026minus;0.0028\u003csup\u003e***\u003c/sup\u003e (0.0011)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026minus;0.0038\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e(0.0011)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026minus;0.0043\u003csup\u003e***\u003c/sup\u003e (0.0011)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel of economic development\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.0817\u003csup\u003e***\u003c/sup\u003e (0.0111)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0730\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e(0.0114)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0759\u003csup\u003e***\u003c/sup\u003e (0.0115)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEgypt\u0026rsquo;s open-door policy\u003c/p\u003e \u003cp\u003etowards the outside world\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026minus;0.0018 (0.0015)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026minus;0.0024\u003c/p\u003e \u003cp\u003e(0.0015)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026minus;0.0021 (0.0015)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel of financial development\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026minus;0.0146\u003csup\u003e**\u003c/sup\u003e (0.0064)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026minus;0.0204\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e(0.0066)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026minus;0.0180\u003csup\u003e***\u003c/sup\u003e (0.0066)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eConstant\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026minus;0.4226\u003csup\u003e***\u003c/sup\u003e (0.1203)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026minus;0.2407\u003csup\u003e*\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e(0.1234)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026minus;0.2432\u003csup\u003e*\u003c/sup\u003e (0.1241)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eIndividual fixed effect\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTime fixed effect\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2099\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2099\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2099\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.9992\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.9992\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.9992\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eYear FE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eId FE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"4\"\u003eNotes:\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003csup\u003e*\u003c/sup\u003e p\u0026thinsp;\u0026lt;\u0026thinsp;0.1 denote the significance level of 10%.\u003c/p\u003e \u003cp\u003e \u003csup\u003e**\u003c/sup\u003e p\u0026thinsp;\u0026lt;\u0026thinsp;0.05 denote the significance level of 5%.\u003c/p\u003e \u003cp\u003e \u003csup\u003e***\u003c/sup\u003e p\u0026thinsp;\u0026lt;\u0026thinsp;0. 01 denote the significance level of 1%.\u003c/p\u003e \u003cp\u003eThe numbers in parentheses are the standard errors.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"5 Mechanism of action analysis","content":"\u003cp\u003eThe previous paper has confirmed that internet infrastructure construction contributes to the development of digital productivity, and according to the inferences obtained from theoretical analysis, data infrastructure construction may promote the development of digital productivity by attracting the concentration of high-skilled talents, improving the degree of marketization, stimulating the vitality of urban innovation, and growing the scientific and technological service industry, so this paper will further develop the study of these mechanisms by combining the characteristics of internet infrastructure.\u003c/p\u003e \u003cdiv id=\"Sec26\" class=\"Section2\"\u003e \u003ch2\u003e5.1 Internet infrastructure attracts concentration of highly skilled personnel\u003c/h2\u003e \u003cp\u003eIn order to test the mechanism impact of internet infrastructure on digital productivity, this paper invokes research technology and other personnel as a new variable, and the regression results, as shown in Table\u0026nbsp;\u003cspan refid=\"Tab9\" class=\"InternalRef\"\u003e9\u003c/span\u003e, columns (1) and (2), show that the internet infrastructure can significantly increase the urban high-skilled talent agglomeration, and at the same time, high-skilled personnel through the internet infrastructure can continue to innovate, optimize the technology and improve the digital capabilities, injecting new enterprise and industrial development Power. The continuous improvement of urban internet infrastructure construction makes it easier for science and technology practitioners, highly educated and highly skilled talents to access digital technology services, which can help them improve efficiency in specific scientific research, innovation and entrepreneurship, and production and operation (Guo et al., \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2020\u003c/span\u003e), especially in the digital economy to get more boosts, thus promoting the development of digital productivity.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec27\" class=\"Section2\"\u003e \u003ch2\u003e5.2 Internet infrastructure contributes to increased marketization\u003c/h2\u003e \u003cp\u003eIn this paper, we refer to the calculation method of Fan et al. on marketization index ( Fan et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2003\u003c/span\u003e), which calculates the marketization index of prefecture-level cities to measure the level of regional marketization. Increased marketization can stimulate competition among enterprises and promote continuous innovation. Provide broader space and opportunities, promote enterprises to increase R\u0026amp;D investment, optimize the allocation of resources, so that a more reasonable flow of resources, to a certain extent, to break the \"information cocoon\" in order to improve the efficiency of the flow of factors of production and efficiency of utilization, which is one of the important driving forces for the continuous development of digital productivity. This paper uses the marketization index of each prefecture-level city to maintain the balance, consistency and completeness of the sample to ensure the validity and reliability of the research results. Its regression results, as shown in Table\u0026nbsp;\u003cspan refid=\"Tab9\" class=\"InternalRef\"\u003e9\u003c/span\u003e, column (3) and column (4), reveal that the study finds that the development of internet infrastructure significantly increases the degree of marketization, and that the degree of marketization also significantly improves digital productivity, which proves that the internet infrastructure helps to improve the market dynamics and promote digital productivity.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab9\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 9\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eMechanism test of highly skilled person and marketization index\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eExplained Variables:\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003ehighly skilled person\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eDigital productivity\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMarketization index\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eDigital productivity\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(1)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e(2)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e(3)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e(4)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDID\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.4998***\u003c/p\u003e \u003cp\u003e(0.0750)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0542*\u003c/p\u003e \u003cp\u003e(0.0318)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ehighly skilled person\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0097***\u003c/p\u003e \u003cp\u003e(0.0013)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMarketization index\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0104***\u003c/p\u003e \u003cp\u003e(0.0032)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eExpenditure on education\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.7387\u003c/p\u003e \u003cp\u003e(1.2427)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.1978***\u003c/p\u003e \u003cp\u003e(0.0717)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0807\u003c/p\u003e \u003cp\u003e(0.5223)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.2026***\u003c/p\u003e \u003cp\u003e(0.0711)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eIndustrialized development\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-0.0662***\u003c/p\u003e \u003cp\u003e(0.0178)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-0.0035***\u003c/p\u003e \u003cp\u003e(0.0010)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-0.0142*\u003c/p\u003e \u003cp\u003e(0.0075)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-0.0035***\u003c/p\u003e \u003cp\u003e(0.0010)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel of services\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-0.0958***\u003c/p\u003e \u003cp\u003e(0.0191)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-0.0033***\u003c/p\u003e \u003cp\u003e(0.0011)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-0.0122\u003c/p\u003e \u003cp\u003e(0.0080)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-0.0034***\u003c/p\u003e \u003cp\u003e(0.0011)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel of economic development\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.7184***\u003c/p\u003e \u003cp\u003e(0.1987)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0663***\u003c/p\u003e \u003cp\u003e(0.0115)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-0.0321\u003c/p\u003e \u003cp\u003e(0.0838)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0660***\u003c/p\u003e \u003cp\u003e(0.0114)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEgypt's open-door policy towards the outside world\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.0668**\u003c/p\u003e \u003cp\u003e(0.0261)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-0.0022\u003c/p\u003e \u003cp\u003e(0.0015)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-0.0217**\u003c/p\u003e \u003cp\u003e(0.0109)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-0.0018\u003c/p\u003e \u003cp\u003e(0.0015)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel of financial development\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.1501\u003c/p\u003e \u003cp\u003e(0.1145)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-0.0194***\u003c/p\u003e \u003cp\u003e(0.0066)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-0.0422\u003c/p\u003e \u003cp\u003e(0.0488)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-0.0215***\u003c/p\u003e \u003cp\u003e(0.0066)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eConstant\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-0.3600\u003c/p\u003e \u003cp\u003e(2.1485)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-0.2211*\u003c/p\u003e \u003cp\u003e(0.1230)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e13.5035***\u003c/p\u003e \u003cp\u003e(0.9024)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-0.3216**\u003c/p\u003e \u003cp\u003e(0.1297)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eIndividual fixed effect\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYES\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eYES\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eYES\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eYES\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTime fixed effect\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYES\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eYES\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eYES\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eYES\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2099\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2099\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2063\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2063\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.9723\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.9992\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.9769\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.9992\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"5\"\u003e\u003cem\u003et\u003c/em\u003e statistics in parentheses\u003c/td\u003e\u003c/tr\u003e \u003ctr\u003e\u003ctd colspan=\"5\"\u003e\u003csup\u003e*\u003c/sup\u003e \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.1,\u003csup\u003e**\u003c/sup\u003e \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.05,\u003csup\u003e***\u003c/sup\u003e \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.01\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec28\" class=\"Section2\"\u003e \u003ch2\u003e5.3 Cyberinfrastructure effectively stimulates urban innovation\u003c/h2\u003e \u003cp\u003eInnovation is one of the key elements of modern economic development. It is no coincidence that urban innovation is still true for digital productivity, as it promotes the development of the digital economy and productivity through technological innovation, industrial upgrading, talent attraction and other aspects. Urban innovation and digital productivity complement each other, realizing the \"symbiotic effect\" and jointly promoting the sustainable development and competitiveness of urban economy. Columns (1) and (2) of Table\u0026nbsp;\u003cspan refid=\"Tab10\" class=\"InternalRef\"\u003e10\u003c/span\u003e show the results of the urban innovation path. The results show that the promotion effects of the \"Broadband China\" pilot policy on the urban innovation index and the urban innovation index on digital productivity are both significant at the 1% level, suggesting that cities with better internet infrastructure can stimulate urban innovation and thus improve the development of digital productivity.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec29\" class=\"Section2\"\u003e \u003ch2\u003e5.4 Cyberinfrastructure can grow the science and technology services industry\u003c/h2\u003e \u003cp\u003eInnovation is the core of scientific and technological progress and the first driving force leading social development. In the context of the innovation-driven strategy and in the face of the double superposition of the globalization of innovation and the era of service economy, the science and technology service industry has become one of the most active industries in the current global layout of the whole chain around innovation and entrepreneurship. In order to promote the rapid transformation of scientific and technological achievements into real-life productivity, policies have been introduced to promote the development of science and technology service industry, and a variety of new forms, new models and new industries have constantly emerged in the science and technology service industry, which has become a hotspot for the development of new economy. At the same time, digital productivity is a contemporary advanced productive force spawned by revolutionary breakthroughs in technology, innovative allocation of production factors, and deep transformation and upgrading of industries. This makes the deep cross-fertilization of science and technology service industry and digital productivity, and the estimation results, as shown in Table\u0026nbsp;\u003cspan refid=\"Tab10\" class=\"InternalRef\"\u003e10\u003c/span\u003e Column (3) Column (4), indicate that the internet infrastructure significantly enhances the total amount of science and technology service industry at the level of 1%, while the development of science and technology service industry can provide enterprises with more digital technology and solutions to help them improve productivity, optimize management and promote innovation, etc., thus promoting the enhancement of digital productivity, and the results of the estimation results are further shown in Table\u0026nbsp;\u003cspan refid=\"Tab10\" class=\"InternalRef\"\u003e10\u003c/span\u003e Column (4). 10 Column (4) The estimation results further show that the science and technology service industry can significantly promote the development of digital productivity at the 1% level. This also indicates that internet infrastructure can effectively contribute to digital productivity.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab10\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 10\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eMechanism test of urban innovation index and science and technology services\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eexplanatory variable\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eUrban Innovation Index\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eDigital productivity\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eScience and technology services\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eDigital productivity\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(1)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e(2)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e(3)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e(4)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDID\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.2397***\u003c/p\u003e \u003cp\u003e(0.0409)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.1528***\u003c/p\u003e \u003cp\u003e(0.0203)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eUrban Innovation Index\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0225***\u003c/p\u003e \u003cp\u003e(0.0024)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eScience and technology services\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0229***\u003c/p\u003e \u003cp\u003e(0.0049)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eExpenditure on education\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.2605*\u003c/p\u003e \u003cp\u003e(0.6780)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.1862***\u003c/p\u003e \u003cp\u003e(0.0711)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.3340\u003c/p\u003e \u003cp\u003e(0.3362)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.2076***\u003c/p\u003e \u003cp\u003e(0.0723)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eIndustrialized development\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-0.0387***\u003c/p\u003e \u003cp\u003e(0.0097)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-0.0032***\u003c/p\u003e \u003cp\u003e(0.0010)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-0.0162***\u003c/p\u003e \u003cp\u003e(0.0048)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-0.0038***\u003c/p\u003e \u003cp\u003e(0.0010)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel of services\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-0.0627***\u003c/p\u003e \u003cp\u003e(0.0104)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-0.0028***\u003c/p\u003e \u003cp\u003e(0.0011)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-0.0247***\u003c/p\u003e \u003cp\u003e(0.0052)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-0.0037***\u003c/p\u003e \u003cp\u003e(0.0011)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel of economic development\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.2355**\u003c/p\u003e \u003cp\u003e(0.1084)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0681***\u003c/p\u003e \u003cp\u003e(0.0113)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0751\u003c/p\u003e \u003cp\u003e(0.0538)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0713***\u003c/p\u003e \u003cp\u003e(0.0115)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEgypt's open-door policy towards the outside world\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.0457***\u003c/p\u003e \u003cp\u003e(0.0142)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-0.0026*\u003c/p\u003e \u003cp\u003e(0.0015)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0227***\u003c/p\u003e \u003cp\u003e(0.0071)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-0.0021\u003c/p\u003e \u003cp\u003e(0.0015)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel of financial development\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.1006\u003c/p\u003e \u003cp\u003e(0.0625)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-0.0201***\u003c/p\u003e \u003cp\u003e(0.0065)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0019\u003c/p\u003e \u003cp\u003e(0.0310)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-0.0182***\u003c/p\u003e \u003cp\u003e(0.0066)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eConstant\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.2672\u003c/p\u003e \u003cp\u003e(1.1722)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-0.2550**\u003c/p\u003e \u003cp\u003e(0.1220)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.8319\u003c/p\u003e \u003cp\u003e(0.5813)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-0.2390*\u003c/p\u003e \u003cp\u003e(0.1242)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eIndividual fixed effect\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYES\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eYES\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eYES\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eYES\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTime fixed effect\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYES\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eYES\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eYES\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eYES\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2099\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2099\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2099\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2099\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.7964\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.9992\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.8405\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.9992\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"6 Conclusions and policy implications","content":"\u003cp\u003eThe digital economy has emerged as a powerful force, driving economic growth and becoming a \"new engine\" of development. This growth is fundamentally reflected in the advancement of digital productivity, with the construction of internet infrastructure serving as a crucial foundation for fostering digital productivity. This paper uses the \"Broadband China\" pilot policy as a quasi-natural experiment and employs panel data from prefecture-level cities between 2011 and 2019 to empirically examine the impact of internet infrastructure development on digital productivity. The findings indicate that the development of internet infrastructure significantly promotes digital productivity, and the results remain robust after various robustness checks, including PSM-DID, parallel trend tests, sensitivity tests, exclusion of special cities, Goodman-Bacon decomposition, instrumental variable analysis, and double machine learning techniques. The heterogeneity analysis reveals that the impact of internet infrastructure development on digital productivity varies significantly across regions, cities of different administrative levels, and urban versus non-urban agglomerations. Furthermore, the mechanism analysis identifies four key channels through which internet infrastructure construction influences digital productivity: attracting the concentration of highly skilled talent, improving marketization, stimulating urban innovation, and fostering the growth of the science and technology service industry.\u003c/p\u003e \u003cp\u003eBased on the above conclusions, the policy implications of this paper are as follows: internet infrastructure is important for the development of digital productivity, based on the new characteristics and new needs of the Chinese government's urban development, on the one hand, we should continue to steadily promote the \"Broadband China\" strategy, increase the construction of internet infrastructure, and give full play to the positive effect of internet infrastructure construction on digital workers, digital labor means, and digital labor objects. On the one hand, we should continue to steadily push forward the \"Broadband China\" strategy, increase the construction of internet infrastructure, and give full play to the positive effects of internet infrastructure construction on digital workers, digital labor materials and digital labor objects. On the other hand, according to the need to develop new productivity according to local conditions, in the process of internet infrastructure construction, we should focus on mending the shortcomings and strengthening the weaknesses, combining the differences of different regions, relying on the level of the existing internet infrastructure construction according to the local actual situation and practical needs, further attracting highly skilled talents, optimizing the business environment, increasing investment in innovation, and developing the scientific and technological service industry, so as to provide support for the continuous promotion of the development of digital productivity.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eAuthor Contributions Statement：Z. Y. conceptualized the research, developed the methodology, wrote the main manuscript, conducted the empirical analysis and prepared the data visualization. J. L. and J. L. contributed to the policy analysis and mechanism investigation. J. Z. assisted with data collection and preliminary analysis. J. D. contributed to the literature review and theoretical framework. All authors contributed to the manuscript revision, read, and approved the final version.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eAcemoglu D (2002) Directed technical change. Rev Econ Stud 69(4):781\u0026ndash;809.https://doi.org/10.1111/1467-937X.00226\u003c/li\u003e\n\u003cli\u003eBaker AC, Larcker DF, Wang CCY (2022) How much should we trust staggered difference-in-differences estimates? J Financ Econ 144(2):370\u0026ndash;395.https://doi.org/10.1016/j.jfineco.2022.01.004\u003c/li\u003e\n\u003cli\u003eBeck T, Levine R, Levkov A (2010) Big bad banks? 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Manag World 40(1):196\u0026ndash;222.https://link.cnki.net/doi/10.19744/j.cnki.11-1235/f.2024.0010\u003c/li\u003e\n\u003cli\u003eZheng Y (2023) The mechanism of digital infrastructure construction on corporate innovation: an empirical examination based on the quasi-natural experiment of \u0026quot;Broadband China\u0026quot; strategy pilot. J Cent Univ Finance Econ (4):90\u0026ndash;104. https://link.cnki.net/doi/10.19681/j.cnki.jcufe.2023.04.008\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Internet infrastructure, digital productivity, broadband China, double difference","lastPublishedDoi":"10.21203/rs.3.rs-5814647/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5814647/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eInternet infrastructure construction is an important condition to promote the development of digital productivity, and an important guarantee to promote the digital economy as a new driving force for economic growth. This paper analyzes the impact of internet infrastructure development on digital productivity using 2011\u0026ndash;2019 prefecture-level city panel data and a quasi-natural experiment on the \"Broadband China\" pilot policy. The study concludes that internet infrastructure development significantly promotes the development of digital productivity, and the result passes several robustness tests. The promotion effect of internet infrastructure construction on digital productivity has significant heterogeneity among regions, between cities of different administrative levels, and between cities in urban agglomerations and non-urban agglomerations. Meanwhile, the mechanism analysis finds that internet infrastructure development affects digital productivity development through four ways: attracting the concentration of highly skilled personnel, improving the level of marketization, stimulating the city's innovation vitality, and growing the science and technology service industry.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e","manuscriptTitle":"Internet Infrastructure Construction and Digital Productive Forces: Empirical Evidence from China","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-01-23 06:11:03","doi":"10.21203/rs.3.rs-5814647/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"6188c6c4-dbc9-44aa-8d83-812b3d02c96e","owner":[],"postedDate":"January 23rd, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":43185471,"name":"Business and commerce/Information systems and information technology"},{"id":43185472,"name":"Social science/Economics"}],"tags":[],"updatedAt":"2025-04-09T13:53:41+00:00","versionOfRecord":[],"versionCreatedAt":"2025-01-23 06:11:03","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-5814647","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5814647","identity":"rs-5814647","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}