# Does Digital Economy Contribute to Regional Carbon Productivity? Evidence of China

Authors: Zheng Li; Congling Pang
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

With breakthroughs in big data, communication networks, artificial intelligence, and other next-generation information technologies, intelligent production methods and digital lifestyles have risen rapidly. Digital economy has become a significant force in promoting regional low-carbon development as a new economic form in the important period of the intersection of digitalization and “carbon peaking and carbon neutrality goals.” This paper empirically explores the moderating role and threshold role of human capital in digital economy and regional carbon productivity by systematically measuring digital economy indicators. Research shows that China’s digital economy development index is rising annually. However, the development of digital economy varies significantly between different regions. The results of moderating effect showed that human capital accumulation could dramatically strengthen the role of digital economy in promoting regional carbon productivity. The results of the threshold effect showed that human capital plays an important threshold role in the relationship between digital economy and regional carbon productivity. This paper provides a practical reference for exploring power sources, policy design, and path selection of low-carbon development.


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## Body

## 1. Introduction

According to the white paper on Global Digital Economy 2021, the scale of global digital economy reached 32.6 trillion US dollars in 2020, with a year-on-year growth of 3% [1]. Among them, the growth rate of China’s digital economy still significantly exceeded the GDP growth rate, with a total size of 5.4 trillion US dollars, second only to that of the United States, showing a growing trend [2]. Under the “triple pressure” of shrinking demand for economic development, supply shocks, and weakening expectations, digital economy as a new type of business takes the Internet as the carrier; driving the innovation of production methods and governance methods through information technology can promote economic growth in terms of stimulating consumption, stimulating investment, and creating employment and alleviate downward pressure on the economy [3]. Because of this, how to effectively use digital economy to promote sustainable development has gradually turned into a hot topic of widespread concern in practice and academia [4]. Under the dual pressure of economic downturn and structural adjustment, General Secretary Xi pointed out that developing the digital economy is a strategic choice to promote the stable development of China’s economy based on international development and China’s actual conditions. The digital economy has risen as a national strategy in China, becoming the “new engine” of national economic development during the “fourteenth five-year plan.” There is no doubt that the construction of “digital China” and “network power” is inseparable from digital economy [5, 6].Then, there are several practical problems worthy of attention. Under pressure from “dual carbon” goal, does rapid development of digital economy significantly boost economy sustainable development? Based on China’s regional heterogeneity, is there “digital divide” in development of digital economy? Accurately assessing the role of digital economy in regional all-round development and in-depth discussion of its influence mechanism and mechanism of action have essential theoretical and practical significance for China to achieve low-carbon development goal and “digital China” strategy.Existing literature mainly analyzes regional carbon productivity from the dimensions of environmental regulation [7], industrial structure [8], policy support [9, 10], and financial development [11]. Direct research on digital economy and regional carbon productivity is rare, and more literature concentrates on the connection between digital economy and innovation efficiency [12]. Some documents discuss the relevance of digital economy and high-quality development theoretically [13]. The research above provides particular theoretical and empirical support for revealing the driving effect of digital economy on economic and social development. Still, there are little researches on the low-carbon effects of digital economy. Particularly in the historical convergence period of digital economy and the “dual carbon” strategy, few documents have responded positively to the inherent relevance of digital economy and regional carbon productivity. Therefore, it is impossible to directly judge digital economy’s impact and specific mechanism on regional carbon productivity.Unlike previous studies, this paper innovatively incorporates digital economy into the regional carbon productivity analysis framework. Possible contributions of this paper include the following.First, based on the strategic goals of “digital China” and “dual carbon,” this paper connects the digital economy with regional carbon productivity and explores the deep relationship between them. Secondly, this paper constructs a digital economy evaluation index system from three dimensions of digital environment, digital industrialization, and industrial digitization and measures the regional digital economy index more comprehensively, thereby improving the reliability of the research conclusions. Thirdly, the paper attempts to explore the mechanism behind the relationship between digital economy and regional carbon productivity from the perspective of human capital so as to provide theoretical support for deepening the cognition of the low-carbon effect of the digital economy. Finally, based on the heterogeneity of my country’s regional development, the paper puts forward the management enlightenment of promoting regional low-carbon development based on digital economy, which contributes certain theoretical and practical value to China’s digital power low-carbon competition and the goal of building a digital power.


## 2. Theoretical Analysis and Research Hypothesis

The scale of the digital economy has grown, and academic research on the digital economy has gradually increased. At present, scholars have also gradually shifted their research focus from the Internet and informatization to the digital economy [14].


### 2.1. The Impact of Digital Economy on Regional Carbon Productivity

First, digital economy can use intelligent digital technologies such as the AI, cloud platforms, and blockchain [15] to strengthen the degree of information coupling between regions and enterprises [16], break the boundaries of regional development [17], promote elements to cross the boundaries of time and space, realize the accumulation of green elements in the invisible virtual space [18], and then promote regional carbon productivity through collaborative innovation.Second, based on the theory of environmental adaptation, drastic changes in the external environment will inevitably require a rapid response from regional governments and enterprises relying on the new environment of digital development gradually formed by digital technology. The extensive development model with high emissions and heavy contamination is unsustainable. To enhance local core competitiveness, local governments are promoting the digital transformation of local enterprises through taxation and financial policies [19]. Specifically, digital economy promotes the innovative development of business models in related industries [20]; it can reduce resource consumption in the industrial chain and the cost of information search between enterprises [21]; it also helps to obtain innovation in the value network resources, and green technology innovation will be realized; and it promotes regional carbon productivity.Third, digital economy is based on value cocreation theory, using digital intelligent technologies and elements, and based on cloud platforms to build an intelligent digital ecosystem covering government, enterprises, consumers, and other entities. Based on this, digital economy can satisfy consumers from design, production, sales, and other links, help reduce ineffective marketing and resource redundancy, help correct factor distortions, provide resource allocation efficiency and production efficiency, and achieve regional carbon productivity.Hypothesis 1.
Under the premise that other conditions remain the same, the higher the degree of digital economy, the higher the degree of regional carbon productivity.


### 2.2. The Role of Human Capital in Moderating and Thresholding the Relationship between Digital Economy and Regional Carbon Productivity

First, the level of human capital accumulation has an essential impact on the economic effect of digital economy. Based on the Lucas model and endogenous economic theory, we know that the fundamental drivers of economic growth are an investment in human capital and physical capital. Under the background of the “new normal” of the economy, the economic development model has changed from a resource-input type to an efficiency-driven one. The regulating role of human capital is more significant. For example, Langnel et al. [22] verified that human capital can effectively reduce ecological pressure, promoting sustainable economic development. Moreover, based on the theory of disruptive innovation and the theory of industrial structure, the development of digital economy must be based on breaking the traditional industrial structure development model. This process is full of contradictions and conflicts. Human capital, especially high-end human capital, can effectively promote enterprise innovation and industrial transformation with excellent knowledge accumulation and adaptability. As Zhao and Ma [23] point out, human capital plays an essential role in the cohesion of resources such as capital, technology, and management required for green innovation.Second, from the knowledge spillover and technology accumulation standpoint, at a higher level of human capital accumulation, enterprises in the region, through face-to-face technical exchanges and information interaction [24], can quickly realize the spillover of knowledge and technology in the industry and, through professional services, can facilitate the exchange, sharing and diffusion of energy-saving information, environmental understanding, and low-carbon technology among enterprises, thereby promoting green technology innovation and low-carbon development. Meanwhile, the accumulation of high-end human capital can help strengthen corporate competition by motivating regional companies to carry out technological and process innovation [25]; they can stimulate the endogenous motivation of enterprises, accelerate knowledge absorption and low-carbon technological progress, and promote regional carbon productivity.Third, from sharing and matching of input elements standpoint, while digital economy promotes the innovation of factor agglomeration models, it also accelerates the agglomeration of high-end human capital in the region and realizes the sharing of professional talents in the industry and diversified talents across industries [26]; it saves the cost of searching for skills from the demand side and reduces the cost of adapting talents to the job from the supply side. In short, at a higher level of human capital accumulation, digital economy reduces cost stickiness through factor sharing and matching, which will help promote regional carbon productivity.According to the preamble analysis, this paper argues that the effective accumulation of human capital can strengthen digital economy’s low-carbon development effect. Therefore, this paper points out the second and third hypotheses.Hypothesis 2.
Under the circumstance that other conditions remain unchanged, improving human capital levels can reinforce the positive effect of digital economy on regional carbon productivity.Hypothesis 3.
Under the circumstance that other conditions remain unchanged, digital economy is more conducive to promoting regional carbon productivity under the higher accumulation of human capital.


## 2.1. The Impact of Digital Economy on Regional Carbon Productivity

First, digital economy can use intelligent digital technologies such as the AI, cloud platforms, and blockchain [15] to strengthen the degree of information coupling between regions and enterprises [16], break the boundaries of regional development [17], promote elements to cross the boundaries of time and space, realize the accumulation of green elements in the invisible virtual space [18], and then promote regional carbon productivity through collaborative innovation.Second, based on the theory of environmental adaptation, drastic changes in the external environment will inevitably require a rapid response from regional governments and enterprises relying on the new environment of digital development gradually formed by digital technology. The extensive development model with high emissions and heavy contamination is unsustainable. To enhance local core competitiveness, local governments are promoting the digital transformation of local enterprises through taxation and financial policies [19]. Specifically, digital economy promotes the innovative development of business models in related industries [20]; it can reduce resource consumption in the industrial chain and the cost of information search between enterprises [21]; it also helps to obtain innovation in the value network resources, and green technology innovation will be realized; and it promotes regional carbon productivity.Third, digital economy is based on value cocreation theory, using digital intelligent technologies and elements, and based on cloud platforms to build an intelligent digital ecosystem covering government, enterprises, consumers, and other entities. Based on this, digital economy can satisfy consumers from design, production, sales, and other links, help reduce ineffective marketing and resource redundancy, help correct factor distortions, provide resource allocation efficiency and production efficiency, and achieve regional carbon productivity.Hypothesis 1.
Under the premise that other conditions remain the same, the higher the degree of digital economy, the higher the degree of regional carbon productivity.


## 2.2. The Role of Human Capital in Moderating and Thresholding the Relationship between Digital Economy and Regional Carbon Productivity

First, the level of human capital accumulation has an essential impact on the economic effect of digital economy. Based on the Lucas model and endogenous economic theory, we know that the fundamental drivers of economic growth are an investment in human capital and physical capital. Under the background of the “new normal” of the economy, the economic development model has changed from a resource-input type to an efficiency-driven one. The regulating role of human capital is more significant. For example, Langnel et al. [22] verified that human capital can effectively reduce ecological pressure, promoting sustainable economic development. Moreover, based on the theory of disruptive innovation and the theory of industrial structure, the development of digital economy must be based on breaking the traditional industrial structure development model. This process is full of contradictions and conflicts. Human capital, especially high-end human capital, can effectively promote enterprise innovation and industrial transformation with excellent knowledge accumulation and adaptability. As Zhao and Ma [23] point out, human capital plays an essential role in the cohesion of resources such as capital, technology, and management required for green innovation.Second, from the knowledge spillover and technology accumulation standpoint, at a higher level of human capital accumulation, enterprises in the region, through face-to-face technical exchanges and information interaction [24], can quickly realize the spillover of knowledge and technology in the industry and, through professional services, can facilitate the exchange, sharing and diffusion of energy-saving information, environmental understanding, and low-carbon technology among enterprises, thereby promoting green technology innovation and low-carbon development. Meanwhile, the accumulation of high-end human capital can help strengthen corporate competition by motivating regional companies to carry out technological and process innovation [25]; they can stimulate the endogenous motivation of enterprises, accelerate knowledge absorption and low-carbon technological progress, and promote regional carbon productivity.Third, from sharing and matching of input elements standpoint, while digital economy promotes the innovation of factor agglomeration models, it also accelerates the agglomeration of high-end human capital in the region and realizes the sharing of professional talents in the industry and diversified talents across industries [26]; it saves the cost of searching for skills from the demand side and reduces the cost of adapting talents to the job from the supply side. In short, at a higher level of human capital accumulation, digital economy reduces cost stickiness through factor sharing and matching, which will help promote regional carbon productivity.According to the preamble analysis, this paper argues that the effective accumulation of human capital can strengthen digital economy’s low-carbon development effect. Therefore, this paper points out the second and third hypotheses.Hypothesis 2.
Under the circumstance that other conditions remain unchanged, improving human capital levels can reinforce the positive effect of digital economy on regional carbon productivity.Hypothesis 3.
Under the circumstance that other conditions remain unchanged, digital economy is more conducive to promoting regional carbon productivity under the higher accumulation of human capital.


## 3. Measurement and Analysis of Digital Economy Index

### 3.1. Establish an Indicator System

Regarding the digital economy index measurement, there is no official statistics department in China to disclose digitization and digital technology [27]. When conducting related research, most scholars use a single indicator to measure digital economy, such as the output of the electronic information manufacturing industry, the number of broadband access ports, e-commerce sales, and other indicators. However, the development of digital economy is a systematic project and an open system. Although a single indicator can characterize it from a particular aspect, it is not comprehensive and objective enough [28].Because of this, based on a broad perspective, this paper considers the views of Tsinghua University School of Social Sciences, Soochow University, Suzhou Development and Planning Research Institute, and other institutions, as well as scholars such as Xiao and Qi [29], Zhao et al. [30], and Yang and Jiang [31]. This paper divides the value dimension of digital economy into two aspects: digitization foundation and digitization integration; the specific measurement indicators are reported in Table 1.Table 1
China’s regional digital economy evaluation index system.
Level 1 indicatorsLevel 2 indicatorsLevel 3 indicatorsThe basis of regional digitalizationSize and revenueEnterprise quantity in the digital economy industryQuantity of people employed in digital economy industryPrimary business income of the digital economy industryInnovation abilityQuantity of R&D personnel in the digital economy industryInternal expenditure of R&D expenditure in digital economy industryQuantity of patent applications for digital economy industryDigital baseInternet penetrationNumber of mobile phone users at year-endLength of long-distance optical cable lineRegional digital integration capabilitiesIntegrated development of the primary industryAgricultural and rural informatization demonstration baseRural electricity consumptionThe added value of the primary industryIntegrated development of the secondary industryIncome from the main business of high-tech industry/above-scale industrial primary business incomeIndustrial added valueNumber of industrial Internet platformsIntegrated development of tertiary industryPer capita expenditure on transportation and communicationPer capita expenditure on education, culture, and entertainmentE-commerce salesOnline retail salesDigital financial inclusion indexValue added of tertiary industry


### 3.2. Evaluation Model Construction

The projection tracking model analyzes the high-dimensional data by looking for feature projections of high-dimensional data in lower-dimensional space [32]. In this paper, the projection pursuit model is improved by accelerating genetic algorithm based on a new accurate coding, making the evaluation of digital economy indexes in regions of China more objective and scientific. The process is as follows.By optimizing the projection direction, the multidimensional output data is reduced in dimension, with the goal of reflecting the structure and characteristics of the inherited high-dimensional data to the hilt. The projection direction of the original high-dimensional data is globally optimized to reach the maximum value of the projection index function, and then the one-dimensional optimal output projection value of the development level of the digital economy is obtained:(1)maxQat=SzDz,s.t.∑j=13a2jt=1,(2)zi=∑j=1Pajxi,j,i=1,2,…,n.Among them,SZ is the standard deviation of zi, and DZ is the local density of zi.Furthermore, this paper chooses the accelerated genetic algorithm based on a new accurate coding to solve the obstacles of the projection pursuit solution. The reason is that this method can significantly improve the optimization of the algorithm. Specifically, this method has significant advantages in overcoming the Hamming cliff problem of the binary algorithm and compressing the optimization interval of SGA, which is conducive to quickly obtaining the optimal solution [32].


### 3.3. Analysis of Digital Economy Index

Based on the above computing method, this paper calculates China’s 30 inland provinces (except Tibet) from 2011 to 2019.From 2011 to 2019, China’s digital economy level rose from 0.4063 in 2011 to 0.9279 in 2019, more than doubled; it shows that digital economy is developing quickly. However, limited by the economic foundation, innovation level, and digital barriers, the development of digital economy in different regions is uneven, and there is an obvious “digital divide.” On the whole, digital economy shows the difference of “high in the east and low in the west.”Specifically, the level of digital economy generally shows a downward trend from east to middle to west. The top three cities in China’s digital economy are Guangdong, Jiangsu, and Zhejiang; in 2019, the total GDP of these three regions accounted for 27% of the country’s total GDP.Since 2015, the digital economy level of Guangdong began to lead other regions. In 2019, the digital economy level continued to lead other provinces, and the gap widened. In recent years, Guangdong Province has actively responded to the national strategy, determined the strategic position of the digital economy, and issued the “Guangdong Province Digital Economy Development Plan (2018–2025).” It has made clear that Guangdong will be built into a national data economy pilot zone, a digital Silk Road strategic hub, a global digital economy innovation center, and vigorous expansion of the digital industry. To help improve the digital economy development of Guangdong Province, with the government’s support, Guangdong vigorously develops a new generation of information technology and sets up R&D centers, network technology, and so on. The digital economy of Guangdong Province is in a leading position in China. Of course, it is inseparable from the efforts of local enterprises. The most representative company is Huawei. Huawei has established a high-tech terminal headquarters base in Dongguan-Huawei Europe City, which not only attracts a large number of high-end capital and human capital to gather here but also, more importantly, dramatically enhances the development potential of Guangdong Province and enhances economic resilience.Overall, the GDP and digital economy in western China are the lowest; this is because historical factors and geographical factors limit western China, the infrastructure construction and high-tech industry foundation are relatively poor, and digital economy does not have intense penetration of local industries. Although the gap between the level of digital economy in central and eastern regions is still huge, the annual growth rate is relatively fast. Northeast China has seen slower growth in recent years, mainly due to brain drain, making it difficult for industrial enterprises to transform. Areas with a low level of digital economy especially have the following shortcomings:(1)
The foundation of digital economy is poor. In recent years, China’s investment in new infrastructure in various regions has increased significantly, and the Party Central Committee has repeatedly mentioned the content of “new digital infrastructure.” New infrastructure is an essential foundation of digital economy, such as speeding up 5G networks, cloud computing, artificial intelligence, and big data. However, China has a vast territory, and the level of digital economy varies significantly among regions, especially in western China, which faces a shortage of talents and poor information infrastructure.(2)
The digital industry foundation is relatively weak. The total amount of basic digital industries is relatively small, related emerging industries are in their infancy, and the core competitiveness of digital industries is rather poor, making it difficult to realize the complete application of digital resources effectively.(3)
Driving force for continuous innovation is insufficient. Innovation is the power source of digital economy, and relevant digital industry practitioners are the premise of innovation. But the digital economy is a relatively weak area, and there is a shortage of talents. It is mainly reflected in the small number of top universities, difficulties in talent introduction, serious brain drain, and other problems.


## 3.1. Establish an Indicator System

Regarding the digital economy index measurement, there is no official statistics department in China to disclose digitization and digital technology [27]. When conducting related research, most scholars use a single indicator to measure digital economy, such as the output of the electronic information manufacturing industry, the number of broadband access ports, e-commerce sales, and other indicators. However, the development of digital economy is a systematic project and an open system. Although a single indicator can characterize it from a particular aspect, it is not comprehensive and objective enough [28].Because of this, based on a broad perspective, this paper considers the views of Tsinghua University School of Social Sciences, Soochow University, Suzhou Development and Planning Research Institute, and other institutions, as well as scholars such as Xiao and Qi [29], Zhao et al. [30], and Yang and Jiang [31]. This paper divides the value dimension of digital economy into two aspects: digitization foundation and digitization integration; the specific measurement indicators are reported in Table 1.Table 1
China’s regional digital economy evaluation index system.
Level 1 indicatorsLevel 2 indicatorsLevel 3 indicatorsThe basis of regional digitalizationSize and revenueEnterprise quantity in the digital economy industryQuantity of people employed in digital economy industryPrimary business income of the digital economy industryInnovation abilityQuantity of R&D personnel in the digital economy industryInternal expenditure of R&D expenditure in digital economy industryQuantity of patent applications for digital economy industryDigital baseInternet penetrationNumber of mobile phone users at year-endLength of long-distance optical cable lineRegional digital integration capabilitiesIntegrated development of the primary industryAgricultural and rural informatization demonstration baseRural electricity consumptionThe added value of the primary industryIntegrated development of the secondary industryIncome from the main business of high-tech industry/above-scale industrial primary business incomeIndustrial added valueNumber of industrial Internet platformsIntegrated development of tertiary industryPer capita expenditure on transportation and communicationPer capita expenditure on education, culture, and entertainmentE-commerce salesOnline retail salesDigital financial inclusion indexValue added of tertiary industry


## 3.2. Evaluation Model Construction

The projection tracking model analyzes the high-dimensional data by looking for feature projections of high-dimensional data in lower-dimensional space [32]. In this paper, the projection pursuit model is improved by accelerating genetic algorithm based on a new accurate coding, making the evaluation of digital economy indexes in regions of China more objective and scientific. The process is as follows.By optimizing the projection direction, the multidimensional output data is reduced in dimension, with the goal of reflecting the structure and characteristics of the inherited high-dimensional data to the hilt. The projection direction of the original high-dimensional data is globally optimized to reach the maximum value of the projection index function, and then the one-dimensional optimal output projection value of the development level of the digital economy is obtained:(1)maxQat=SzDz,s.t.∑j=13a2jt=1,(2)zi=∑j=1Pajxi,j,i=1,2,…,n.Among them,SZ is the standard deviation of zi, and DZ is the local density of zi.Furthermore, this paper chooses the accelerated genetic algorithm based on a new accurate coding to solve the obstacles of the projection pursuit solution. The reason is that this method can significantly improve the optimization of the algorithm. Specifically, this method has significant advantages in overcoming the Hamming cliff problem of the binary algorithm and compressing the optimization interval of SGA, which is conducive to quickly obtaining the optimal solution [32].


## 3.3. Analysis of Digital Economy Index

Based on the above computing method, this paper calculates China’s 30 inland provinces (except Tibet) from 2011 to 2019.From 2011 to 2019, China’s digital economy level rose from 0.4063 in 2011 to 0.9279 in 2019, more than doubled; it shows that digital economy is developing quickly. However, limited by the economic foundation, innovation level, and digital barriers, the development of digital economy in different regions is uneven, and there is an obvious “digital divide.” On the whole, digital economy shows the difference of “high in the east and low in the west.”Specifically, the level of digital economy generally shows a downward trend from east to middle to west. The top three cities in China’s digital economy are Guangdong, Jiangsu, and Zhejiang; in 2019, the total GDP of these three regions accounted for 27% of the country’s total GDP.Since 2015, the digital economy level of Guangdong began to lead other regions. In 2019, the digital economy level continued to lead other provinces, and the gap widened. In recent years, Guangdong Province has actively responded to the national strategy, determined the strategic position of the digital economy, and issued the “Guangdong Province Digital Economy Development Plan (2018–2025).” It has made clear that Guangdong will be built into a national data economy pilot zone, a digital Silk Road strategic hub, a global digital economy innovation center, and vigorous expansion of the digital industry. To help improve the digital economy development of Guangdong Province, with the government’s support, Guangdong vigorously develops a new generation of information technology and sets up R&D centers, network technology, and so on. The digital economy of Guangdong Province is in a leading position in China. Of course, it is inseparable from the efforts of local enterprises. The most representative company is Huawei. Huawei has established a high-tech terminal headquarters base in Dongguan-Huawei Europe City, which not only attracts a large number of high-end capital and human capital to gather here but also, more importantly, dramatically enhances the development potential of Guangdong Province and enhances economic resilience.Overall, the GDP and digital economy in western China are the lowest; this is because historical factors and geographical factors limit western China, the infrastructure construction and high-tech industry foundation are relatively poor, and digital economy does not have intense penetration of local industries. Although the gap between the level of digital economy in central and eastern regions is still huge, the annual growth rate is relatively fast. Northeast China has seen slower growth in recent years, mainly due to brain drain, making it difficult for industrial enterprises to transform. Areas with a low level of digital economy especially have the following shortcomings:(1)
The foundation of digital economy is poor. In recent years, China’s investment in new infrastructure in various regions has increased significantly, and the Party Central Committee has repeatedly mentioned the content of “new digital infrastructure.” New infrastructure is an essential foundation of digital economy, such as speeding up 5G networks, cloud computing, artificial intelligence, and big data. However, China has a vast territory, and the level of digital economy varies significantly among regions, especially in western China, which faces a shortage of talents and poor information infrastructure.(2)
The digital industry foundation is relatively weak. The total amount of basic digital industries is relatively small, related emerging industries are in their infancy, and the core competitiveness of digital industries is rather poor, making it difficult to realize the complete application of digital resources effectively.(3)
Driving force for continuous innovation is insufficient. Innovation is the power source of digital economy, and relevant digital industry practitioners are the premise of innovation. But the digital economy is a relatively weak area, and there is a shortage of talents. It is mainly reflected in the small number of top universities, difficulties in talent introduction, serious brain drain, and other problems.


## 4. Measurement Model Setup and Data Handling

### 4.1. Static Panel Model Construction

This paper first constructs the following linear regression model:(3)RCPit=μi+α1DEit+α2DEit∗HCit+βXit+εit.Among them,RCPit is the explained variable, representing the regional carbon productivity level of region i in period t. DEit is an explanatory variable, representing the degree of digital economy. DEit∗HCit is the intersection of digital economy and human capital accumulation, which is used to examine the moderating effect of human capital accumulation in the low-carbon development of digital economy. The estimated coefficient α2 of the cross-product term is this paper’s research key. According to the previous mechanism analysis, it is expected that α2 is significantly positive; μi is an unknown individual effect; εit represents the random error term; Xit is a series of control variables affecting regional carbon productivity. By selecting appropriate samples and estimation methods, the unknown coefficients α1, α2, β, and so on can be obtained to analyze the relationship between digital economy and regional carbon productivity.


### 4.2. Construction of Dynamic Panel Threshold Model

Model (3) implies a homogeneity hypothesis; it is assumed that the role of digital economy on regional carbon productivity is the same in all regions and periods. For every additional unit of DEit, RCPit will increase by α1 unit. However, as we mentioned above, there is likely to be a complex nonlinear relationship between digital economy and regional innovation performance. The single coefficient given by the linear model cannot reflect this mechanism.This paper further adopts the threshold regression model for empirical research to test the nonlinear influence between digital economy and regional carbon productivity. Although the traditional static threshold model can make up for the deficiencies of the group regression method, the model still faces the endogenous problem between variables, leading to biases in the model estimation [33]. In addition, taking into account the early stage dependence and dynamic characteristics of regional carbon productivity, this paper introduces the core explanatory variable lagging term RCPit−1 variable; the difference GMM estimation method is used to construct a dynamic threshold panel model, with human capital accumulation as the threshold variable, to solve the above problems better.The dynamic threshold model is constructed as follows:Based on human capital accumulation, the single threshold model of the digital economy for regional carbon productivity is as follows:(4)RCPit=θ+ω1RCPit−1+α1URit+α2CAit+α3FDLit+α4ISit+β1DEitIHCit≤η+β2DEitIHCit>η+ui+εit.Based on the accumulation of human capital, the dual-threshold model of the digital economy for regional carbon productivity is as follows:(5)RCPit=θ1+ω2RCPit−1+α5URit+α6CAit+α7FDLit+α8ISit+β3DEitIHCit≤η1+β4DEitIη1<HCit≤η2+β5DEitIHCit>η2+ui+εit.Among them,i denotes the province, and t denotes the year. The control variables mainly include the following: URit indicates the level of urbanization; CAit indicates the degree of capital abundance; FDLit indicates the level of financial development; ISit indicates the industrial structure. I• is an indicative function; η1 and η2 are single and two threshold values, respectively. The remaining variables are consistent with those described above.In addition, the multithreshold panel model can be deduced by analogy, so that this paper will not repeat it here.


### 4.3. Variable Description and Data Processing

(1)
Explained variable includes regional carbon productivity (RCP). Unlike traditional productivity, which only includes economic input and output efficiency, carbon productivity can effectively make up for the defect that traditional productivity cannot measure negative economic externalities by introducing environmental pollution indices such as carbon emissions as undesired outputs [34]. Scholars have used a variety of methods to evaluate and analyze carbon productivity, including single-index measurement methods such as carbon emissions per unit of output value and multi-index measurement methods. The multi-index method is based on the input-output perspective, using SFA and DEA methods to measure carbon productivity in economic development [18]. However, research methods and the research perspectives of scholars are different; there are significant differences in research results [35]. The single-index method directly uses GDP divided by carbon emissions to characterize carbon productivity. Because of its simple structure and convenient use, it has been widely used in the literature on carbon productivity. For example, Kaya and Yokobori [36] and Sun and Du [37] defined carbon productivity as the economic interest per unit of carbon dioxide. The specific calculation methods are as follows:(6)RCPit=GDPitCO2=GDPit∑i=18CO2,i=∑i=18Ei×NVCi×CEFi×COFi×44/12.Among them,Ei represents the consumption of fossil fuels such as coal, kerosene, and natgas in the i area. NVCi, CEFi, and COFi, respectively, represent the net calorific power, carbon concentration, and carbon oxidation factor of fossil fuels in i the area. Calculate the carbon emission coefficients of fossil fuels according to IPCC regulations.(2)
Explanatory variable includes digital economyDE. It is calculated by the projection pursuit model introduced above.(3)
Threshold variable includes human capitalHC. High-level human capital accumulation could improve regional knowledge accumulation through effective knowledge spillovers and then affect the level of regional innovation accumulation and environmental protection. By referring to the international comparative series of studies on education acquisition carried out by Barro and Lee [38] and combining China education fixed number of year set, the human capital accumulation variable is represented by the average educational level. To calculate the human capital accumulation level of each region, this paper sets different years of education: primary school, junior middle school, senior high school, junior college, and above education are six years, nine years, twelve years, and sixteen years, respectively; its proportion in the population weights each education level is(7)HC=primary∗6+junior∗9+senior∗12+college∗16.Drawing lessons from existing research, this paper also explores the influence of other variables on regional carbon productivity, specifically including urbanization (UR), expressed in terms of urban population on permanent resident population [39]; capital abundance (CA), measured by the ratio of above-scale owners’ equity to GDP [40]; financial development level (FDL), measurement of the financial industry output value using unit economic efficiency [41]; industrial structure (IS), measured by the ratio of the value-added of the tertiary industry to that of the secondary industry [42].This paper selects 30 regions of China’s mainland from 2011 to 2019 (there are many missing data in Tibet and are not included in the sample) as the research sample. The original data comes from the website of the National Bureau of Statistics of China. Price fluctuations may affect the accuracy and reliability of estimates. In this paper, to eliminate price fluctuations, all monetary quantities have been deflator and then adjusted compared to prices. Moreover, related variables were logarithmic processing. Table2 shows the correlation matrix and descriptive statistics for the variables.Table 2
Correlation matrix and summary statistics of variables.
VariableRCPIDHCURCAISFDLRCP1.000ID0.4031∗∗∗1.000HC0.5737∗∗∗0.3566∗∗∗1.000UR0.5598∗∗∗0.4585∗∗∗0.7612∗∗∗1.000CA0.1728∗∗∗0.1511∗∗∗0.2783∗∗∗0.3539∗∗∗1.000IS0.7536∗∗∗0.1656∗0.6499∗∗∗0.5668∗∗∗0.1980∗∗1.000FDL0.6559∗∗∗0.2620∗∗∗0.6465∗∗∗0.7312∗∗∗0.4281∗∗∗0.7653∗∗∗1.000Sample size270270270270270270270Average0.68120.685510.00210.57640.56501.17450.6701Variance0.68390.55831.19340.12150.14040.66480.0308Standard deviation0.46950.31281.42960.01480.01980.44360.0010Minimum6.41353.849713.70000.89611.11275.16920.1963Maximum0.09770.11075.90180.34970.27710.51800.0196Note. ∗∗∗, ∗∗, and ∗ indicate the significance at the level of 0.01, 0.05, and 0.1, respectively.


## 4.1. Static Panel Model Construction

This paper first constructs the following linear regression model:(3)RCPit=μi+α1DEit+α2DEit∗HCit+βXit+εit.Among them,RCPit is the explained variable, representing the regional carbon productivity level of region i in period t. DEit is an explanatory variable, representing the degree of digital economy. DEit∗HCit is the intersection of digital economy and human capital accumulation, which is used to examine the moderating effect of human capital accumulation in the low-carbon development of digital economy. The estimated coefficient α2 of the cross-product term is this paper’s research key. According to the previous mechanism analysis, it is expected that α2 is significantly positive; μi is an unknown individual effect; εit represents the random error term; Xit is a series of control variables affecting regional carbon productivity. By selecting appropriate samples and estimation methods, the unknown coefficients α1, α2, β, and so on can be obtained to analyze the relationship between digital economy and regional carbon productivity.


## 4.2. Construction of Dynamic Panel Threshold Model

Model (3) implies a homogeneity hypothesis; it is assumed that the role of digital economy on regional carbon productivity is the same in all regions and periods. For every additional unit of DEit, RCPit will increase by α1 unit. However, as we mentioned above, there is likely to be a complex nonlinear relationship between digital economy and regional innovation performance. The single coefficient given by the linear model cannot reflect this mechanism.This paper further adopts the threshold regression model for empirical research to test the nonlinear influence between digital economy and regional carbon productivity. Although the traditional static threshold model can make up for the deficiencies of the group regression method, the model still faces the endogenous problem between variables, leading to biases in the model estimation [33]. In addition, taking into account the early stage dependence and dynamic characteristics of regional carbon productivity, this paper introduces the core explanatory variable lagging term RCPit−1 variable; the difference GMM estimation method is used to construct a dynamic threshold panel model, with human capital accumulation as the threshold variable, to solve the above problems better.The dynamic threshold model is constructed as follows:Based on human capital accumulation, the single threshold model of the digital economy for regional carbon productivity is as follows:(4)RCPit=θ+ω1RCPit−1+α1URit+α2CAit+α3FDLit+α4ISit+β1DEitIHCit≤η+β2DEitIHCit>η+ui+εit.Based on the accumulation of human capital, the dual-threshold model of the digital economy for regional carbon productivity is as follows:(5)RCPit=θ1+ω2RCPit−1+α5URit+α6CAit+α7FDLit+α8ISit+β3DEitIHCit≤η1+β4DEitIη1<HCit≤η2+β5DEitIHCit>η2+ui+εit.Among them,i denotes the province, and t denotes the year. The control variables mainly include the following: URit indicates the level of urbanization; CAit indicates the degree of capital abundance; FDLit indicates the level of financial development; ISit indicates the industrial structure. I• is an indicative function; η1 and η2 are single and two threshold values, respectively. The remaining variables are consistent with those described above.In addition, the multithreshold panel model can be deduced by analogy, so that this paper will not repeat it here.


## 4.3. Variable Description and Data Processing

(1)
Explained variable includes regional carbon productivity (RCP). Unlike traditional productivity, which only includes economic input and output efficiency, carbon productivity can effectively make up for the defect that traditional productivity cannot measure negative economic externalities by introducing environmental pollution indices such as carbon emissions as undesired outputs [34]. Scholars have used a variety of methods to evaluate and analyze carbon productivity, including single-index measurement methods such as carbon emissions per unit of output value and multi-index measurement methods. The multi-index method is based on the input-output perspective, using SFA and DEA methods to measure carbon productivity in economic development [18]. However, research methods and the research perspectives of scholars are different; there are significant differences in research results [35]. The single-index method directly uses GDP divided by carbon emissions to characterize carbon productivity. Because of its simple structure and convenient use, it has been widely used in the literature on carbon productivity. For example, Kaya and Yokobori [36] and Sun and Du [37] defined carbon productivity as the economic interest per unit of carbon dioxide. The specific calculation methods are as follows:(6)RCPit=GDPitCO2=GDPit∑i=18CO2,i=∑i=18Ei×NVCi×CEFi×COFi×44/12.Among them,Ei represents the consumption of fossil fuels such as coal, kerosene, and natgas in the i area. NVCi, CEFi, and COFi, respectively, represent the net calorific power, carbon concentration, and carbon oxidation factor of fossil fuels in i the area. Calculate the carbon emission coefficients of fossil fuels according to IPCC regulations.(2)
Explanatory variable includes digital economyDE. It is calculated by the projection pursuit model introduced above.(3)
Threshold variable includes human capitalHC. High-level human capital accumulation could improve regional knowledge accumulation through effective knowledge spillovers and then affect the level of regional innovation accumulation and environmental protection. By referring to the international comparative series of studies on education acquisition carried out by Barro and Lee [38] and combining China education fixed number of year set, the human capital accumulation variable is represented by the average educational level. To calculate the human capital accumulation level of each region, this paper sets different years of education: primary school, junior middle school, senior high school, junior college, and above education are six years, nine years, twelve years, and sixteen years, respectively; its proportion in the population weights each education level is(7)HC=primary∗6+junior∗9+senior∗12+college∗16.Drawing lessons from existing research, this paper also explores the influence of other variables on regional carbon productivity, specifically including urbanization (UR), expressed in terms of urban population on permanent resident population [39]; capital abundance (CA), measured by the ratio of above-scale owners’ equity to GDP [40]; financial development level (FDL), measurement of the financial industry output value using unit economic efficiency [41]; industrial structure (IS), measured by the ratio of the value-added of the tertiary industry to that of the secondary industry [42].This paper selects 30 regions of China’s mainland from 2011 to 2019 (there are many missing data in Tibet and are not included in the sample) as the research sample. The original data comes from the website of the National Bureau of Statistics of China. Price fluctuations may affect the accuracy and reliability of estimates. In this paper, to eliminate price fluctuations, all monetary quantities have been deflator and then adjusted compared to prices. Moreover, related variables were logarithmic processing. Table2 shows the correlation matrix and descriptive statistics for the variables.Table 2
Correlation matrix and summary statistics of variables.
VariableRCPIDHCURCAISFDLRCP1.000ID0.4031∗∗∗1.000HC0.5737∗∗∗0.3566∗∗∗1.000UR0.5598∗∗∗0.4585∗∗∗0.7612∗∗∗1.000CA0.1728∗∗∗0.1511∗∗∗0.2783∗∗∗0.3539∗∗∗1.000IS0.7536∗∗∗0.1656∗0.6499∗∗∗0.5668∗∗∗0.1980∗∗1.000FDL0.6559∗∗∗0.2620∗∗∗0.6465∗∗∗0.7312∗∗∗0.4281∗∗∗0.7653∗∗∗1.000Sample size270270270270270270270Average0.68120.685510.00210.57640.56501.17450.6701Variance0.68390.55831.19340.12150.14040.66480.0308Standard deviation0.46950.31281.42960.01480.01980.44360.0010Minimum6.41353.849713.70000.89611.11275.16920.1963Maximum0.09770.11075.90180.34970.27710.51800.0196Note. ∗∗∗, ∗∗, and ∗ indicate the significance at the level of 0.01, 0.05, and 0.1, respectively.


## 5. Panel Regression Results

### 5.1. Unit Root Test and Cointegration Test

To avoid false regression, this paper uses LLC, ADF-Fisher, and PP-Fisher tests to perform unit root tests on each variable in turn. The original hypothesis of the three types of inspection methods is that the sequence contains unit roots. The variables are stable when rejecting the original hypothesis at the 0.05 level. Table3 shows that the initial sequence of each variable does not reject the original hypothesis, indicating that the original sequence is not stationary. Under the first-order difference, some variables pass the PP-Fisher and ADF-Fisher tests at the 10% significance level, and all variables are in a nonstationary state. Besides, the second-order difference test shows that most of the test values reject the null hypothesis, indicating that each variable has a second-order single integer characteristic.Table 3
Unit root test results.
VariableTesting methodInitial sequenceFirst differenceSecond differenceStatisticProbStatisticProbStatisticProbRCPLLC0.6480.741−1.360∗0.087−2.630∗∗∗0.004ADF-Fisher0.4120.8143.6810.1596.264∗∗0.044PP-Fisher0.9360.6263.8060.1495.954∗0.051DELLC3.5331.000−0.9070.182−6.240∗∗∗0.000ADF-Fisher0.0050.9982.1530.34116.618∗∗∗0.000PP-Fisher0.0030.9982.9250.23219.352∗∗∗0.000HCLLC1.6680.952−1.817∗∗0.035−4.250∗∗∗0.000ADF-Fisher0.0800.9615.155∗0.07612.191∗∗∗0.002PP-Fisher0.0800.9615.036∗0.08114.204∗∗∗0.001URLLC7.5091.000−0.3790.352−3.366∗∗∗0.000ADF-Fisher0.0001.0001.3270.5159.863∗∗∗0.007PP-Fisher0.0001.0001.0650.58710.556∗∗∗0.005CALLC0.3180.625−2.047∗∗0.020−2.929∗∗∗0.002ADF-Fisher0.5740.7515.908∗0.0528.553∗∗0.014PP-Fisher0.6040.7395.890∗0.0538.602∗∗0.014ISLLC0.3180.625−2.047∗∗0.020−2.929∗∗∗0.002ADF-Fisher0.5740.7515.908∗0.0528.553∗∗0.014PP-Fisher0.6040.7395.890∗0.0538.602∗∗0.014FDLLLC2.0410.979−3.034∗∗0.021−4.834∗∗∗0.000ADF-Fisher0.0650.9689.219∗0.06013.618∗∗∗0.001PP-Fisher0.0040.9989.219∗0.05217.632∗∗∗0.000Note.∗∗∗, ∗∗, and ∗ indicate the significance at the level of 0.01, 0.05, and 0.1, respectively.All variables satisfy the single-integration characteristics of the same order, that is, satisfy the cointegration test premise. To ensure the reliability of the inspection results, this paper mainly uses Pedroni, Kao, and Westerlund tests to perform cointegration tests on variables. Table4 shows that most tests passed the 1% significance testing, that is, rejecting the initial hypothesis that “there is no cointegration relationship.” It means that there is a long-term stable equilibrium relationship between variables. At the same time, the regression residuals of the equations are stable and can be used for subsequent regression analysis of the original data.Table 4
Cointegration test: Kao test results.
Inspection methodsStatisticp-valuePedroniModified Phillips–Perront10.440∗∗∗0.000Phillips–Perront−35.972∗∗∗0.000Augmented Dickey–Fullert−24.054∗∗∗0.000KaoModified Dickey–Fullert3.617∗∗∗0.000Dickey–Fullert4.304∗∗∗0.000Augmented Dickey–Fullert1.599∗0.055Unadjusted modified dickey3.047∗∗0.001Unadjusted Dickey–Fullert3.433∗∗∗0.000WesterlundVariance ratio7.599∗∗∗0.000Note.∗∗∗, ∗∗, and ∗ indicate the significance at the level of 0.01, 0.05, and 0.1, respectively.


### 5.2. Estimated Results of the Static Panel Method

In this paper, the static panel estimation method is used to estimate Model 3, and preliminary results are obtained. Table5 shows the estimation results of the static panel method. The overall model has passed the significance test, indicating that the measurement model is set reasonably. The specific effects of each explanatory variable on innovation performance are as follows.Table 5
Panel data regression estimation results.
Explanatory variablesFixed effectsRandom effectsCoef.P>tCoef.P>tID0.020∗0.0970.057∗∗∗0.000ID∗HC0.074∗∗∗0.0000.073∗∗∗0.000UR0.963∗∗∗0.0000.441∗∗∗0.000CA0.079∗∗0.0050.125∗∗∗0.000IS−0.030∗∗0.011−0.0170.172FDL−0.2620.200−0.0990.673_Cons−0.328∗∗∗0.000−0.0470.213F statistics43.13Hausman testChi-Sq. = 93.69∗∗∗P = 0.000Adjoint probability (F statistic)0.000Note.∗∗∗, ∗∗, and ∗ indicate the significance at the level of 0.01, 0.05, and 0.1, respectively.The panel regression results show that digital economy and regional carbon productivity are positive relationships at a significant level of 10%, showing that digital economy has significantly promoted regional carbon productivity during the sample period, digital economy index is up 1%, innovation performance is up 0.02%, and it accords with the theoretical analysis of this paper, which verifies Hypothesis1. Compared with the effective coefficient of digital economy on regional carbon productivity, the cross-product term of digital economy and human capital is a positive relationship at a significant level of 1%. The coefficient of action is significantly enhanced, showing that human capital improvement can effectively promote the positive impact of the digital economy on regional carbon productivity, which verifies Hypothesis 2.For the control variable, we have the following:(1)
Urbanization positively affects regional carbon productivity at a significant level of 1%. van Winden [43] pointed out that, in promoting the accumulation of capital, human capital, and other elements, along with the continuous advancement of the urbanization process, urbanization first inhibited and then promoted sustainable economic growth. Although China’s urbanization construction shows a particular phenomenon of unbalanced and insufficient development, on the whole, the urbanization development has achieved remarkable results, and the urbanization process has passed the stage of extensive expansion. The high concentration of high-quality talents and capital in cities will help the generation of green innovation and promote regional carbon productivity.(2)
Capital abundance positively affects regional carbon productivity at a significant level of 5%. The capital abundance in the region can attract more investment and provide a good trading environment and high-tech industries accumulation, and the flow of high-end capital makes the green region development. More significantly, it has promoted regional carbon productivity.(3)
The industrial structure harms regional carbon productivity at a significant level of 5%. Since the pillar industries in many provinces in China are secondary industries driven by economic interests, in the process of industrial restructuring, although carbon emissions have been reduced, they also caused slow economic development in some provinces, showing a specific negative impact on regional carbon productivity.(4)
Financial development does not play a prominent role in promoting regional carbon productivity. However, Acheampong et al. [44] proposed that financial development can lead to the progress of green technology and promote sustainable economic development by attracting FDI and reducing borrowing costs and so on. However, this paper believes that this is due to particularity of economic stage and development. First, high degree of Chinese nationalization in financial institutions may lead to financial institutions preferring to provide credit to state-owned enterprises. Their financing policies are also inclined toward large- and medium-sized state-owned enterprises, Financial institutions usually choose to provide credit financing to large and medium-sized state-owned enterprises rather than private enterprises [44]. Financial development may lead to the concentration of financial resources on extensive production technologies [23] rather than on low-carbon technologies, which may be detrimental to the progress of green technologies. Therefore, it is reasonable that the financial development does not reflect the low-carbon economy effect.


### 5.3. Results and Analysis of Panel Threshold Model

According to the method mentioned above, this paper tests the existence and authenticity of the dynamic panel threshold model setting with human capital as the threshold variable as follows.First, perform the following three sets of hypothesis tests: ①H0I: there is no threshold; H1I: there is a threshold; ② H0II: there is only one threshold; H1II: there are two thresholds; ③ H0III: there are only two thresholds; H1III: there are three thresholds. The double threshold model passed the test at the 5% level. In contrast, the triple threshold model failed the test, indicating that there is a double threshold (see Table 6), and the double thresholds were 11.5566 and 12.91, respectively (see Table 7).Table 6
Test results of threshold significance.
ThresholdF-valuep-valueCritical value1%5%10%Single threshold939.20∗∗∗0.000080.222948.116435.7312Double threshold21.52∗∗0.046734.944119.514315.5038Triple threshold10.180.380014.98728.02684.4832∗∗∗, ∗∗, and ∗ denote significant levels at 1%, 5%, and 10%, respectively.Table 7
Threshold values and confidence intervals.
ModelThreshold estimators95% confidence intervalsSingle threshold11.5566[11.2991, 11.6718]Double threshold12.91[12.8300, 13.0952]Second, as shown in Figure1, each threshold estimate’s 95% confidence interval is composed of all the critical values under the significance level of LR values less than 1%, so it passes the authenticity test. Therefore, according to these two threshold values, sample areas can be divided into low human capital (HC≤11.5566), medium human capital 11.5566<HC≤12.91, and high human capital HC>12.91. The above results provide the basis for the analysis of the threshold regression results below.Figure 1
Estimation and confidence interval for the first threshold (a) and the second threshold (b) of energy misallocation.
(a)(b)Based on the calculation results of the above threshold model, this paper conducts a specific analysis of the double threshold effect, as shown in Table8. When the human capital accumulation is less than the threshold of 12.91, digital economy has a specific opposite impact on regional carbon productivity. It shows that, due to the lack of professional talents, the overall level of digital economy is not high, the scale is small, and the proportion is low. At the same time, participating companies cannot fully enjoy the digital dividend, fail to realize their digital transformation, and cannot effectively promote regional carbon productivity. When the human capital level is higher than the threshold of 12.91, the direction of the influence of the development of digital economy on the regional carbon productivity undergoes a structural change, which turns into a significant promotion. At this stage, human capital has been able to develop digital economy, providing an essential foundation for integrating digital resources and various industries. They can use numbers to optimize resource allocation more reasonably, reduce the input of various resources, and effectively increase regional carbon productivity.Table 8
Model parameter estimation result.
RCPCoef.Std. err.TP>t95% conf. intervalL1.RCP0.9954∗∗∗0.019052.500.0000.95671.0342L2.RCP0.1451∗∗∗0.02286.370.0000.09860.1916UR−0.18170.1543−1.180.248−0.49690.1335CA0.0653∗∗0.03162.060.0480.00070.1299FDL−2.4203∗∗∗0.2171−11.150.000−2.8637−1.9769IS0.0643∗∗∗0.00857.600.0000.04700.0816IDHC≤11.5566−0.00340.0107−0.320.755−0.02530.0185ID11.5566<HC≤12.91−0.1023∗0.0514−1.990.056−0.20720.0026IDHC>12.910.0736∗∗∗0.00769.750.0000.05820.0890AR (1)z = −2.17 p = 0.030AR (2)z = −1.28 p = 0.200Hansen test of overidp = 0.971Note. ∗∗∗, ∗∗, and ∗ indicate the significance at the level of 0.01, 0.05, and 0.1, respectively.


### 5.4. Contribution Rate Analysis

Based on the threshold analysis, we can obtain the elastic coefficient of digital economy to regional carbon productivity in different threshold intervals. To describe the contribution rate of the two more accurately, this paper refers to the method of Mao and Sheng [46] to calculate the contribution rate of digital economy to regional carbon productivity.First, based on the average value of the digital economy indicators for each province from 2011 to 2019, subtract the average value of 2011 from the average value of 2019, and get the average change of the digital economy from 2011 to 2019. Similarly, the average variation range of regional carbon productivity from 2011 to 2019 was calculated. Then, during the sample period, multiply the elasticity influence coefficient of the digital economy and its change range to obtain the regional carbon productivity change value caused by the change in the digital economy. At last, divide the calculated changing value of regional carbon productivity by the change value of regional carbon productivity, multiplied by 100%. The computed result is the contribution rate of digital economy to regional carbon productivity.As shown in Table9, when the human capital variable does not cross the threshold value of 11.5566, the contribution rate of digital economy to the regional carbon productivity improvement is 46.08%. When the human capital is in the range of [11.5566, 12.91], the contribution rate of digital economy to regional carbon productivity increases significantly. When the level of human capital exceeds 12.91, the contribution rate of digital economy to the regional carbon productivity continues to increase to 249.68%. From the estimated contribution rate results, in the region of higher human capital, the more digital economy is, the more regional carbon productivity will increase, which further verifies Hypothesis 2.Table 9
Analysis of the contribution of digital economy to low-carbon development.
AreaIDHC≤11.5566ID11.5566<HC≤12.9100IDHC>12.9100Coefficient0.46559232.0535262.523022Contribution rate46.08%203.22%249.68%


### 5.5. Robustness Test

(1)
Referring to the research of Qi and Li [47], this section tests the robustness of the above empirical research by adjusting the method of the research sample. This section accordingly removes the regions with the highest and lowest levels of digital economy. Through the empirical test of 28 provinces, the study found that the robustness test results are consistent with the above empirical results.(2)
Referring to the research of Chen and Wang [48], this section tests the robustness of the above empirical research by adjusting proxy variables. The above measures the digitization of the industry based on the two dimensions of digitization foundation and digitization integration. Based on the investment perspective, the ratio of the intermediate goods invested by the global digital industry in China’s manufacturing industry to the industrial added value in WIOTs is used as a proxy indicator for digital economy. There is no significant difference between the robustness test results and the above empirical results.(3)
Referring to the research of Hou et al. [49] and Balta-Ozkan et al. [50], this section conducts a robustness test of the above empirical research by adjusting the empirical method. According to the endogenous estimation of dynamic panel threshold value, the regions are divided into different intervals from human capital accumulation, and the slope coefficients of different agglomeration levels are estimated using the systematic GMM estimation method.Due to space limitations, this section only reports the results of the third method. According to Table10, AR (1), AR (2), and Hansen tests are passed; this shows that this paper’s dynamic panel threshold model is reasonable. And there is no significant difference in the results, indicating that the empirical results are robust.Table 10
Robustness test.
RCPCoef.Std. err.tP>t95% conf. intervalL1.RCP1.1630∗∗∗0.0084138.850.0001.14591.1801L2.RCP0.0189∗∗0.00912.080.0470.00030.0374UR−0.0740∗∗0.0245−3.020.005−0.1241−0.0239CA0.0441∗∗∗0.01024.340.0000.02330.0649FDL−0.06550.0988−0.660.512−0.26750.1365IS−0.0151∗∗0.0048−3.140.004−0.0249−0.0053IDHC≤11.5566−0.02490.0052−4.800.100−0.0355−0.0143ID11.5566<HC≤12.91−0.0626∗∗0.0116−5.380.033−0.0864−0.0388IDHC>12.910.1655∗∗∗0.015510.660.0000.13370.1973AR (1)z = −2.03 p = 0.043AR (2)z = −1.12 p = 0.263Hansen test of overidp = 1.000Note. ∗∗∗, ∗∗, and ∗ indicate the significance at the level of 0.01, 0.05, and 0.1, respectively.


## 5.1. Unit Root Test and Cointegration Test

To avoid false regression, this paper uses LLC, ADF-Fisher, and PP-Fisher tests to perform unit root tests on each variable in turn. The original hypothesis of the three types of inspection methods is that the sequence contains unit roots. The variables are stable when rejecting the original hypothesis at the 0.05 level. Table3 shows that the initial sequence of each variable does not reject the original hypothesis, indicating that the original sequence is not stationary. Under the first-order difference, some variables pass the PP-Fisher and ADF-Fisher tests at the 10% significance level, and all variables are in a nonstationary state. Besides, the second-order difference test shows that most of the test values reject the null hypothesis, indicating that each variable has a second-order single integer characteristic.Table 3
Unit root test results.
VariableTesting methodInitial sequenceFirst differenceSecond differenceStatisticProbStatisticProbStatisticProbRCPLLC0.6480.741−1.360∗0.087−2.630∗∗∗0.004ADF-Fisher0.4120.8143.6810.1596.264∗∗0.044PP-Fisher0.9360.6263.8060.1495.954∗0.051DELLC3.5331.000−0.9070.182−6.240∗∗∗0.000ADF-Fisher0.0050.9982.1530.34116.618∗∗∗0.000PP-Fisher0.0030.9982.9250.23219.352∗∗∗0.000HCLLC1.6680.952−1.817∗∗0.035−4.250∗∗∗0.000ADF-Fisher0.0800.9615.155∗0.07612.191∗∗∗0.002PP-Fisher0.0800.9615.036∗0.08114.204∗∗∗0.001URLLC7.5091.000−0.3790.352−3.366∗∗∗0.000ADF-Fisher0.0001.0001.3270.5159.863∗∗∗0.007PP-Fisher0.0001.0001.0650.58710.556∗∗∗0.005CALLC0.3180.625−2.047∗∗0.020−2.929∗∗∗0.002ADF-Fisher0.5740.7515.908∗0.0528.553∗∗0.014PP-Fisher0.6040.7395.890∗0.0538.602∗∗0.014ISLLC0.3180.625−2.047∗∗0.020−2.929∗∗∗0.002ADF-Fisher0.5740.7515.908∗0.0528.553∗∗0.014PP-Fisher0.6040.7395.890∗0.0538.602∗∗0.014FDLLLC2.0410.979−3.034∗∗0.021−4.834∗∗∗0.000ADF-Fisher0.0650.9689.219∗0.06013.618∗∗∗0.001PP-Fisher0.0040.9989.219∗0.05217.632∗∗∗0.000Note.∗∗∗, ∗∗, and ∗ indicate the significance at the level of 0.01, 0.05, and 0.1, respectively.All variables satisfy the single-integration characteristics of the same order, that is, satisfy the cointegration test premise. To ensure the reliability of the inspection results, this paper mainly uses Pedroni, Kao, and Westerlund tests to perform cointegration tests on variables. Table4 shows that most tests passed the 1% significance testing, that is, rejecting the initial hypothesis that “there is no cointegration relationship.” It means that there is a long-term stable equilibrium relationship between variables. At the same time, the regression residuals of the equations are stable and can be used for subsequent regression analysis of the original data.Table 4
Cointegration test: Kao test results.
Inspection methodsStatisticp-valuePedroniModified Phillips–Perront10.440∗∗∗0.000Phillips–Perront−35.972∗∗∗0.000Augmented Dickey–Fullert−24.054∗∗∗0.000KaoModified Dickey–Fullert3.617∗∗∗0.000Dickey–Fullert4.304∗∗∗0.000Augmented Dickey–Fullert1.599∗0.055Unadjusted modified dickey3.047∗∗0.001Unadjusted Dickey–Fullert3.433∗∗∗0.000WesterlundVariance ratio7.599∗∗∗0.000Note.∗∗∗, ∗∗, and ∗ indicate the significance at the level of 0.01, 0.05, and 0.1, respectively.


## 5.2. Estimated Results of the Static Panel Method

In this paper, the static panel estimation method is used to estimate Model 3, and preliminary results are obtained. Table5 shows the estimation results of the static panel method. The overall model has passed the significance test, indicating that the measurement model is set reasonably. The specific effects of each explanatory variable on innovation performance are as follows.Table 5
Panel data regression estimation results.
Explanatory variablesFixed effectsRandom effectsCoef.P>tCoef.P>tID0.020∗0.0970.057∗∗∗0.000ID∗HC0.074∗∗∗0.0000.073∗∗∗0.000UR0.963∗∗∗0.0000.441∗∗∗0.000CA0.079∗∗0.0050.125∗∗∗0.000IS−0.030∗∗0.011−0.0170.172FDL−0.2620.200−0.0990.673_Cons−0.328∗∗∗0.000−0.0470.213F statistics43.13Hausman testChi-Sq. = 93.69∗∗∗P = 0.000Adjoint probability (F statistic)0.000Note.∗∗∗, ∗∗, and ∗ indicate the significance at the level of 0.01, 0.05, and 0.1, respectively.The panel regression results show that digital economy and regional carbon productivity are positive relationships at a significant level of 10%, showing that digital economy has significantly promoted regional carbon productivity during the sample period, digital economy index is up 1%, innovation performance is up 0.02%, and it accords with the theoretical analysis of this paper, which verifies Hypothesis1. Compared with the effective coefficient of digital economy on regional carbon productivity, the cross-product term of digital economy and human capital is a positive relationship at a significant level of 1%. The coefficient of action is significantly enhanced, showing that human capital improvement can effectively promote the positive impact of the digital economy on regional carbon productivity, which verifies Hypothesis 2.For the control variable, we have the following:(1)
Urbanization positively affects regional carbon productivity at a significant level of 1%. van Winden [43] pointed out that, in promoting the accumulation of capital, human capital, and other elements, along with the continuous advancement of the urbanization process, urbanization first inhibited and then promoted sustainable economic growth. Although China’s urbanization construction shows a particular phenomenon of unbalanced and insufficient development, on the whole, the urbanization development has achieved remarkable results, and the urbanization process has passed the stage of extensive expansion. The high concentration of high-quality talents and capital in cities will help the generation of green innovation and promote regional carbon productivity.(2)
Capital abundance positively affects regional carbon productivity at a significant level of 5%. The capital abundance in the region can attract more investment and provide a good trading environment and high-tech industries accumulation, and the flow of high-end capital makes the green region development. More significantly, it has promoted regional carbon productivity.(3)
The industrial structure harms regional carbon productivity at a significant level of 5%. Since the pillar industries in many provinces in China are secondary industries driven by economic interests, in the process of industrial restructuring, although carbon emissions have been reduced, they also caused slow economic development in some provinces, showing a specific negative impact on regional carbon productivity.(4)
Financial development does not play a prominent role in promoting regional carbon productivity. However, Acheampong et al. [44] proposed that financial development can lead to the progress of green technology and promote sustainable economic development by attracting FDI and reducing borrowing costs and so on. However, this paper believes that this is due to particularity of economic stage and development. First, high degree of Chinese nationalization in financial institutions may lead to financial institutions preferring to provide credit to state-owned enterprises. Their financing policies are also inclined toward large- and medium-sized state-owned enterprises, Financial institutions usually choose to provide credit financing to large and medium-sized state-owned enterprises rather than private enterprises [44]. Financial development may lead to the concentration of financial resources on extensive production technologies [23] rather than on low-carbon technologies, which may be detrimental to the progress of green technologies. Therefore, it is reasonable that the financial development does not reflect the low-carbon economy effect.


## 5.3. Results and Analysis of Panel Threshold Model

According to the method mentioned above, this paper tests the existence and authenticity of the dynamic panel threshold model setting with human capital as the threshold variable as follows.First, perform the following three sets of hypothesis tests: ①H0I: there is no threshold; H1I: there is a threshold; ② H0II: there is only one threshold; H1II: there are two thresholds; ③ H0III: there are only two thresholds; H1III: there are three thresholds. The double threshold model passed the test at the 5% level. In contrast, the triple threshold model failed the test, indicating that there is a double threshold (see Table 6), and the double thresholds were 11.5566 and 12.91, respectively (see Table 7).Table 6
Test results of threshold significance.
ThresholdF-valuep-valueCritical value1%5%10%Single threshold939.20∗∗∗0.000080.222948.116435.7312Double threshold21.52∗∗0.046734.944119.514315.5038Triple threshold10.180.380014.98728.02684.4832∗∗∗, ∗∗, and ∗ denote significant levels at 1%, 5%, and 10%, respectively.Table 7
Threshold values and confidence intervals.
ModelThreshold estimators95% confidence intervalsSingle threshold11.5566[11.2991, 11.6718]Double threshold12.91[12.8300, 13.0952]Second, as shown in Figure1, each threshold estimate’s 95% confidence interval is composed of all the critical values under the significance level of LR values less than 1%, so it passes the authenticity test. Therefore, according to these two threshold values, sample areas can be divided into low human capital (HC≤11.5566), medium human capital 11.5566<HC≤12.91, and high human capital HC>12.91. The above results provide the basis for the analysis of the threshold regression results below.Figure 1
Estimation and confidence interval for the first threshold (a) and the second threshold (b) of energy misallocation.
(a)(b)Based on the calculation results of the above threshold model, this paper conducts a specific analysis of the double threshold effect, as shown in Table8. When the human capital accumulation is less than the threshold of 12.91, digital economy has a specific opposite impact on regional carbon productivity. It shows that, due to the lack of professional talents, the overall level of digital economy is not high, the scale is small, and the proportion is low. At the same time, participating companies cannot fully enjoy the digital dividend, fail to realize their digital transformation, and cannot effectively promote regional carbon productivity. When the human capital level is higher than the threshold of 12.91, the direction of the influence of the development of digital economy on the regional carbon productivity undergoes a structural change, which turns into a significant promotion. At this stage, human capital has been able to develop digital economy, providing an essential foundation for integrating digital resources and various industries. They can use numbers to optimize resource allocation more reasonably, reduce the input of various resources, and effectively increase regional carbon productivity.Table 8
Model parameter estimation result.
RCPCoef.Std. err.TP>t95% conf. intervalL1.RCP0.9954∗∗∗0.019052.500.0000.95671.0342L2.RCP0.1451∗∗∗0.02286.370.0000.09860.1916UR−0.18170.1543−1.180.248−0.49690.1335CA0.0653∗∗0.03162.060.0480.00070.1299FDL−2.4203∗∗∗0.2171−11.150.000−2.8637−1.9769IS0.0643∗∗∗0.00857.600.0000.04700.0816IDHC≤11.5566−0.00340.0107−0.320.755−0.02530.0185ID11.5566<HC≤12.91−0.1023∗0.0514−1.990.056−0.20720.0026IDHC>12.910.0736∗∗∗0.00769.750.0000.05820.0890AR (1)z = −2.17 p = 0.030AR (2)z = −1.28 p = 0.200Hansen test of overidp = 0.971Note. ∗∗∗, ∗∗, and ∗ indicate the significance at the level of 0.01, 0.05, and 0.1, respectively.


## 5.4. Contribution Rate Analysis

Based on the threshold analysis, we can obtain the elastic coefficient of digital economy to regional carbon productivity in different threshold intervals. To describe the contribution rate of the two more accurately, this paper refers to the method of Mao and Sheng [46] to calculate the contribution rate of digital economy to regional carbon productivity.First, based on the average value of the digital economy indicators for each province from 2011 to 2019, subtract the average value of 2011 from the average value of 2019, and get the average change of the digital economy from 2011 to 2019. Similarly, the average variation range of regional carbon productivity from 2011 to 2019 was calculated. Then, during the sample period, multiply the elasticity influence coefficient of the digital economy and its change range to obtain the regional carbon productivity change value caused by the change in the digital economy. At last, divide the calculated changing value of regional carbon productivity by the change value of regional carbon productivity, multiplied by 100%. The computed result is the contribution rate of digital economy to regional carbon productivity.As shown in Table9, when the human capital variable does not cross the threshold value of 11.5566, the contribution rate of digital economy to the regional carbon productivity improvement is 46.08%. When the human capital is in the range of [11.5566, 12.91], the contribution rate of digital economy to regional carbon productivity increases significantly. When the level of human capital exceeds 12.91, the contribution rate of digital economy to the regional carbon productivity continues to increase to 249.68%. From the estimated contribution rate results, in the region of higher human capital, the more digital economy is, the more regional carbon productivity will increase, which further verifies Hypothesis 2.Table 9
Analysis of the contribution of digital economy to low-carbon development.
AreaIDHC≤11.5566ID11.5566<HC≤12.9100IDHC>12.9100Coefficient0.46559232.0535262.523022Contribution rate46.08%203.22%249.68%


## 5.5. Robustness Test

(1)
Referring to the research of Qi and Li [47], this section tests the robustness of the above empirical research by adjusting the method of the research sample. This section accordingly removes the regions with the highest and lowest levels of digital economy. Through the empirical test of 28 provinces, the study found that the robustness test results are consistent with the above empirical results.(2)
Referring to the research of Chen and Wang [48], this section tests the robustness of the above empirical research by adjusting proxy variables. The above measures the digitization of the industry based on the two dimensions of digitization foundation and digitization integration. Based on the investment perspective, the ratio of the intermediate goods invested by the global digital industry in China’s manufacturing industry to the industrial added value in WIOTs is used as a proxy indicator for digital economy. There is no significant difference between the robustness test results and the above empirical results.(3)
Referring to the research of Hou et al. [49] and Balta-Ozkan et al. [50], this section conducts a robustness test of the above empirical research by adjusting the empirical method. According to the endogenous estimation of dynamic panel threshold value, the regions are divided into different intervals from human capital accumulation, and the slope coefficients of different agglomeration levels are estimated using the systematic GMM estimation method.Due to space limitations, this section only reports the results of the third method. According to Table10, AR (1), AR (2), and Hansen tests are passed; this shows that this paper’s dynamic panel threshold model is reasonable. And there is no significant difference in the results, indicating that the empirical results are robust.Table 10
Robustness test.
RCPCoef.Std. err.tP>t95% conf. intervalL1.RCP1.1630∗∗∗0.0084138.850.0001.14591.1801L2.RCP0.0189∗∗0.00912.080.0470.00030.0374UR−0.0740∗∗0.0245−3.020.005−0.1241−0.0239CA0.0441∗∗∗0.01024.340.0000.02330.0649FDL−0.06550.0988−0.660.512−0.26750.1365IS−0.0151∗∗0.0048−3.140.004−0.0249−0.0053IDHC≤11.5566−0.02490.0052−4.800.100−0.0355−0.0143ID11.5566<HC≤12.91−0.0626∗∗0.0116−5.380.033−0.0864−0.0388IDHC>12.910.1655∗∗∗0.015510.660.0000.13370.1973AR (1)z = −2.03 p = 0.043AR (2)z = −1.12 p = 0.263Hansen test of overidp = 1.000Note. ∗∗∗, ∗∗, and ∗ indicate the significance at the level of 0.01, 0.05, and 0.1, respectively.


## 6. Conclusions and Recommendations

The contradiction between us and the natural world is increasing; protecting the environment and developing a low-carbon economy are the top priority. Like most other developing countries, China is at a critical stage of economic structural transformation. Achieving balanced development between economic growth and completing the “carbon peaking and carbon neutrality goals” dual carbon target has become the most urgent problem at hand. This paper constructs a complex model of digital economy, human capital, and regional carbon productivity from heterogeneity. It demonstrates the complex interaction mechanism among variables. The following conclusions were drawn through analysis:(1)
China’s digital economy development level continues to improve, but there is a relatively noticeable “digital gap” between regions. The development of digital economy in China’s central and western regions is lagging behind and urgently needs improvement. Particularly in economically underdeveloped areas such as Qinghai and Gansu, vigorously developing the digital economy will help to achieve economic “overtaking” and achieve high-quality development.(2)
The development of digital economy can positively affect regional carbon productivity, and the accumulation of human capital can effectively strengthen the low-carbon effect of digital economy. Human capital accumulation can effectively promote the low-carbon effect of digital economy.(3)
Digital economy has a significant double threshold effect on regional carbon productivity. When the level of regional human capital crosses a certain threshold, the impact of digital economy on regional carbon productivity undergoes a structural mutation, changing from negative to positive.The conclusions of this study have specific policy implications for fully demonstrating the promoting effect of digital economy on regional carbon productivity:(1)
Strengthen talent support and guarantee, multilevel training, multichannel introduction, and multimeasures to encourage talents. Firstly, increase the training efforts for management teams, scientific research teams, and professional workers related to the digital industry. Secondly, actively hire relevant professionals from various universities, strengthen talent exchanges with developed areas of the digital industry, and establish a sound talent introduction system and environment. Finally, implement the new policy for talents in the digital industry, accurately introduce a group of high-end talents received by the digital industry, and give critical support from many aspects such as housing, subsidies, scientific research start-up funds, and children’s education.(2)
The “driving dividend” of the digital economy on carbon productivity still needs to be explored in depth. Firstly, while improving digital economy in various regions, we need to integrate digital into constructing a low-carbon economic system and strengthen the interaction mechanism between digital and carbon productivity. Secondly, local governments must use digital management models to exercise macrocontrol over regional enterprises and seize the opportunities of the global green technological revolution. Formulate a digital industry citation policy based on regional differences. We should further strengthen the internal and external interaction mechanism for the eastern region to optimize and upgrade industrial structures. Finally, through digital industry to promote carbon technology innovation, improve the low-carbon level of industrial development, use digital industry-related technologies to analyze regional carbon emissions data, formulate related environmental regulatory policies, transform and upgrade high-polluting industries, and use numbers to release the vitality of the low-carbon economy.It should be pointed out that this study also has certain limitations. At present, there is a lack of unified standards for the measurement of the digital economy. However, this paper builds a digital economy evaluation system as comprehensively as possible. However, due to the broad definition of the digital economy, it may be difficult to accurately measure during the research process. This is an issue that needs to be further explored in future research. In addition, this paper only explores the nonlinear interaction path between the digital economy and regional carbon productivity from human capital. The test and identification of other influence pathways still need to be explored in the follow-up research.



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*Source: 6815133-2022-07-01.xml*