How does digital economy affect the development of common prosperity level?

How does digital economy affect the development of common prosperity level? | 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 Research Article How does digital economy affect the development of common prosperity level? Linhan Luo, Guangqin Xiong This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3923573/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 Digital economy is not only a new driving force for economic growth, but also a new way to promote common prosperity. This paper examines how digital economy affects common prosperity development in China, using spatial Durbin model and panel data of 30 provinces from 2012 to 2022 to empirically analyze the direct effect, spatial spillover effect, and marginal incremental effect of the digital economy in terms of driving the development of common prosperity. The research results show that the digital economy has a significant positive direct effect and spatial spillover effect on the development of common prosperity, and there is a marginal incremental effect, i.e., the higher the level of the digital economy, the greater the promotion of the development of common prosperity. Plus, total factor productivity enhances the relationship between digital economy and common prosperity. The paper reveals the mechanism and path of digital economy’s impact on common prosperity, and provides theoretical and policy implications for improving digital economy strategy and promoting high-quality development and common prosperity. Digital economy Marginal incremental effect Common prosperity Total factor productivity Spatial Durbin modeling Figures Figure 1 Figure 2 Figure 3 1. Introduction common prosperity is an essential requirement of socialism, an important feature of socialism with Chinese characteristics, and an inevitable requirement for realizing the great rejuvenation of the Chinese nation. At the 10th meeting of the Central Financial and Economic Commission, General Secretary Xi Jinping emphasized the importance of adhering to the people-centered development ideology, promoting common prosperity in high-quality development, accelerating the formation of a policy framework to promote common prosperity, and focusing on solving outstanding problems such as unreasonable income distribution and the excessive gap between the rich and the poor, so as to enable all people to share in the fruits of development and create a better life together. To realize common prosperity, it is necessary to ensure both the growth of material wealth and the reasonable distribution of wealth, as well as the basic living standards of all people and their comprehensive development. Therefore, the connotation of common prosperity includes not only fairness in income distribution but also the quality of economic growth, not only the sharing of material wealth but also spiritual culture, and not only the sharing of urban and rural residents but also the sharing between regions. The digital economy refers to a new economic form based on digital technology, with data as the core resource, a network platform as the carrier, driven by innovation, aiming at improving efficiency and quality, and oriented towards promoting economic and social development and improving people's lives. Digital economy is an important outcome of the new round of scientific and technological revolution and industrial change, a new engine for economic and social development, and a new impetus for building a new development pattern. Digital economy is not only a new driving force for economic growth, but also a new way to promote common prosperity. Based on the spillover effect brought about by digital diffusion and network externalities, the digital economy is able to break the geographical and time constraints, form synergistic effects between digital platforms and business ecological vendors, between industrial chains and supply chains, and between data elements and other production factors, improve total factor productivity, and promote the quality and balance of economic growth. The digital economy, based on the innovative and sharing nature of digital technology, can lower the threshold of innovation and participation, expand the scope of innovation and participation, increase the benefits of innovation and participation, and promote the fairness and inclusiveness of income distribution. The digital economy, based on the universality and convenience of digital services, can raise the level of public service provision, expand the coverage of public services, enhance the satisfaction of public services, and promote the sharing and diversity of spiritual culture. Based on the transparency and synergy of digital governance, the digital economy can optimize the efficiency and effectiveness of government governance, enhance the credibility and fairness of government governance, improve the participation and interaction of government governance, and promote the sharing and oneness of urban and rural residents. Therefore, there is an intrinsic connection and interaction between the digital economy and common prosperity, and the development of the digital economy is both an important support for common prosperity and an important path to common prosperity. Exploring the mechanism and path of the digital economy's impact on common prosperity is of great theoretical and policy significance for deeply understanding the intrinsic connection between the digital economy and common prosperity, improving the development strategy of the digital economy, and promoting high-quality development and common prosperity. This paper takes digital economy as the core explanatory variable, common prosperity development level as the explanatory variable, total factor productivity as the moderating variable, adopts the spatial Durbin model, and utilizes the panel data of China's 31 provincial-level administrative regions from 2012–2022 to empirically analyze, from the three aspects of the direct effect, the spatial spillover effect, and the marginal incremental effect (threshold effect) of the digital economy in driving the development of the common prosperity The mechanism and path of the digital economy's impact on common prosperity. The purpose of this paper is to explore the mechanism of the digital economy's impact on common prosperity and the moderating role of total factor productivity in it. Total factor productivity is an important indicator of the quality and efficiency of economic growth, reflecting the comprehensive performance of an economy in terms of technological progress, innovation capacity, resource allocation and institutional arrangements. We believe that the digital economy can not only directly enhance the level of common prosperity development, but also indirectly enhance the sustainability of common prosperity by promoting the increase of total factor productivity. At the same time, we also consider the spatial interaction between different regions, i.e., the development level of digital economy and common prosperity in one region will be affected by other regions, forming spatial spillover effects. In order to empirically analyze this issue, we adopt the Spatial Durbin Model (SDM), which is used to analyze the spatial spillover effects of the dependent and independent variables in a region, as well as the spatial interactions between the independent variables. The main contributions of this paper are the following: First, from the perspective of digital economy, the mechanism and path of the impact of digital economy on common prosperity are systematically analyzed, which expands the perspective and content of the study of common prosperity; second, from the perspective of spatial spillover effect and marginal incremental effect, the nonlinear impact of digital economy on common prosperity is deeply explored, which enriches the research methodology and conclusions of the digital economy; third, from the perspective of total factor productivity, the regulatory effect of total factor productivity on common prosperity is analyzed, which provides new perspectives and evidence for the study of digital economy and common prosperity, and improves the precision and credibility of the study. The third is to analyze the moderating effect of total factor productivity on common prosperity, which provides new perspectives and evidence for the research on digital economy and common prosperity, and improves the precision and credibility of the research. 1.1. Related literature The relationship between digital economy and common prosperity is an emerging field of research, and the relevant literature at home and abroad has been explored from the following three aspects. 1.1.1. Direct effects of the digital economy driving the development of common prosperity level The direct effect of the digital economy driving the development of common prosperity is mainly reflected in the fact that the digital economy can directly promote the realization of common prosperity by improving the quality and balance of economic growth, promoting the fairness and inclusiveness of income distribution, upgrading the sharing and diversity of spiritual culture, and enhancing the sharing and oneness of urban and rural residents. Relevant literature at home and abroad mainly includes the following categories. The impact of the digital economy on economic growth is an important part of the study of the digital economy and underlies the relationship between the digital economy and common prosperity. The digital economy has a significant positive impact on economic growth through improving production efficiency, reducing transaction costs, promoting innovative activities, and expanding consumer demand. For example, Zhao Tao et al. (2020) empirically examined the impact of the digital economy on economic growth by using urban panel data in China and a two-way fixed-effects model, and the results showed that the digital economy has a significant positive effect on economic growth, and there is a marginal incremental effect, i.e., the higher the level of the digital economy, the greater the promotion of economic growth. [1] In addition, the digital economy can improve the quality and balance of economic growth, promote the optimization and upgrading of economic structure, narrow the regional development gap, and enhance the sustainability and resilience of the economy. For example,Zhao T, Zhang Z and Liang S K (2020) found that the role of the digital economy on economic growth is mainly reflected in the tertiary industry, rather than the primary and secondary industries, indicating that the digital economy has an important role in promoting the optimization of economic structure. Hou L, Tian C, and Xiang R (2023) found that the role of the digital economy on economic growth is more significant in the central and western regions, indicating that the digital economy has an important role in promoting the balance of regional development. Shen W, Xia W and Li S. ( 2022 ) found that the role of digital economy on economic growth was more significant during the financial crisis, indicating that the digital economy has an important role in guaranteeing economic stability. The impact of the digital economy on income distribution is at the core of the relationship between the digital economy and common prosperity, and is also a hot spot in digital economy research. The impact of the digital economy on income distribution is complex and dual, with both positive facilitating and negative constraining effects. On the one hand, the digital economy can improve the fairness and inclusiveness of income distribution by lowering the threshold of innovation and participation, expanding the scope of innovation and participation, and increasing the benefits of innovation and participation. For example, Jiang Q, Li Y and Si H ( 2022 ) concluded through empirical analysis that the digital economy has a significant positive impact on the income level and income growth rate of urban and rural residents, and the impact on the income level and income growth rate of rural residents is more significant, indicating that the digital economy is conducive to narrowing the income gap between urban and rural areas, and promoting the fairness of income distribution. Yan J, Tu X and Zheng J (2023) found that the impact of the digital economy on the residents' income has a marginal incremental effect, that is, the higher the level of the digital economy, the greater the promotion of residents' income, indicating that the digital economy is conducive to increasing the level of residents' income and promoting the inclusion of income distribution. On the other hand, the digital economy may also have a negative impact on income distribution by exacerbating skill differences, expanding returns to scale, and reinforcing market monopoly, leading to unfair and non-inclusive income distribution. For example, Li Y and Ke J S (2021) point out that the digital economy has a significant positive impact on both the urban-rural residents' income gap and the regional residents' income gap, indicating that the digital economy may exacerbate the imbalance of income distribution and constrain the fairness of income distribution. Han X, Fu L and Lv C (2023) found that there is a stage difference in the impact of the digital economy on the Gini coefficient, that is, when the level of the digital economy is low, the impact on the Gini coefficient is negative, while when the level of the digital economy is high, the impact on the Gini coefficient is positive, which indicates that the digital economy may have an "inverted U-shaped" impact on income distribution, restricting the fairness of income distribution. Inclusion in Income Distribution. 1.1.2. Spatial spillover effects of digital economy-driven common prosperity development The spatial spillover effect of the digital economy in driving the development of common prosperity is mainly reflected in the fact that the digital economy can break the geographical and temporal constraints through the formation of network externalities and digital diffusion, forming synergistic effects between digital platforms and business ecological vendors, between industrial chains and supply chains, and between data elements and other factors of production, and facilitating spatial diffusion and regional harmonization of common prosperity. A distinctive feature of the digital economy is its strong network externality, which means that the value and benefits of the digital economy increase with the expansion of the scale of the network, thus forming a positive feedback loop that promotes the rapid development and wide dissemination of the digital economy. The network externality of the digital economy is not only reflected in the supply and demand of digital products and services, but also in the upstream and downstream of digital platforms and business ecology, thus forming the spatial spillover effect of the digital economy and promoting the spatial diffusion of common prosperity. For example, Yan J, Tu X and Zheng J (2023) found that there is a significant spatial spillover effect of the impact of the digital economy on economic growth, that is, the higher the level of the digital economy, the greater the promotion of the economic growth of the neighboring regions, suggesting that the digital economy can drive the economic development of neighboring regions and promote inter-regional common prosperity through network externalities (Su J & Su K & Wang S, 2021). Another distinctive feature of the digital economy is its strong digital diffusion, which means that the development of the digital economy can promote the digital transformation of other industries and fields through the innovation and application of digital technologies, thus forming cross-border integration and industrial upgrading of the digital economy and promoting the rapid development and wide dissemination of the digital economy. The digital diffusion of the digital economy is not only reflected in the integration of digital technology with other technologies, but also in the integration of digital industries with other industries, thus forming the spatial spillover effect of the digital economy and promoting the regional coordination of common prosperity. For example, Man J, Liu J and Cui B (2023) found that there is a significant spatial spillover effect of the impact of the digital economy on economic growth, i.e., the higher the level of the digital economy, the greater the promotion of economic growth in other regions. 1.1.3. Marginal incremental effects of the digital economy driving the development of common prosperity level The marginal incremental effect (threshold effect) of the digital economy driving the development of common prosperity is mainly reflected in the fact that the level and quality of the development of the digital economy have a stage difference in its impact on common prosperity, i.e., the higher the level of the digital economy, the greater the promotion of common prosperity, but at the same time there exists a certain threshold, i.e., when the level of the digital economy is lower than a certain degree, the promotion of common prosperity is not significant or even negative (Mirdamad M G, 2020). 1.2. Model construction 1.2.1. Econometric modeling To verify the direct effect of the digital economy driving the development of common prosperity, the following benchmark regression model is constructed: $${lnindex}_{i,t}={\alpha }_{0}+{\alpha }_{1}{lndigital}_{i,t}+{\phi }_{z}{Z}_{i,t}+{\mu }_{i}+{\delta }_{t}+{\epsilon }_{i,t}$$ 1 In Eq. ( 1 ), the \({lnindex}_{i,t}\) represents the level of common prosperity development of province i in year t; \({lndigital}_{i,t}\) represents the level of development of digital economy of province i in year t; \({Z}_{i,t}\) represents each control variable, the \({\mu }_{i}\) and \({\delta }_{t}\) represent the control area fixed effects and time fixed effects, respectively; \({\epsilon }_{i,t}\) represents the randomized disturbance term; \({\alpha }_{0}\) is the constant term, and \({\alpha }_{1}\) are the estimated coefficients of the core explanatory variables. Estimated coefficients greater than 0 represent a positive effect of digital economy on common prosperity, otherwise a negative effect. In order to explore the spatial spillover effect of China's digital economy development on the development of common prosperity, this paper adds a spatial weight matrix on the basis of the baseline regression model, so as to further construct a spatial Durbin model (SDM) as shown below: $${lnindex}_{i,t}={l}_{0}+\rho {W}_{i.j}{lnindex}_{i,t}+{\theta }_{1}{W}_{i,j}{lndigital}_{i,t}+{\beta }_{1}{lndigital}_{i,t}+\sum {\beta }_{Z}{Z}_{i,t}+{\theta }_{Z}{W}_{i,j}\sum {Z}_{i,t}+{\mu }_{i}+{\delta }_{t}+{\epsilon }_{i,t}$$ 2 $${\epsilon }_{i,t}=\lambda W{\epsilon }_{i,t}+{\zeta }_{i,t}$$ 3 In the above equation, the \({\rho }\) is the spatial autoregressive coefficient; \({\theta }_{1}\) is the coefficient of the spatial lag term of the explanatory variables; \({\theta }_{Z}\) is expressed as the control variable spatial lag term coefficient; \({\zeta }_{i,t}∼N(0,{\delta }^{2}{I}_{n})\) ; \({\mu }_{i}\) and \({\delta }_{t}\) denote spatial fixed effects and time fixed effects, respectively; \({\epsilon }_{i,t}\) denotes the error term; \({\lambda }\) is the spatial lag term coefficient of the error term; \({W}_{i,j}\) represents the spatial weight matrix; \({\beta }_{1}\) represents the coefficients of the explanatory variables, and \({\beta }_{Z}\) represents the control variable coefficients; \(\text{W}{{\epsilon }}_{\text{i},\text{t}}\) represents the spatial effect of the error term; \({l}_{0}\) is the constant term; \({Z}_{i,t}\) represents a series of control variables such as industrial structure. 1.2.2. Mechanism testing model In order to study the indirect effect of the digital economy driving the development of common prosperity, this paper selects the total factor productivity of each province as a moderating variable to be tested, and constructs the moderating effect model as follows: $${\text{l}\text{n}\text{i}\text{n}\text{d}\text{e}\text{x}}_{\text{i},\text{t}}={{\gamma }}_{0}+{{\gamma }}_{1}{\text{l}\text{n}\text{d}\text{i}\text{g}\text{i}\text{t}\text{a}\text{l}}_{\text{i},\text{t}}+{{\gamma }}_{2}{\text{l}\text{n}\text{t}\text{f}\text{p}}_{\text{i},\text{t}}+{{\gamma }}_{3}{\text{l}\text{n}\text{d}\text{i}\text{g}\text{i}\text{t}\text{a}\text{l}}_{\text{i},\text{t}}\ast {\text{l}\text{n}\text{t}\text{f}\text{p}}_{\text{i},\text{t}}+{{\phi }}_{\text{z}}{\text{Z}}_{\text{i},\text{t}}+{{\mu }}_{\text{i}}+{{\delta }}_{\text{t}}+{{\epsilon }}_{\text{i},\text{t}}$$ 4 Based on the baseline regression equation for the direct impact of the digital economy driving common prosperity level, total factor productivity (TFP) and the cross-multiplier term between the digital economy and TFP are introduced. Where. \({lntfp}_{i,t}\) represents the total factor productivity of province i in year t; \({lndigital}_{i,t}\ast {lntfp}_{i,t}\) represents the cross-multiplication term between digital economy and total factor productivity. By observing \({\gamma }\) , the \({\beta }\) the magnitude as well as the significance of the other parameters to analyze the degree of influence of total factor productivity on the promotion of common prosperity development. In order to further study the nonlinear dynamic spillover effects of industrial structure upgrading as well as the degree of innovation within a province on the development of digital economy driving the development of common prosperity, the following threshold effect model is constructed: $${lnindex}_{i,t}={\phi }_{0}+{\phi }_{1}{lndigital}_{i,t}\times I({Tℎr}_{i,t}\le \vartheta )+{\phi }_{2}{lndigital}_{i,t}\times I({Tℎr}_{i,t}>\vartheta )+{\phi }_{Z}{Z}_{i,t}+{\mu }_{i}+{\epsilon }_{i,t}$$ 5 In the above equation, the \({Tℎr}_{i,t}\) represents the threshold variable of industrial structure upgrading of province i in year t. The threshold effect model is a single-threshold scenario; \(\text{I}(\bullet )\) is the indicator function, which takes the value of 1 if the condition in parentheses is satisfied, otherwise it takes the value of 0. This paper uses the threshold effect model in the single-threshold case. 2. Variable measurement and description 2.1. Measurement of explanatory variables This paper refers to the system proposed by Han Liangliang,Peng Yi,Meng Qingna (2023) to measure the degree of development of common prosperity, and takes the three perspectives of development, sharing and sustainability as the first-level indicators, utilizes the entropy weight method to construct the indicators, and the composition of indicators at all levels is shown in Table 1 . Table 1 Indicators at all levels of the common prosperity Development Index under the entropy weighting approach Level 1 indicators Secondary indicators Tertiary indicators developmental affluence Disposable income per capita (yuan) Consumption expenditure per inhabitant (yuan) Engel's coefficient commonality Gini coefficient (a measure of statistical dispersion) Income multiplier for urban and rural residents Urbanization rate (%) shareability educational attainment Public library holdings per capita (books) Average years of education Level of medical modernization Number of practicing (assistant) physicians per 10,000 persons (persons) Number of beds in medical institutions per 10,000 population infrastructure Public transportation vehicles per 10,000 population (standard units) Public toilets per 10,000 population (seats) degree of informatization Internet broadband access per 100 population Cell phone subscribers per 100 population Level of social security Social security expenditure as a share of GDP (%) sustainability Level of science, technology and innovation RD input intensity (%) Patents granted per 10,000 persons (pieces) Ecological health Forest cover (%) Carbon intensity (million tons/billion dollars) Level of economic development GDP per capita ( $ /person) Labor productivity of society as a whole (yuan) 2.2. Measurement of explanatory variables For the core explanatory variable - digital economy development index, this paper refers to the research method of Yang Q, Ma H and Wang Y (2022) to construct the digital economy index system, selects the four dimensions of digital infrastructure, digital industrialization, industrial digitization and digital innovation capacity as the first level indicators, and uses the entropy weight method to measure the level of digital economy development. 2.3. Mechanism variables Against total factor productivity ( \({lntfp}_{i,t}\) ). This paper refers to the accounting method of Chen X, Chen Y, Huang W (2023), using real GDP as the output indicator, the level of capital stock under the perpetual inventory method and the number of social employees as the input indicator, and adopting the DEA algorithm to calculate the total factor productivity level of each province in the country. Targeting the degree of education in digital technology ( \({lnde}_{i,t}\) ). This paper quantifies it in four dimensions, namely human capital, educational input, years of education, and educational literacy. For the human capital dimension, it is quantified by the ratio of the number of students enrolled in general higher education to the number of household members; for education input, it is quantified by the ratio of research expenditure to local GDP; for years of education, it is quantified by the average number of years of education and years of labor in the provinces (standardized at 40 years); and for education literacy, it is quantified by the regional innovation capacity of each province in China. 2.4. Control variables This process of digital economy-driven common prosperity development will be affected by many aspects such as industrial structure, urbanization level, human capital level and so on. Therefore, this paper selects industrial structure, urbanization level, human capital level, foreign direct investment, degree of opening up to the outside world, level of financial development, degree of government intervention, research and development intensity, and innovation level as control variables. (1) Industrial structure. This paper chooses the ratio of the output value of the tertiary industry to the output value of the secondary industry to quantify the industrial structure. (2) Level of urbanization. This paper chooses the ratio of urban population to quantify the level of urbanization. (3) Level of economic development. In this paper, the logarithm of the GDP level of the provinces in the past years is chosen to quantify the level of economic development. (4) Foreign direct investment. This paper quantifies foreign direct investment in terms of the ratio of foreign direct investment to gross regional product. (5) Social consumption level. This paper quantifies total retail sales of consumer goods as a percentage of regional GDP. (6) Level of financial development. This paper quantifies the sum of regional savings and loans as a percentage of regional GDP. (7) Degree of government intervention. This paper quantifies this as the ratio of local government general public budget expenditures to regional GDP. (8) R&D intensity. This paper quantifies internal expenditure on RD as a percentage of GDP. (9) Level of innovation. This paper quantifies this in terms of the number of domestic patent applications received for inventions. 2.5. Spatial weighting matrix In this paper, we use the spatial economic geography nested matrix (latitude, longitude and GDP per capita), as the spatial weighting matrix for the spatial Durbin model \({W}_{ij}\) . It is constructed as follows: $$\text{W}=\left(\begin{array}{cccc}0& \frac{1}{{\text{d}}_{12}}\times \frac{1}{|{\text{Y}}_{1}-{\text{Y}}_{2}|}& \cdots & \frac{1}{{\text{d}}_{1\text{n}}}\times \frac{1}{|{\text{Y}}_{1}-{\text{Y}}_{\text{n}}|}\\ \frac{1}{{\text{d}}_{21}}\times \frac{1}{|{\text{Y}}_{2}-{\text{Y}}_{1}|}& 0& \cdots & \frac{1}{{\text{d}}_{2\text{n}}}\times \frac{1}{|{\text{Y}}_{2}-{\text{Y}}_{\text{n}}|}\\ ⋮& ⋮& ⋮& ⋮\\ \frac{1}{{\text{d}}_{\text{n}1}}\times \frac{1}{|{\text{Y}}_{\text{n}}-{\text{Y}}_{1}|}& \frac{1}{{\text{d}}_{\text{n}2}}\times \frac{1}{|{\text{Y}}_{\text{n}}-{\text{Y}}_{2}|}& \cdots & 0\end{array}\right)$$ where. \({d}_{ij}\) represents the geographic distance between two regions i and j; \({Y}_{i}\) and \({Y}_{j}\) represent the level of economic development of each region, then \(|{\text{Y}}_{\text{i}}-{\text{Y}}_{\text{j}}|\) represents the economic distance between the two. In this paper, the level of GDP per capita is used to measure the economic development level of each province. The data for the empirical study in this paper come from the China Statistical Yearbook and the White Paper on the Development of China's Digital Economy, and some of the missing values are filled in by linear interpolation. To ensure the smoothness of each variable, the above data are logarithmized. The variables involved in this paper and the descriptive statistical analysis of each variable are shown in Table 2 . The common prosperity development index has a mean value of 0.3005, a minimum value of 0.074 and a maximum value of 0.988; the digital economy index has a mean value of 0.127, a minimum value of 0.017 and a maximum value of 0.590. The specific values of the other control variables are also given. Table 2 Variable category variable name Number of observations average value (statistics) standard deviation minimum value maximum values explanatory variable common prosperity Development Index \({lnindex}_{i,t}\) 330 0.3005 0.216 0.074 0.988 Core explanatory variables Digital Economy Index \({lndigital}_{i,t}\) 330 0.127 0.100 0.017 0.590 Mechanism variables Total factor productivity \({lntfp}_{i,t}\) 330 0.606 0.273 0.096 1.477 control variable industrial structure \({lnstr}_{i,t}\) 330 1.304 0.708 0.549 5.297 urbanization level (of a city or town) \({lncivil}_{i,t}\) 330 0.600 0.128 0.229 0.896 Level of economic development \({lngdp}_{i,t}\) 330 9.907 0.887 7.332 11.768 overseas foreign direct investment (OFDI) \({lnfi}_{i,t}\) 330 0.018 0.014 −0.006 0.080 social consumption level \({lncons}_{i,t}\) 330 0.388 0.067 0.219 0.538 Level of financial development \({lnfinan}_{i,t}\) 330 3.429 1.209 1.568 8.131 Level of government intervention \({lngovern}_{i,t}\) 330 0.271 0.190 0.094 1.334 R&D intensity \({lnresearcℎ}_{i,t}\) 330 0.018 0.012 0.002 0.066 Innovation level \({lninno}_{i,t}\) 330 9.693 1.538 4.394 14.311 Descriptive statistical analysis of variables 3. Empirical analysis of digital economy-driven common prosperity development 3.1. Baseline regression analysis The results of the benchmark regression are shown in Table 3 . The results show that the regression coefficient of digital economy is positive at 1% significance level, which indicates that the development of digital economy in China can drive the development of common prosperity. On average, for every percentage increase in the digital economy development index, the common prosperity development index rises by 0.168 units. As for the control variables, industrial structure, urbanization level, economic development level, degree of opening up to the outside world, social consumption level, and R&D intensity have a positive effect on the development of common prosperity, which are significant at the 1% and 10% levels, respectively. The regression results show that the development of digital economy has a positive contribution to the realization of common prosperity, and this effect is influenced by the economic structure and development characteristics. Table 3 Benchmark regression results variant \({lnindex}_{i,t}\) (1) \({lnindex}_{i,t}\) (2) The Digital Economy Index ( \({lndigital}_{i,t}\) ) 0.168*** 0.049** Industrial structure ( \({lnstr}_{i,t}\) ) 0.010* Level of urbanization ( \({lncivil}_{i,t}\) ) −0.114* Level of economic development ( \({lngdp}_{i,t}\) ) 0.095*** Foreign direct investment ( \({lnfi}_{i,t}\) ) 0.200* Social consumption level ( \({lncons}_{i,t}\) ) 0.032 Level of financial development ( \({lnfinan}_{i,t}\) ) 0.005 Level of government intervention ( \({lngovern}_{i,t}\) ) −0.132*** R&D intensity ( \({lnresearcℎ}_{i,t}\) ) 1.252* Level of innovation ( \({lninno}_{i,t}\) ) −0.006* area fixed effect be be time fixed effect be be Number of provinces 30 30 \({R}^{2}\) 0.993 0.997 Note: ***, **, * indicate significant at the 1%, 5% and 10% levels, respectively. 3.2. Moderating effects test Total Factor Productivity (TFP) is a key factor in the digital economy's effect on the common prosperity, this paper chooses the moderating effect model to analyze its transmission mechanism, and the regression results are shown in Table 4 .The results show that the regression coefficients of the Digital Economy Development Index and the Total Factor Productivity are positive, both of them have a positive effect on the common prosperity Development Index, that is, when they increase by one unit respectively, the common prosperity Development Index will increase by a certain amount accordingly. amount, indicating that the increase of both the digital economy and total factor productivity is conducive to the promotion of the wealth and happiness of all the people; the negative regression coefficient of the cross-multiplier term indicates that total factor productivity plays a negative moderating role between the digital economy development index and the common prosperity development index, i.e., it will weaken the positive impact of the digital economy development index on the common prosperity development index. The moderating levels of the moderating variables are shown in Fig. 1 . Specifically, when total factor productivity increases by one unit, the impact coefficient of the digital economy development index on the common prosperity development index decreases by 0.19 units. In other words, the higher the total factor productivity, the weaker the positive effect of the digital economy development index on the common prosperity development index. This may be due to the fact that an increase in total factor productivity does not necessarily benefit all people in a balanced manner, but may lead to faster growth in income and welfare for some people or regions than for others, thus exacerbating inequality and inequity and undermining the realization of common prosperity. This implies that the goal of common prosperity level cannot be fully realized by relying on the development of the digital economy alone, and that the distributional effects of total factor productivity, as well as other factors affecting common prosperity level, such as education, health care and social security, need to be taken into account. Table 4 Results of moderating effects variant \({lnindex}_{i,t}\) \({lnindex}_{i,t}\) The Digital Economy Index ( \({lndigital}_{i,t}\) ) 0.256*** 0.265*** Total factor productivity ( \({lntfp}_{i,t}\) ) 0.005* 0.010* intermodal term (math.) −0.134* −0.190* control variable clogged be area fixed effect be be time fixed effect be be Number of provinces 30 30 \({R}^{2}\) 0.584 0.905 Note: ***, * indicate significant at 1% and 10% level respectively. Diagram of moderating effect 3.3. Spatial spillover effects 3.3.1 Spatial autocorrelation test In the regression analysis using the spatial Durbin model, it is necessary to calculate the Moran index to test the spatial correlation of the driving role of the digital economy on the common prosperity, and the software used is stata17.0.The formula for the calculation of the Moran index is as follows. $$\text{I}=\frac{\sum _{\text{i}=1}^{\text{n}}\sum _{\text{j}=1}^{\text{n}}{\text{W}}_{\text{i}\text{j}}({\text{Y}}_{\text{i}}-\overline{\text{Y}})({\text{Y}}_{\text{j}}-\overline{\text{Y}})}{{\text{S}}^{2}\sum _{\text{i}=1}^{\text{n}}\sum _{\text{j}=1}^{\text{n}}{\text{W}}_{\text{i}\text{j}}}$$ In the above equation, the \({S}^{2}=\frac{1}{n}\sum _{i=1}^{n}{({Y}_{i}-\overline{Y})}^{2}\) . \(\overline{Y}=\frac{1}{n}\sum _{i=1}^{n}{Y}_{i}\) . where n is the 30 provinces in China except Tibet, and \({W}_{ij}\) is the spatial weight matrix, and \({Y}_{i}\) represents the province common prosperity development index or the province's digital economy development index, and \(\overline{Y}\) represents the mean value of the province common prosperity development index or the province's digital economy development index. The value range of Moran index is [-1,1]. The measurement results are shown in Table 5 . Table 5 Results of spatial autocorrelation test particular year common prosperity Development Index Digital Economy Index Moran Index Z-statistic P-value Moran Index Z-statistic P-value 2012 0.368 5.003 0.000 0.265 3.708 0.000 2013 0.375 5.079 0.000 0.354 4.573 0.000 2014 0.364 4.961 0.000 0.384 4.900 0.000 2015 0.362 4.949 0.000 0.346 4.441 0.000 2016 0.359 4.910 0.000 0.342 4.395 0.000 2017 0.357 4.898 0.000 0.355 4.568 0.000 2018 0.353 4.882 0.000 0.307 4.035 0.000 2019 0.351 4.859 0.000 0.309 4.083 0.000 2020 0.352 4.833 0.000 0.312 4.134 0.000 2021 0.373 5.071 0.000 0.310 4.123 0.000 2022 0.387 5.153 0.000 0.220 3.076 0.000 The above table shows that the overall development trend of China's Moran Index from 2012 to 2022 is relatively stable, and all of them are significantly positive at the 1% level, which indicates that there is a spatial correlation between common prosperity and digital economy, and that China's provinces will be affected by the common prosperity development index of their neighboring provinces. Spatial positive correlation, that is, high-income areas (or low-income areas) tend to be adjacent to the surrounding high-income areas (or low-income areas), the formation of "high-high" or "low-low" agglomeration effect. The distribution of the Moran Index for 2012, 2016, 2019, and 2022 is shown in Fig. 2 , and there is a certain clustering effect in the data, which is basically distributed in quadrants one and three, indicating that it is suitable for using spatial measurement models for analysis. Distribution of Moran's index in 2012, 2016, 2019 and 2022 3.3.2. Spatial Durbin model results First of all, this paper carried out a smoothness test for each variable, and the method used was the individual double fixed-effects unit root test with a lag operator of 6. The results showed that the variables were smooth and good, avoiding the pseudo-regression problem. Before analyzing the spatial spillover effect, this paper conducted LM test, Hausmann test, SDM fixed effect test, LR test, and the test results are shown in Table 6 , which determined the spatial Durbin model with double fixed effects as the best estimation model. Table 6 Results of spatial panel model tests Spatial panel model testing Value P-Value LM test Moran's I 7.772*** 0.000 LM-lag 56.649*** 0.000 Robust-LM-lag 0.325 0.568 LM-error 75.836*** 0.000 Robust-LM-error 19.512*** 0.000 LR test LR-SDM/SEM 84.68*** 0.000 LR-SDM/SAR 54.57*** 0.000 Wald test Wald-SDM/SEM 80.03*** 0.000 Wald-SDM/SAR 76.36*** 0.000 Spatio-temporal/time fixed effects test LR-both/ind 23.61* 0.051 LR-both/time 779.13*** 0.000 Note: ***, **, * indicate significant at the 1%, 5% and 10% levels, respectively. In this paper, the estimation method of partial differentiation is used to carry out the analysis of spatial effects, and the estimation results are shown in Table 7 . The results show that, whether it is the regression results under the inverse distance matrix or the regression results under the economic matrix obtained based on the spatial economic geographic nested matrix (latitude, longitude and GDP per capita), the direct effect of the digital economy to drive the development of the common prosperity is significantly positive at the level of 5% and 1%, respectively, which indicates that the digital economy has a positive spatial spillover effect on the development of the common prosperity of China's provinces. Table 7 SDM regression results explanatory variable inverse distance matrix nested matrix (1) (2) The Digital Economy Index ( \({\text{l}\text{n}\text{d}\text{i}\text{g}\text{i}\text{t}\text{a}\text{l}}_{\text{i},\text{t}}\) ) 0.095** 0.180*** \(\text{W}\cdot {\text{l}\text{n}\text{d}\text{i}\text{g}\text{i}\text{t}\text{a}\text{l}}_{\text{i},\text{t}}\) 0.132* 0.009** control variable be be time fixed effect be be area fixed effect be be direct effect 0.126** 0.182*** indirect effect 0.495* 0.049* aggregate effect 0.621** 0.095* Number of provinces 30 30 Note: ***, **, * indicate significant at the 1%, 5% and 10% levels, respectively. 3.4. Analysis of threshold effects In this paper, the degree of digital technology education is selected as a threshold variable, and the threshold effect model is used to analyze the impact of China's digital economy driving the development of common prosperity, and the estimation of the three threshold models and the test results of the threshold effect are obtained through bootstrap method by repeating the sampling for 300 times, as shown in the table below. Table 8 Significance test of effect with digital technology education level as a threshold variable threshold effect model F-value P-value BS Index threshold value Threshold estimate 1% 5% 10% single threshold 45.09 0.000 300 37.390 26.003 21.754 0.409 double threshold 45.01 0.000 300 31.268 24.542 21.567 0.409 - - - 34.974 25.031 20.858 0.550 triple threshold 43.16 0.000 300 48.727 35.797 31.813 0.182 In this paper, the likelihood ratio test LR is used to analyze the truthfulness of the threshold estimates, and the test results are shown in the figure. The results show that when LR is equal to 0, the single threshold estimates of digital technology education level are 0.409 and are all below the dotted line in the figure (LR = 7.35), which indicates that the threshold estimates are consistent with the true value. It can be divided into two intervals based on the level of digital technology education: low digital technology education ( \({lndc}_{i,t}\le 0.409\) ) and high digital technology education level ( \({lndc}_{i,t}>0.409\) ). Threshold effect results graph The digital economy can improve productivity and social welfare through its own innovative activities and synergies, while also realizing common prosperity level and social equity through inclusive services and the distribution of digital dividends. Among them, the level of digital technology education is a key factor in the development of the digital economy, which can foster digital competence, innovation and adaptability, thus driving the growth and transformation of the digital economy. The estimated results of the threshold effect of the level of digital technology education on the development of a digital economy driving common prosperity are shown in the table below. Table 10 Threshold effect regression results variant Threshold variables Level of education in digital technology (Threshold q = 0.409) Digital Economy Index \({lndigital}_{i,t}\bullet I(Tℎ\le q)\) 0.010* Digital Economy Index \({lndigital}_{i,t}\bullet I(Tℎ>q)\) 0.102** control variable be Number of periods 11 \({R}^{2}\) 0.582 Note: **, * indicate significant at the 5% and 10% levels, respectively. When digital technology education is less than the threshold value of 0.409, the estimated coefficient of the digital economy driving the development of common prosperity is 0.010 at the 10% significance level, indicating that for every 1% increase in the digital economy, the level of common prosperity development will increase by 0.010%; when digital technology education is higher than the threshold value of 0.409, the estimated coefficient of the digital economy driving the development of common prosperity is 0.102 at the 5% significance level is 0.102, indicating that for every 1% increase in the digital economy, the level of common prosperity development will increase by 0.102%. This demonstrates the existence of a threshold variable of digital technology educational attainment, i.e., digital technology educational attainment has different impacts on the driving effect of the digital economy at different levels. When the level of digital technology education is lower than the threshold, the digital economy has a weaker role in promoting common prosperity; when the level of digital technology education is higher than the threshold, the digital economy has a significantly stronger role in promoting common prosperity development, which indicates that increasing the level of digital technology education is an important way to achieve high-quality development of the digital economy and common prosperity. 4. Endogeneity test There may be an endogeneity problem between the digital economy index and the common prosperity development index, that is, there is not only a causal relationship between the two, but also a feedback relationship or interference from confounding factors. For example, the development of the digital economy may raise the income level of the population and the level of social welfare, thus raising the common prosperity Development Index; however, at the same time, the realization of common prosperity may also provide broader market space and stronger social support for the development of the digital economy, thus raising the Digital Economy Index. In addition, the relationship between the Digital Economy Index and the common prosperity Development Index may be affected by other variables, such as government policies, human capital, innovation capacity, institutional environment, and so on. In order to verify the reasonableness of the model setting, this paper conducts endogeneity test of the model from the perspectives of omitted explanatory variables test and instrumental variables respectively. 4.1. Omitted explanatory variables test The omission of important explanatory variables in the model setting process may cause bias in the regression results. In this paper, two methods, Ramsey RESET test and Selection-ratio test, are used respectively to test whether there is any omission of variables in the model setting. The results show that the Ramsey RESET test has a p-value of 0.227, which does not reject the original hypothesis - the regression model has no omitted variables or non-linear relationships, i.e., the model is correctly set up; the Selection-ratio test of \({\delta }\) is greater than 1 regardless of the inclusion of control variables, proving that the variables in the model are reasonably controlled and the omitted variables are not enough to change the current results. 4.2. Instrumental variables testing In order to more robustly assess the driving effect of China's digital economy on the development of common prosperity, this paper uses the frequency of words related to the digital economy over the years as an instrumental variable, and the two-stage least squares (2SLS) method is used for the test. Firstly Eq. ( 1 ) performs the first-stage regression, the \(\text{p}\text{o}\text{l}\text{i}\text{c}\text{y}\) represents the digital economy policy word frequency of province i in year t, and vector Z is a series of control variables; Eq. ( 2 ) is the second-stage regression, in which \({\widehat{lndigital}}_{i,t}\) is the fitted value of the digital economy index variables in the first stage. The estimation results are shown in Table 11 . $${lndigital}_{i,t}={\gamma }_{0}+{\gamma }_{1}{policy}_{i,t}+{\gamma }_{2}{Z}_{i,t}+{\mu }_{i}+{\phi }_{t}+{\epsilon }_{i,t}$$ $${index}_{i,t}={\gamma }_{0}+{\gamma }_{1}{\widehat{lndigital}}_{i,t}+{\gamma }_{2}{Z}_{i,t}+{\mu }_{i}+{\phi }_{t}+{\epsilon }_{i,t}$$ Table 11 Instrumental variable test results explanatory variable (1) (2) Phase II Phase I explanatory variable Index lndigital \({lndigital}_{i,t}\) 0.474* (0.286) \({policy}_{i,t}\) 0.001** (0.000) control variable containment containment Province fixed effects containment containment Year fixed effects containment containment Phase I F-value 76.77 sample size 330 330 Note: ** and * indicate significant at 5% and 10% level respectively. Table 11 reports the estimation results. In the first stage regression in Column (2), the regression result of the instrumental variable POLICY on the level of development of the digital economy is significantly positive, indicating that the enactment of policies related to the digital economy has a significant facilitating effect on the digital economy. In the second stage regression of Column (1), the promotion effect of digital economy on common prosperity is still significantly positive after adopting the instrumental variable, which is consistent with the results of the benchmark regression. In addition, the F-value of the first stage regression is 76.77, which is much larger than 10, which indicates that there is no weak instrumental variable problem, and the regression results are valid, i.e., there is no reverse causality problem between the digital economy index and the common prosperity, and the model is reasonable. 5. Robustness tests In order to further verify the stability of the research results, this paper further performs the following tests. 5.1. Shrink-tailed regression. In order to avoid the impact of data outliers on the regression results, this paper shrinks the core explanatory variables at the 1% level, and the regression results after shrinking are shown in column (1) of Table 12 . The empirical results show that the regression coefficient of the digital economy index is still significantly positive and close to the benchmark regression coefficient, confirming the robustness of the empirical results of this paper. 5.2. Replacement of variables. This paper uses the digital economy index synthesized by principal component analysis to replace the core explanatory variables, and the regression results after replacement are shown in column (2) of Table 12 , and the regression coefficient of digital economy is significantly positive, which verifies the reliability of the research results. 5.3. Moving average processing. In order to avoid the impact of panel data fluctuations on the analysis results, this paper adopts the moving average to smooth the data before conducting regression analysis. The results in column (3) of Table 12 show that the regression coefficient of the smoothed digital economy is significantly positive, indicating that the regression results are robust. Table 12 Robustness test results variant (1) have one's tail reduced (2) Substitution of variables (3) moving average \({lndigital}_{i,t}\) 0.092*** (0.029) 0.094*** (0.030) 0.063** control variable containment containment containment Province fixed effects containment containment containment Year fixed effects containment containment containment sample size 330 330 330 \({R}^{2}\) 0.995 0.995 0.995 Note: *** and ** indicate significant at 1% and 5% level respectively. 6. Conclusion With digital economy as the core explanatory variable, common prosperity development level as the explanatory variable, and total factor productivity as the moderating variable, this paper adopts the spatial Durbin model, and utilizes the panel data of 30 provincial-level administrative regions in China from 2012 to 2022 to empirically analyze, from the three aspects of the direct effect, the spatial spillover effect, and the marginal incremental effect (the threshold effect) of the digital economy in driving the development of common prosperity, the mechanism and path of the digital economy's impact on common prosperity. The study finds: The digital economy has a significant positive direct effect and spatial spillover effect on the development of common prosperity, and there is a marginal incremental effect, i.e., the higher the level of the digital economy, the greater the contribution to the development of common prosperity. This shows that the digital economy is not only a new driving force for economic growth, but also a new way to promote the common prosperity, through improving efficiency and quality, to promote economic and social development and improve people's lives; total factor productivity plays a positive moderating role in the relationship between the digital economy and the development of the common prosperity, i.e., the higher the total factor productivity, the stronger the role of the digital economy in promoting the development of the common prosperity. This suggests that total factor productivity is a key factor in the role of the digital economy in the common good, reflecting the innovative capacity and competitiveness of the digital economy and an important indicator of the quality of the digital economy. The level of digital technology education is an important threshold variable affecting the development of the digital economy on common prosperity, and when the level of digital technology education is higher than a certain level, the promotion of the digital economy on the development of common prosperity is significantly enhanced, which indicates that improving the level of digital technology education is an important way to achieve high-quality development of the digital economy and common prosperity, and is also a necessary condition for narrowing the digital divide and promoting digital inclusion. Based on the findings of this paper, in order to better utilize the role of digital economy in promoting common prosperity, the top-level design of the digital economy should be strengthened, the development strategy of the digital economy should be improved, laws, regulations and standards related to the digital economy should be formulated, the security and stability of the digital economy should be safeguarded, and the in-depth fusion of the digital economy with the real economy should be promoted, so as to facilitate the transformation, upgrading and innovative development of the digital economy. Declarations Declaration of Competing Interest There’s no conflict of interest. Funding There’s no funding. Author Contribution L.L. and X.G. conceived the research idea and designed the empirical model. L.L. collected and processed the data, and performed the spatial econometric analysis. X.G. wrote the introduction, literature review, and conclusion sections. Both authors contributed to the discussion and interpretation of the results, and revised the manuscript. All authors read and approved the final version of the manuscript. Data availability Data will be made available on request. References Chen X, Chen Y, Huang W et al (2023) A new Malmquist-type green total factor productivity measure: An application to China. Energy Econ 117:106408 Fu L, Han X, Lv C et al (2023) Measurement and spatio-temporal heterogeneity analysis of the coupling coordinated development among the digital economy, technological innovation and ecological environment. Ecol Ind 151:110325 Han L, Peng Y, Meng Q (2023) Digital financial inclusion, entrepreneurial activity and common prosperity - an empirical study based on inter-provincial panel data in China. Soft Sci 37(3):18–24 Hou L, Tian C, Xiang R et al (2023) Research on the Impact Mechanism and Spatial Spillover Effect of Digital Economy on Rural Revitalization: An Empirical Study Based on China’s Provinces. Sustainability 15(15):11607 Jiang Q, Li Y, Si H (2022) Digital Economy Development and the Urban–Rural Income Gap: Intensifying or Reducing, Land, 11(11), 1980 Li Y, Ke JS (2021) Three-level digital divide: Income growth and income distribution effects of the rural digital economy. Agric Technol Econ 8:119–132 Liu J, Man J, Cui B et al (2023) Coupling and Coordination between Digital Economy and Urban–Rural Integration in China. Sustainability 15(9):7299 Mirdamad MG (2020) Innovative Tools for Investment Management in the Digital Economy: A Guide for Post-Socialist Countries. Mark Manage Innovations, (4), 1–12 Shen W, Xia W, Li S (2022) Dynamic coupling trajectory and spatial-temporal characteristics of high-quality economic development and the digital economy. Sustainability 14(8):4543 Su J, Su K, Wang S (2021) Does the digital economy promote industrial structural upgrading?—A test of mediating effects based on heterogeneous technological innovation. Sustainability 13(18):10105 Tao Z, Zhang Z, Shangkun L (2022) Digital economy, entrepreneurship, and high-quality economic development: Empirical evidence from urban China. Front Econ China 17(3):393–414 Tu X, Yan J, Zheng J (2023) Does digital economy strengthen the income distribution effect of fiscal expenditure? Evidence from China. PLoS ONE, 18(8), e0290041 Yang Q, Ma H, Wang Y et al (2022) Research on the influence mechanism of the digital economy on regional sustainable development. Procedia Comput Sci 202:178–183 Zhao T, Zhang Z, Liang SK (2020) Digital economy, entrepreneurial activity and high-quality development: Empirical evidence from Chinese cities. Manage world 36(10):65–76 Zhang Z, Tao Z, Shangkun L (2020) Digital economy, entrepreneurship, and high-quality economic development: Empirical evidence from urban China. Front Econ China 17(3):393–414 Additional Declarations No competing interests reported. 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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-3923573","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":271106441,"identity":"08ae686b-1597-4b8a-82bd-657a1fce67e4","order_by":0,"name":"Linhan Luo","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA/UlEQVRIie3RsUoDMQDG8S8E7pZY1xSRe4WEDl0UXyXhwOlmcSqFgzh2tVjfIaOdTMlwS3FWdOghtEuFruLiXesk3nGjQ/4kGUJ+JBAgFPqH9QDiFBwQj3+24mqyFhJV80CYIwdEu5D94Kor4alz5cNbMuxvNu8MIz2hIKsPg2TYSC6V08u1nN9lMmeI9DQHlfcGcj5uIplw2nhiXzNSEaatR3RyZKCEaycX9qUoK8L1o0f81YVo+4z6YUJbioi2ErZWNUntMpPTmVCDW0/y/uyJS9tAjuN0UX4af26LYrXbXo9OJzf5Yre9OkuabvmVqJf9//BO50OhUCj0d98GjlwL/FQb+wAAAABJRU5ErkJggg==","orcid":"","institution":"Zhongnan University of Economics and Law","correspondingAuthor":true,"prefix":"","firstName":"Linhan","middleName":"","lastName":"Luo","suffix":""},{"id":271106442,"identity":"bbca97b2-aa6e-4044-a138-6ddc506fae54","order_by":1,"name":"Guangqin Xiong","email":"","orcid":"","institution":"Zhongnan University of Economics and Law","correspondingAuthor":false,"prefix":"","firstName":"Guangqin","middleName":"","lastName":"Xiong","suffix":""}],"badges":[],"createdAt":"2024-02-03 10:29:19","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3923573/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3923573/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":50792007,"identity":"9c0955f8-e371-4719-89ce-5f1de90bbc89","added_by":"auto","created_at":"2024-02-07 10:52:57","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":10439,"visible":true,"origin":"","legend":"\u003cp\u003eDiagram of moderating effect\u003c/p\u003e","description":"","filename":"F1.png","url":"https://assets-eu.researchsquare.com/files/rs-3923573/v1/63dea60e3d159f1c6959af10.png"},{"id":50792008,"identity":"f09d5555-9748-43ff-8f3b-233d06b10cdb","added_by":"auto","created_at":"2024-02-07 10:52:57","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":85121,"visible":true,"origin":"","legend":"\u003cp\u003eDistribution of Moran's index in 2012, 2016, 2019 and 2022\u003c/p\u003e","description":"","filename":"F2.png","url":"https://assets-eu.researchsquare.com/files/rs-3923573/v1/f55d6e71bfe5c93cc05fb17a.png"},{"id":50792009,"identity":"9ed4ba8d-c46b-4496-a335-1e8297f4823d","added_by":"auto","created_at":"2024-02-07 10:52:57","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":22033,"visible":true,"origin":"","legend":"\u003cp\u003eThreshold effect results graph\u003c/p\u003e","description":"","filename":"F3.png","url":"https://assets-eu.researchsquare.com/files/rs-3923573/v1/b5f0e3bc5fc9e4622fb4492f.png"},{"id":65951338,"identity":"ed62257c-55a7-4b86-938c-4d55f4378d49","added_by":"auto","created_at":"2024-10-04 20:16:38","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1215378,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3923573/v1/a5c2dc2e-9fe1-4df6-9bca-7b8e2130bafa.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"How does digital economy affect the development of common prosperity level?","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003ecommon prosperity is an essential requirement of socialism, an important feature of socialism with Chinese characteristics, and an inevitable requirement for realizing the great rejuvenation of the Chinese nation. At the 10th meeting of the Central Financial and Economic Commission, General Secretary Xi Jinping emphasized the importance of adhering to the people-centered development ideology, promoting common prosperity in high-quality development, accelerating the formation of a policy framework to promote common prosperity, and focusing on solving outstanding problems such as unreasonable income distribution and the excessive gap between the rich and the poor, so as to enable all people to share in the fruits of development and create a better life together. To realize common prosperity, it is necessary to ensure both the growth of material wealth and the reasonable distribution of wealth, as well as the basic living standards of all people and their comprehensive development. Therefore, the connotation of common prosperity includes not only fairness in income distribution but also the quality of economic growth, not only the sharing of material wealth but also spiritual culture, and not only the sharing of urban and rural residents but also the sharing between regions.\u003c/p\u003e \u003cp\u003eThe digital economy refers to a new economic form based on digital technology, with data as the core resource, a network platform as the carrier, driven by innovation, aiming at improving efficiency and quality, and oriented towards promoting economic and social development and improving people's lives. Digital economy is an important outcome of the new round of scientific and technological revolution and industrial change, a new engine for economic and social development, and a new impetus for building a new development pattern. Digital economy is not only a new driving force for economic growth, but also a new way to promote common prosperity. Based on the spillover effect brought about by digital diffusion and network externalities, the digital economy is able to break the geographical and time constraints, form synergistic effects between digital platforms and business ecological vendors, between industrial chains and supply chains, and between data elements and other production factors, improve total factor productivity, and promote the quality and balance of economic growth. The digital economy, based on the innovative and sharing nature of digital technology, can lower the threshold of innovation and participation, expand the scope of innovation and participation, increase the benefits of innovation and participation, and promote the fairness and inclusiveness of income distribution. The digital economy, based on the universality and convenience of digital services, can raise the level of public service provision, expand the coverage of public services, enhance the satisfaction of public services, and promote the sharing and diversity of spiritual culture. Based on the transparency and synergy of digital governance, the digital economy can optimize the efficiency and effectiveness of government governance, enhance the credibility and fairness of government governance, improve the participation and interaction of government governance, and promote the sharing and oneness of urban and rural residents.\u003c/p\u003e \u003cp\u003eTherefore, there is an intrinsic connection and interaction between the digital economy and common prosperity, and the development of the digital economy is both an important support for common prosperity and an important path to common prosperity. Exploring the mechanism and path of the digital economy's impact on common prosperity is of great theoretical and policy significance for deeply understanding the intrinsic connection between the digital economy and common prosperity, improving the development strategy of the digital economy, and promoting high-quality development and common prosperity. This paper takes digital economy as the core explanatory variable, common prosperity development level as the explanatory variable, total factor productivity as the moderating variable, adopts the spatial Durbin model, and utilizes the panel data of China's 31 provincial-level administrative regions from 2012\u0026ndash;2022 to empirically analyze, from the three aspects of the direct effect, the spatial spillover effect, and the marginal incremental effect (threshold effect) of the digital economy in driving the development of the common prosperity The mechanism and path of the digital economy's impact on common prosperity.\u003c/p\u003e \u003cp\u003eThe purpose of this paper is to explore the mechanism of the digital economy's impact on common prosperity and the moderating role of total factor productivity in it. Total factor productivity is an important indicator of the quality and efficiency of economic growth, reflecting the comprehensive performance of an economy in terms of technological progress, innovation capacity, resource allocation and institutional arrangements. We believe that the digital economy can not only directly enhance the level of common prosperity development, but also indirectly enhance the sustainability of common prosperity by promoting the increase of total factor productivity. At the same time, we also consider the spatial interaction between different regions, i.e., the development level of digital economy and common prosperity in one region will be affected by other regions, forming spatial spillover effects. In order to empirically analyze this issue, we adopt the Spatial Durbin Model (SDM), which is used to analyze the spatial spillover effects of the dependent and independent variables in a region, as well as the spatial interactions between the independent variables.\u003c/p\u003e \u003cp\u003eThe main contributions of this paper are the following:\u003c/p\u003e \u003cp\u003eFirst, from the perspective of digital economy, the mechanism and path of the impact of digital economy on common prosperity are systematically analyzed, which expands the perspective and content of the study of common prosperity; second, from the perspective of spatial spillover effect and marginal incremental effect, the nonlinear impact of digital economy on common prosperity is deeply explored, which enriches the research methodology and conclusions of the digital economy; third, from the perspective of total factor productivity, the regulatory effect of total factor productivity on common prosperity is analyzed, which provides new perspectives and evidence for the study of digital economy and common prosperity, and improves the precision and credibility of the study. The third is to analyze the moderating effect of total factor productivity on common prosperity, which provides new perspectives and evidence for the research on digital economy and common prosperity, and improves the precision and credibility of the research.\u003c/p\u003e \u003cdiv id=\"Sec2\" class=\"Section2\"\u003e \u003ch2\u003e1.1. Related literature\u003c/h2\u003e \u003cp\u003eThe relationship between digital economy and common prosperity is an emerging field of research, and the relevant literature at home and abroad has been explored from the following three aspects.\u003c/p\u003e \u003cdiv id=\"Sec3\" class=\"Section3\"\u003e \u003ch2\u003e1.1.1. Direct effects of the digital economy driving the development of common prosperity level\u003c/h2\u003e \u003cp\u003eThe direct effect of the digital economy driving the development of common prosperity is mainly reflected in the fact that the digital economy can directly promote the realization of common prosperity by improving the quality and balance of economic growth, promoting the fairness and inclusiveness of income distribution, upgrading the sharing and diversity of spiritual culture, and enhancing the sharing and oneness of urban and rural residents. Relevant literature at home and abroad mainly includes the following categories.\u003c/p\u003e \u003cp\u003eThe impact of the digital economy on economic growth is an important part of the study of the digital economy and underlies the relationship between the digital economy and common prosperity. The digital economy has a significant positive impact on economic growth through improving production efficiency, reducing transaction costs, promoting innovative activities, and expanding consumer demand. For example, Zhao Tao et al. (2020) empirically examined the impact of the digital economy on economic growth by using urban panel data in China and a two-way fixed-effects model, and the results showed that the digital economy has a significant positive effect on economic growth, and there is a marginal incremental effect, i.e., the higher the level of the digital economy, the greater the promotion of economic growth. \u003csup\u003e[1]\u003c/sup\u003eIn addition, the digital economy can improve the quality and balance of economic growth, promote the optimization and upgrading of economic structure, narrow the regional development gap, and enhance the sustainability and resilience of the economy. For example,Zhao T, Zhang Z and Liang S K (2020) found that the role of the digital economy on economic growth is mainly reflected in the tertiary industry, rather than the primary and secondary industries, indicating that the digital economy has an important role in promoting the optimization of economic structure. Hou L, Tian C, and Xiang R (2023) found that the role of the digital economy on economic growth is more significant in the central and western regions, indicating that the digital economy has an important role in promoting the balance of regional development. Shen W, Xia W and Li S. (\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) found that the role of digital economy on economic growth was more significant during the financial crisis, indicating that the digital economy has an important role in guaranteeing economic stability.\u003c/p\u003e \u003cp\u003eThe impact of the digital economy on income distribution is at the core of the relationship between the digital economy and common prosperity, and is also a hot spot in digital economy research. The impact of the digital economy on income distribution is complex and dual, with both positive facilitating and negative constraining effects. On the one hand, the digital economy can improve the fairness and inclusiveness of income distribution by lowering the threshold of innovation and participation, expanding the scope of innovation and participation, and increasing the benefits of innovation and participation. For example, Jiang Q, Li Y and Si H (\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) concluded through empirical analysis that the digital economy has a significant positive impact on the income level and income growth rate of urban and rural residents, and the impact on the income level and income growth rate of rural residents is more significant, indicating that the digital economy is conducive to narrowing the income gap between urban and rural areas, and promoting the fairness of income distribution. Yan J, Tu X and Zheng J (2023) found that the impact of the digital economy on the residents' income has a marginal incremental effect, that is, the higher the level of the digital economy, the greater the promotion of residents' income, indicating that the digital economy is conducive to increasing the level of residents' income and promoting the inclusion of income distribution. On the other hand, the digital economy may also have a negative impact on income distribution by exacerbating skill differences, expanding returns to scale, and reinforcing market monopoly, leading to unfair and non-inclusive income distribution. For example, Li Y and Ke J S (2021) point out that the digital economy has a significant positive impact on both the urban-rural residents' income gap and the regional residents' income gap, indicating that the digital economy may exacerbate the imbalance of income distribution and constrain the fairness of income distribution. Han X, Fu L and Lv C (2023) found that there is a stage difference in the impact of the digital economy on the Gini coefficient, that is, when the level of the digital economy is low, the impact on the Gini coefficient is negative, while when the level of the digital economy is high, the impact on the Gini coefficient is positive, which indicates that the digital economy may have an \"inverted U-shaped\" impact on income distribution, restricting the fairness of income distribution. Inclusion in Income Distribution.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section3\"\u003e \u003ch2\u003e1.1.2. Spatial spillover effects of digital economy-driven common prosperity development\u003c/h2\u003e \u003cp\u003eThe spatial spillover effect of the digital economy in driving the development of common prosperity is mainly reflected in the fact that the digital economy can break the geographical and temporal constraints through the formation of network externalities and digital diffusion, forming synergistic effects between digital platforms and business ecological vendors, between industrial chains and supply chains, and between data elements and other factors of production, and facilitating spatial diffusion and regional harmonization of common prosperity.\u003c/p\u003e \u003cp\u003eA distinctive feature of the digital economy is its strong network externality, which means that the value and benefits of the digital economy increase with the expansion of the scale of the network, thus forming a positive feedback loop that promotes the rapid development and wide dissemination of the digital economy. The network externality of the digital economy is not only reflected in the supply and demand of digital products and services, but also in the upstream and downstream of digital platforms and business ecology, thus forming the spatial spillover effect of the digital economy and promoting the spatial diffusion of common prosperity. For example, Yan J, Tu X and Zheng J (2023) found that there is a significant spatial spillover effect of the impact of the digital economy on economic growth, that is, the higher the level of the digital economy, the greater the promotion of the economic growth of the neighboring regions, suggesting that the digital economy can drive the economic development of neighboring regions and promote inter-regional common prosperity through network externalities (Su J \u0026amp; Su K \u0026amp; Wang S, 2021).\u003c/p\u003e \u003cp\u003eAnother distinctive feature of the digital economy is its strong digital diffusion, which means that the development of the digital economy can promote the digital transformation of other industries and fields through the innovation and application of digital technologies, thus forming cross-border integration and industrial upgrading of the digital economy and promoting the rapid development and wide dissemination of the digital economy. The digital diffusion of the digital economy is not only reflected in the integration of digital technology with other technologies, but also in the integration of digital industries with other industries, thus forming the spatial spillover effect of the digital economy and promoting the regional coordination of common prosperity. For example, Man J, Liu J and Cui B (2023) found that there is a significant spatial spillover effect of the impact of the digital economy on economic growth, i.e., the higher the level of the digital economy, the greater the promotion of economic growth in other regions.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section3\"\u003e \u003ch2\u003e1.1.3. Marginal incremental effects of the digital economy driving the development of common prosperity level\u003c/h2\u003e \u003cp\u003eThe marginal incremental effect (threshold effect) of the digital economy driving the development of common prosperity is mainly reflected in the fact that the level and quality of the development of the digital economy have a stage difference in its impact on common prosperity, i.e., the higher the level of the digital economy, the greater the promotion of common prosperity, but at the same time there exists a certain threshold, i.e., when the level of the digital economy is lower than a certain degree, the promotion of common prosperity is not significant or even negative (Mirdamad M G, 2020).\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e1.2. Model construction\u003c/h2\u003e \u003cdiv id=\"Sec7\" class=\"Section3\"\u003e \u003ch2\u003e1.2.1. Econometric modeling\u003c/h2\u003e \u003cp\u003eTo verify the direct effect of the digital economy driving the development of common prosperity, the following benchmark regression model is constructed:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$${lnindex}_{i,t}={\\alpha }_{0}+{\\alpha }_{1}{lndigital}_{i,t}+{\\phi }_{z}{Z}_{i,t}+{\\mu }_{i}+{\\delta }_{t}+{\\epsilon }_{i,t}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn Eq.\u0026nbsp;(\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e), the\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({lnindex}_{i,t}\\)\u003c/span\u003e\u003c/span\u003erepresents the level of common prosperity development of province i in year t;\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({lndigital}_{i,t}\\)\u003c/span\u003e\u003c/span\u003erepresents the level of development of digital economy of province i in year t;\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({Z}_{i,t}\\)\u003c/span\u003e\u003c/span\u003erepresents each control variable, the\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\mu }_{i}\\)\u003c/span\u003e\u003c/span\u003eand\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\delta }_{t}\\)\u003c/span\u003e\u003c/span\u003erepresent the control area fixed effects and time fixed effects, respectively;\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\epsilon }_{i,t}\\)\u003c/span\u003e\u003c/span\u003erepresents the randomized disturbance term;\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\alpha }_{0}\\)\u003c/span\u003e\u003c/span\u003e is the constant term, and\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\alpha }_{1}\\)\u003c/span\u003e\u003c/span\u003eare the estimated coefficients of the core explanatory variables. Estimated coefficients greater than 0 represent a positive effect of digital economy on common prosperity, otherwise a negative effect.\u003c/p\u003e \u003cp\u003eIn order to explore the spatial spillover effect of China's digital economy development on the development of common prosperity, this paper adds a spatial weight matrix on the basis of the baseline regression model, so as to further construct a spatial Durbin model (SDM) as shown below:\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$${lnindex}_{i,t}={l}_{0}+\\rho {W}_{i.j}{lnindex}_{i,t}+{\\theta }_{1}{W}_{i,j}{lndigital}_{i,t}+{\\beta }_{1}{lndigital}_{i,t}+\\sum {\\beta }_{Z}{Z}_{i,t}+{\\theta }_{Z}{W}_{i,j}\\sum {Z}_{i,t}+{\\mu }_{i}+{\\delta }_{t}+{\\epsilon }_{i,t}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$${\\epsilon }_{i,t}=\\lambda W{\\epsilon }_{i,t}+{\\zeta }_{i,t}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn the above equation, the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\rho }\\)\u003c/span\u003e\u003c/span\u003e is the spatial autoregressive coefficient;\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\theta }_{1}\\)\u003c/span\u003e\u003c/span\u003eis the coefficient of the spatial lag term of the explanatory variables;\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\theta }_{Z}\\)\u003c/span\u003e\u003c/span\u003eis expressed as the control variable spatial lag term coefficient;\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\zeta }_{i,t}\u0026#8764;N(0,{\\delta }^{2}{I}_{n})\\)\u003c/span\u003e\u003c/span\u003e ;\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\mu }_{i}\\)\u003c/span\u003e\u003c/span\u003eand\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\delta }_{t}\\)\u003c/span\u003e\u003c/span\u003edenote spatial fixed effects and time fixed effects, respectively;\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\epsilon }_{i,t}\\)\u003c/span\u003e\u003c/span\u003edenotes the error term;\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\lambda }\\)\u003c/span\u003e\u003c/span\u003e is the spatial lag term coefficient of the error term;\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({W}_{i,j}\\)\u003c/span\u003e\u003c/span\u003e represents the spatial weight matrix;\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\beta }_{1}\\)\u003c/span\u003e\u003c/span\u003e represents the coefficients of the explanatory variables, and\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\beta }_{Z}\\)\u003c/span\u003e\u003c/span\u003e represents the control variable coefficients;\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{W}{{\\epsilon }}_{\\text{i},\\text{t}}\\)\u003c/span\u003e\u003c/span\u003e represents the spatial effect of the error term;\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({l}_{0}\\)\u003c/span\u003e\u003c/span\u003eis the constant term;\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({Z}_{i,t}\\)\u003c/span\u003e\u003c/span\u003erepresents a series of control variables such as industrial structure.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section3\"\u003e \u003ch2\u003e1.2.2. Mechanism testing model\u003c/h2\u003e \u003cp\u003eIn order to study the indirect effect of the digital economy driving the development of common prosperity, this paper selects the total factor productivity of each province as a moderating variable to be tested, and constructs the moderating effect model as follows:\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$${\\text{l}\\text{n}\\text{i}\\text{n}\\text{d}\\text{e}\\text{x}}_{\\text{i},\\text{t}}={{\\gamma }}_{0}+{{\\gamma }}_{1}{\\text{l}\\text{n}\\text{d}\\text{i}\\text{g}\\text{i}\\text{t}\\text{a}\\text{l}}_{\\text{i},\\text{t}}+{{\\gamma }}_{2}{\\text{l}\\text{n}\\text{t}\\text{f}\\text{p}}_{\\text{i},\\text{t}}+{{\\gamma }}_{3}{\\text{l}\\text{n}\\text{d}\\text{i}\\text{g}\\text{i}\\text{t}\\text{a}\\text{l}}_{\\text{i},\\text{t}}\\ast {\\text{l}\\text{n}\\text{t}\\text{f}\\text{p}}_{\\text{i},\\text{t}}+{{\\phi }}_{\\text{z}}{\\text{Z}}_{\\text{i},\\text{t}}+{{\\mu }}_{\\text{i}}+{{\\delta }}_{\\text{t}}+{{\\epsilon }}_{\\text{i},\\text{t}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eBased on the baseline regression equation for the direct impact of the digital economy driving common prosperity level, total factor productivity (TFP) and the cross-multiplier term between the digital economy and TFP are introduced. Where.\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({lntfp}_{i,t}\\)\u003c/span\u003e\u003c/span\u003e represents the total factor productivity of province i in year t;\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({lndigital}_{i,t}\\ast {lntfp}_{i,t}\\)\u003c/span\u003e\u003c/span\u003e represents the cross-multiplication term between digital economy and total factor productivity. By observing\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\gamma }\\)\u003c/span\u003e\u003c/span\u003e, the\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\beta }\\)\u003c/span\u003e\u003c/span\u003e the magnitude as well as the significance of the other parameters to analyze the degree of influence of total factor productivity on the promotion of common prosperity development.\u003c/p\u003e \u003cp\u003eIn order to further study the nonlinear dynamic spillover effects of industrial structure upgrading as well as the degree of innovation within a province on the development of digital economy driving the development of common prosperity, the following threshold effect model is constructed:\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$${lnindex}_{i,t}={\\phi }_{0}+{\\phi }_{1}{lndigital}_{i,t}\\times I({Tℎr}_{i,t}\\le \\vartheta )+{\\phi }_{2}{lndigital}_{i,t}\\times I({Tℎr}_{i,t}\u0026gt;\\vartheta )+{\\phi }_{Z}{Z}_{i,t}+{\\mu }_{i}+{\\epsilon }_{i,t}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn the above equation, the\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({Tℎr}_{i,t}\\)\u003c/span\u003e\u003c/span\u003e represents the threshold variable of industrial structure upgrading of province i in year t. The threshold effect model is a single-threshold scenario;\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{I}(\\bullet )\\)\u003c/span\u003e\u003c/span\u003e is the indicator function, which takes the value of 1 if the condition in parentheses is satisfied, otherwise it takes the value of 0. This paper uses the threshold effect model in the single-threshold case.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"2. Variable measurement and description","content":"\u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e2.1. Measurement of explanatory variables\u003c/h2\u003e \u003cp\u003eThis paper refers to the system proposed by Han Liangliang,Peng Yi,Meng Qingna (2023) to measure the degree of development of common prosperity, and takes the three perspectives of development, sharing and sustainability as the first-level indicators, utilizes the entropy weight method to construct the indicators, and the composition of indicators at all levels is shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\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\u003eIndicators at all levels of the common prosperity Development Index under the entropy weighting approach\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\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 \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"5\" rowspan=\"6\"\u003e \u003cp\u003edevelopmental\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eaffluence\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eDisposable income per capita (yuan)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eConsumption expenditure per inhabitant (yuan)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eEngel's coefficient\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003ecommonality\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGini coefficient (a measure of statistical dispersion)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eIncome multiplier for urban and rural residents\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eUrbanization rate (%)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"8\" rowspan=\"9\"\u003e \u003cp\u003eshareability\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eeducational attainment\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePublic library holdings per capita (books)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eAverage years of education\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eLevel of medical modernization\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eNumber of practicing (assistant) physicians per 10,000 persons (persons)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eNumber of beds in medical institutions per 10,000 population\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003einfrastructure\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePublic transportation vehicles per 10,000 population (standard units)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePublic toilets per 10,000 population (seats)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003edegree of informatization\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eInternet broadband access per 100 population\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCell phone subscribers per 100 population\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLevel of social security\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSocial security expenditure as a share of GDP (%)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"5\" rowspan=\"6\"\u003e \u003cp\u003esustainability\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eLevel of science, technology and innovation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eRD input intensity (%)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePatents granted per 10,000 persons (pieces)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eEcological health\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eForest cover (%)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCarbon intensity (million tons/billion dollars)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eLevel of economic development\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGDP per capita (\u003cspan\u003e$\u003c/span\u003e/person)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eLabor productivity of society as a whole (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 \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e2.2. Measurement of explanatory variables\u003c/h2\u003e \u003cp\u003eFor the core explanatory variable - digital economy development index, this paper refers to the research method of Yang Q, Ma H and Wang Y (2022) to construct the digital economy index system, selects the four dimensions of digital infrastructure, digital industrialization, industrial digitization and digital innovation capacity as the first level indicators, and uses the entropy weight method to measure the level of digital economy development.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003e2.3. Mechanism variables\u003c/h2\u003e \u003cp\u003eAgainst total factor productivity (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({lntfp}_{i,t}\\)\u003c/span\u003e\u003c/span\u003e ). This paper refers to the accounting method of Chen X, Chen Y, Huang W (2023), using real GDP as the output indicator, the level of capital stock under the perpetual inventory method and the number of social employees as the input indicator, and adopting the DEA algorithm to calculate the total factor productivity level of each province in the country.\u003c/p\u003e \u003cp\u003eTargeting the degree of education in digital technology (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({lnde}_{i,t}\\)\u003c/span\u003e\u003c/span\u003e ). This paper quantifies it in four dimensions, namely human capital, educational input, years of education, and educational literacy. For the human capital dimension, it is quantified by the ratio of the number of students enrolled in general higher education to the number of household members; for education input, it is quantified by the ratio of research expenditure to local GDP; for years of education, it is quantified by the average number of years of education and years of labor in the provinces (standardized at 40 years); and for education literacy, it is quantified by the regional innovation capacity of each province in China.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003e2.4. Control variables\u003c/h2\u003e \u003cp\u003eThis process of digital economy-driven common prosperity development will be affected by many aspects such as industrial structure, urbanization level, human capital level and so on. Therefore, this paper selects industrial structure, urbanization level, human capital level, foreign direct investment, degree of opening up to the outside world, level of financial development, degree of government intervention, research and development intensity, and innovation level as control variables.\u003c/p\u003e \u003cp\u003e(1) Industrial structure. This paper chooses the ratio of the output value of the tertiary industry to the output value of the secondary industry to quantify the industrial structure.\u003c/p\u003e \u003cp\u003e(2) Level of urbanization. This paper chooses the ratio of urban population to quantify the level of urbanization.\u003c/p\u003e \u003cp\u003e(3) Level of economic development. In this paper, the logarithm of the GDP level of the provinces in the past years is chosen to quantify the level of economic development.\u003c/p\u003e \u003cp\u003e(4) Foreign direct investment. This paper quantifies foreign direct investment in terms of the ratio of foreign direct investment to gross regional product.\u003c/p\u003e \u003cp\u003e(5) Social consumption level. This paper quantifies total retail sales of consumer goods as a percentage of regional GDP.\u003c/p\u003e \u003cp\u003e(6) Level of financial development. This paper quantifies the sum of regional savings and loans as a percentage of regional GDP.\u003c/p\u003e \u003cp\u003e(7) Degree of government intervention. This paper quantifies this as the ratio of local government general public budget expenditures to regional GDP.\u003c/p\u003e \u003cp\u003e(8) R\u0026amp;D intensity. This paper quantifies internal expenditure on RD as a percentage of GDP.\u003c/p\u003e \u003cp\u003e(9) Level of innovation. This paper quantifies this in terms of the number of domestic patent applications received for inventions.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003e2.5. Spatial weighting matrix\u003c/h2\u003e \u003cp\u003eIn this paper, we use the spatial economic geography nested matrix (latitude, longitude and GDP per capita), as the spatial weighting matrix for the spatial Durbin model\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({W}_{ij}\\)\u003c/span\u003e\u003c/span\u003e. It is constructed as follows:\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\text{W}=\\left(\\begin{array}{cccc}0\u0026amp; \\frac{1}{{\\text{d}}_{12}}\\times \\frac{1}{|{\\text{Y}}_{1}-{\\text{Y}}_{2}|}\u0026amp; \\cdots \u0026amp; \\frac{1}{{\\text{d}}_{1\\text{n}}}\\times \\frac{1}{|{\\text{Y}}_{1}-{\\text{Y}}_{\\text{n}}|}\\\\ \\frac{1}{{\\text{d}}_{21}}\\times \\frac{1}{|{\\text{Y}}_{2}-{\\text{Y}}_{1}|}\u0026amp; 0\u0026amp; \\cdots \u0026amp; \\frac{1}{{\\text{d}}_{2\\text{n}}}\\times \\frac{1}{|{\\text{Y}}_{2}-{\\text{Y}}_{\\text{n}}|}\\\\ ⋮\u0026amp; ⋮\u0026amp; ⋮\u0026amp; ⋮\\\\ \\frac{1}{{\\text{d}}_{\\text{n}1}}\\times \\frac{1}{|{\\text{Y}}_{\\text{n}}-{\\text{Y}}_{1}|}\u0026amp; \\frac{1}{{\\text{d}}_{\\text{n}2}}\\times \\frac{1}{|{\\text{Y}}_{\\text{n}}-{\\text{Y}}_{2}|}\u0026amp; \\cdots \u0026amp; 0\\end{array}\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere.\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({d}_{ij}\\)\u003c/span\u003e\u003c/span\u003e represents the geographic distance between two regions i and j;\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({Y}_{i}\\)\u003c/span\u003e\u003c/span\u003e and\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({Y}_{j}\\)\u003c/span\u003e\u003c/span\u003e represent the level of economic development of each region, then\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(|{\\text{Y}}_{\\text{i}}-{\\text{Y}}_{\\text{j}}|\\)\u003c/span\u003e\u003c/span\u003e represents the economic distance between the two. In this paper, the level of GDP per capita is used to measure the economic development level of each province.\u003c/p\u003e \u003cp\u003eThe data for the empirical study in this paper come from the China Statistical Yearbook and the White Paper on the Development of China's Digital Economy, and some of the missing values are filled in by linear interpolation. To ensure the smoothness of each variable, the above data are logarithmized.\u003c/p\u003e \u003cp\u003eThe variables involved in this paper and the descriptive statistical analysis of each variable are shown in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. The common prosperity development index has a mean value of 0.3005, a minimum value of 0.074 and a maximum value of 0.988; the digital economy index has a mean value of 0.127, a minimum value of 0.017 and a maximum value of 0.590. The specific values of the other control variables are also given.\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\u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\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=\"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=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eVariable category\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\u003eNumber of observations\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eaverage value\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e(statistics) standard deviation\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eminimum value\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\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\u003eexplanatory variable\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ecommon prosperity Development Index\u003c/p\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({lnindex}_{i,t}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e330\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.3005\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.216\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.074\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.988\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\u003eDigital Economy Index\u003c/p\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({lndigital}_{i,t}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e330\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.127\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.017\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.590\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMechanism variables\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTotal factor productivity\u003c/p\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({lntfp}_{i,t}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e330\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.606\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.273\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.096\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e1.477\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"8\" rowspan=\"9\"\u003e \u003cp\u003econtrol variable\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eindustrial structure\u003c/p\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({lnstr}_{i,t}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e330\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.304\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.708\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.549\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e5.297\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eurbanization level (of a city or town)\u003c/p\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({lncivil}_{i,t}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e330\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.600\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.128\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.229\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.896\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLevel of economic development\u003c/p\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({lngdp}_{i,t}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e330\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e9.907\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.887\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e7.332\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e11.768\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eoverseas foreign direct investment (OFDI)\u003c/p\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({lnfi}_{i,t}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e330\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.018\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.014\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e\u0026minus;0.006\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.080\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003esocial consumption level\u003c/p\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({lncons}_{i,t}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e330\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.388\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.067\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.219\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.538\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 \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({lnfinan}_{i,t}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e330\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3.429\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.209\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1.568\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e8.131\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLevel of government intervention\u003c/p\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({lngovern}_{i,t}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e330\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.271\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.190\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.094\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e1.334\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eR\u0026amp;D intensity\u003c/p\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({lnresearcℎ}_{i,t}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e330\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.018\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.012\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.002\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.066\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eInnovation level\u003c/p\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({lninno}_{i,t}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e330\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e9.693\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.538\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e4.394\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e14.311\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"7\"\u003eDescriptive statistical analysis of variables\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"3. Empirical analysis of digital economy-driven common prosperity development","content":"\u003cdiv id=\"Sec16\" class=\"Section2\"\u003e \u003ch2\u003e3.1. Baseline regression analysis\u003c/h2\u003e \u003cp\u003eThe results of the benchmark regression are shown in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. The results show that the regression coefficient of digital economy is positive at 1% significance level, which indicates that the development of digital economy in China can drive the development of common prosperity. On average, for every percentage increase in the digital economy development index, the common prosperity development index rises by 0.168 units. As for the control variables, industrial structure, urbanization level, economic development level, degree of opening up to the outside world, social consumption level, and R\u0026amp;D intensity have a positive effect on the development of common prosperity, which are significant at the 1% and 10% levels, respectively. The regression results show that the development of digital economy has a positive contribution to the realization of common prosperity, and this effect is influenced by the economic structure and development characteristics.\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\u003eBenchmark regression results\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\u003evariant\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({lnindex}_{i,t}\\)\u003c/span\u003e\u003c/span\u003e(1)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({lnindex}_{i,t}\\)\u003c/span\u003e\u003c/span\u003e(2)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eThe Digital Economy Index (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({lndigital}_{i,t}\\)\u003c/span\u003e\u003c/span\u003e )\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.168***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.049**\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eIndustrial structure (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({lnstr}_{i,t}\\)\u003c/span\u003e\u003c/span\u003e )\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.010*\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel of urbanization (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({lncivil}_{i,t}\\)\u003c/span\u003e\u003c/span\u003e )\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026minus;0.114*\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel of economic development (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({lngdp}_{i,t}\\)\u003c/span\u003e\u003c/span\u003e )\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.095***\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eForeign direct investment (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({lnfi}_{i,t}\\)\u003c/span\u003e\u003c/span\u003e )\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.200*\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSocial consumption level (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({lncons}_{i,t}\\)\u003c/span\u003e\u003c/span\u003e )\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.032\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel of financial development (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({lnfinan}_{i,t}\\)\u003c/span\u003e\u003c/span\u003e )\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.005\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel of government intervention (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({lngovern}_{i,t}\\)\u003c/span\u003e\u003c/span\u003e )\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026minus;0.132***\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eR\u0026amp;D intensity (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({lnresearcℎ}_{i,t}\\)\u003c/span\u003e\u003c/span\u003e )\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.252*\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel of innovation (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({lninno}_{i,t}\\)\u003c/span\u003e\u003c/span\u003e )\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026minus;0.006*\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003earea fixed effect\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ebe\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ebe\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\u003ebe\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ebe\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNumber of provinces\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({R}^{2}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.993\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.997\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c3\" namest=\"c1\"\u003e \u003cp\u003eNote: ***, **, * indicate significant at the 1%, 5% and 10% levels, respectively.\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=\"Sec17\" class=\"Section2\"\u003e \u003ch2\u003e3.2. Moderating effects test\u003c/h2\u003e \u003cp\u003eTotal Factor Productivity (TFP) is a key factor in the digital economy's effect on the common prosperity, this paper chooses the moderating effect model to analyze its transmission mechanism, and the regression results are shown in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e.The results show that the regression coefficients of the Digital Economy Development Index and the Total Factor Productivity are positive, both of them have a positive effect on the common prosperity Development Index, that is, when they increase by one unit respectively, the common prosperity Development Index will increase by a certain amount accordingly. amount, indicating that the increase of both the digital economy and total factor productivity is conducive to the promotion of the wealth and happiness of all the people; the negative regression coefficient of the cross-multiplier term indicates that total factor productivity plays a negative moderating role between the digital economy development index and the common prosperity development index, i.e., it will weaken the positive impact of the digital economy development index on the common prosperity development index. The moderating levels of the moderating variables are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. Specifically, when total factor productivity increases by one unit, the impact coefficient of the digital economy development index on the common prosperity development index decreases by 0.19 units. In other words, the higher the total factor productivity, the weaker the positive effect of the digital economy development index on the common prosperity development index. This may be due to the fact that an increase in total factor productivity does not necessarily benefit all people in a balanced manner, but may lead to faster growth in income and welfare for some people or regions than for others, thus exacerbating inequality and inequity and undermining the realization of common prosperity. This implies that the goal of common prosperity level cannot be fully realized by relying on the development of the digital economy alone, and that the distributional effects of total factor productivity, as well as other factors affecting common prosperity level, such as education, health care and social security, need to be taken into account.\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\u003eResults of moderating effects\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\u003evariant\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({lnindex}_{i,t}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({lnindex}_{i,t}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eThe Digital Economy Index (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({lndigital}_{i,t}\\)\u003c/span\u003e\u003c/span\u003e )\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.256***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.265***\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTotal factor productivity (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({lntfp}_{i,t}\\)\u003c/span\u003e\u003c/span\u003e )\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.005*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.010*\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eintermodal term (math.)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026minus;0.134*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026minus;0.190*\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003econtrol variable\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eclogged\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ebe\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003earea fixed effect\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ebe\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ebe\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\u003ebe\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ebe\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNumber of provinces\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({R}^{2}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.584\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.905\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c3\" namest=\"c1\"\u003e \u003cp\u003eNote: ***, * indicate significant at 1% and 10% level respectively.\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 \u003cp\u003eDiagram of moderating effect\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec18\" class=\"Section2\"\u003e \u003ch2\u003e3.3. Spatial spillover effects\u003c/h2\u003e \u003cdiv id=\"Sec19\" class=\"Section3\"\u003e \u003ch2\u003e3.3.1 Spatial autocorrelation test\u003c/h2\u003e \u003cp\u003eIn the regression analysis using the spatial Durbin model, it is necessary to calculate the Moran index to test the spatial correlation of the driving role of the digital economy on the common prosperity, and the software used is stata17.0.The formula for the calculation of the Moran index is as follows.\u003cdiv id=\"Equb\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equb\" name=\"EquationSource\"\u003e\n$$\\text{I}=\\frac{\\sum _{\\text{i}=1}^{\\text{n}}\\sum _{\\text{j}=1}^{\\text{n}}{\\text{W}}_{\\text{i}\\text{j}}({\\text{Y}}_{\\text{i}}-\\overline{\\text{Y}})({\\text{Y}}_{\\text{j}}-\\overline{\\text{Y}})}{{\\text{S}}^{2}\\sum _{\\text{i}=1}^{\\text{n}}\\sum _{\\text{j}=1}^{\\text{n}}{\\text{W}}_{\\text{i}\\text{j}}}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn the above equation, the\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({S}^{2}=\\frac{1}{n}\\sum _{i=1}^{n}{({Y}_{i}-\\overline{Y})}^{2}\\)\u003c/span\u003e\u003c/span\u003e .\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\overline{Y}=\\frac{1}{n}\\sum _{i=1}^{n}{Y}_{i}\\)\u003c/span\u003e\u003c/span\u003e. where n is the 30 provinces in China except Tibet, and\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({W}_{ij}\\)\u003c/span\u003e\u003c/span\u003e is the spatial weight matrix, and\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({Y}_{i}\\)\u003c/span\u003e\u003c/span\u003e represents the province common prosperity development index or the province's digital economy development index, and\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\overline{Y}\\)\u003c/span\u003e\u003c/span\u003e represents the mean value of the province common prosperity development index or the province's digital economy development index. The value range of Moran index is [-1,1]. The measurement results are shown in Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e.\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\u003eResults of spatial autocorrelation test\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\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 \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eparticular year\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e \u003cp\u003ecommon prosperity Development Index\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c7\" namest=\"c5\"\u003e \u003cp\u003eDigital Economy Index\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMoran Index\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eZ-statistic\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eP-value\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eMoran Index\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eZ-statistic\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eP-value\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2012\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.368\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e5.003\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.265\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e3.708\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2013\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.375\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e5.079\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.354\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e4.573\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2014\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.364\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4.961\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.384\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e4.900\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2015\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.362\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4.949\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.346\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e4.441\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2016\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.359\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4.910\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.342\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e4.395\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2017\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.357\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4.898\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.355\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e4.568\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2018\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.353\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4.882\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.307\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e4.035\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2019\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.351\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4.859\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.309\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e4.083\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2020\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.352\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4.833\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.312\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e4.134\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2021\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.373\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e5.071\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.310\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e4.123\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2022\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.387\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e5.153\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.220\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e3.076\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.000\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\u003eThe above table shows that the overall development trend of China's Moran Index from 2012 to 2022 is relatively stable, and all of them are significantly positive at the 1% level, which indicates that there is a spatial correlation between common prosperity and digital economy, and that China's provinces will be affected by the common prosperity development index of their neighboring provinces. Spatial positive correlation, that is, high-income areas (or low-income areas) tend to be adjacent to the surrounding high-income areas (or low-income areas), the formation of \"high-high\" or \"low-low\" agglomeration effect.\u003c/p\u003e \u003cp\u003eThe distribution of the Moran Index for 2012, 2016, 2019, and 2022 is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, and there is a certain clustering effect in the data, which is basically distributed in quadrants one and three, indicating that it is suitable for using spatial measurement models for analysis.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eDistribution of Moran's index in 2012, 2016, 2019 and 2022\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec20\" class=\"Section3\"\u003e \u003ch2\u003e3.3.2. Spatial Durbin model results\u003c/h2\u003e \u003cp\u003eFirst of all, this paper carried out a smoothness test for each variable, and the method used was the individual double fixed-effects unit root test with a lag operator of 6. The results showed that the variables were smooth and good, avoiding the pseudo-regression problem. Before analyzing the spatial spillover effect, this paper conducted LM test, Hausmann test, SDM fixed effect test, LR test, and the test results are shown in Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e, which determined the spatial Durbin model with double fixed effects as the best estimation model.\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\u003eResults of spatial panel model tests\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\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003eSpatial panel model testing\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eValue\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eP-Value\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"4\" rowspan=\"5\"\u003e \u003cp\u003eLM test\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMoran's I\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e7.772***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLM-lag\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e56.649***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRobust-LM-lag\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.325\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.568\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLM-error\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e75.836***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRobust-LM-error\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e19.512***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eLR test\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLR-SDM/SEM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e84.68***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLR-SDM/SAR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e54.57***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eWald test\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWald-SDM/SEM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e80.03***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWald-SDM/SAR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e76.36***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eSpatio-temporal/time fixed effects test\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLR-both/ind\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e23.61*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.051\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLR-both/time\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e779.13***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"4\" nameend=\"c4\" namest=\"c1\"\u003e \u003cp\u003eNote: ***, **, * indicate significant at the 1%, 5% and 10% levels, respectively.\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\u003eIn this paper, the estimation method of partial differentiation is used to carry out the analysis of spatial effects, and the estimation results are shown in Table\u0026nbsp;\u003cspan refid=\"Tab7\" class=\"InternalRef\"\u003e7\u003c/span\u003e. The results show that, whether it is the regression results under the inverse distance matrix or the regression results under the economic matrix obtained based on the spatial economic geographic nested matrix (latitude, longitude and GDP per capita), the direct effect of the digital economy to drive the development of the common prosperity is significantly positive at the level of 5% and 1%, respectively, which indicates that the digital economy has a positive spatial spillover effect on the development of the common prosperity of China's provinces.\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\u003eSDM regression results\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\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eexplanatory variable\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003einverse distance matrix\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003enested matrix\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 \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eThe Digital Economy Index (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\text{l}\\text{n}\\text{d}\\text{i}\\text{g}\\text{i}\\text{t}\\text{a}\\text{l}}_{\\text{i},\\text{t}}\\)\u003c/span\u003e\u003c/span\u003e )\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.095**\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.180***\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{W}\\cdot {\\text{l}\\text{n}\\text{d}\\text{i}\\text{g}\\text{i}\\text{t}\\text{a}\\text{l}}_{\\text{i},\\text{t}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.132*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.009**\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003econtrol variable\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ebe\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ebe\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\u003ebe\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ebe\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003earea fixed effect\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ebe\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ebe\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003edirect effect\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.126**\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.182***\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eindirect effect\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.495*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.049*\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eaggregate effect\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.621**\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.095*\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNumber of provinces\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c3\" namest=\"c1\"\u003e \u003cp\u003eNote: ***, **, * indicate significant at the 1%, 5% and 10% levels, respectively.\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=\"Sec21\" class=\"Section2\"\u003e \u003ch2\u003e3.4. Analysis of threshold effects\u003c/h2\u003e \u003cp\u003eIn this paper, the degree of digital technology education is selected as a threshold variable, and the threshold effect model is used to analyze the impact of China's digital economy driving the development of common prosperity, and the estimation of the three threshold models and the test results of the threshold effect are obtained through bootstrap method by repeating the sampling for 300 times, as shown in the table below.\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\u003eSignificance test of effect with digital technology education level as a threshold variable\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\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003ethreshold effect model\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eF-value\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eP-value\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eBS Index\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c7\" namest=\"c5\"\u003e \u003cp\u003ethreshold value\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eThreshold estimate\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1%\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e5%\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003e10%\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003esingle threshold\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e45.09\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e300\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e37.390\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e26.003\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e21.754\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.409\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003edouble threshold\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e45.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e300\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e31.268\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e24.542\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e21.567\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.409\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\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\u003e34.974\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e25.031\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e20.858\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.550\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003etriple threshold\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e43.16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e300\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e48.727\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e35.797\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e31.813\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.182\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\u003eIn this paper, the likelihood ratio test LR is used to analyze the truthfulness of the threshold estimates, and the test results are shown in the figure. The results show that when LR is equal to 0, the single threshold estimates of digital technology education level are 0.409 and are all below the dotted line in the figure (LR\u0026thinsp;=\u0026thinsp;7.35), which indicates that the threshold estimates are consistent with the true value. It can be divided into two intervals based on the level of digital technology education: low digital technology education (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({lndc}_{i,t}\\le 0.409\\)\u003c/span\u003e\u003c/span\u003e ) and high digital technology education level (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({lndc}_{i,t}\u0026gt;0.409\\)\u003c/span\u003e\u003c/span\u003e ).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThreshold effect results graph\u003c/p\u003e \u003cp\u003eThe digital economy can improve productivity and social welfare through its own innovative activities and synergies, while also realizing common prosperity level and social equity through inclusive services and the distribution of digital dividends. Among them, the level of digital technology education is a key factor in the development of the digital economy, which can foster digital competence, innovation and adaptability, thus driving the growth and transformation of the digital economy. The estimated results of the threshold effect of the level of digital technology education on the development of a digital economy driving common prosperity are shown in the table below.\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 10\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThreshold effect regression results\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"2\"\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 \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003evariant\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eThreshold variables\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLevel of education in digital technology\u003c/p\u003e \u003cp\u003e(Threshold q\u0026thinsp;=\u0026thinsp;0.409)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDigital Economy Index\u003c/p\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({lndigital}_{i,t}\\bullet I(Tℎ\\le q)\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.010*\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDigital Economy Index\u003c/p\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({lndigital}_{i,t}\\bullet I(Tℎ\u0026gt;q)\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.102**\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003econtrol variable\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ebe\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNumber of periods\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({R}^{2}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.582\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003eNote: **, * indicate significant at the 5% and 10% levels, respectively.\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\u003eWhen digital technology education is less than the threshold value of 0.409, the estimated coefficient of the digital economy driving the development of common prosperity is 0.010 at the 10% significance level, indicating that for every 1% increase in the digital economy, the level of common prosperity development will increase by 0.010%; when digital technology education is higher than the threshold value of 0.409, the estimated coefficient of the digital economy driving the development of common prosperity is 0.102 at the 5% significance level is 0.102, indicating that for every 1% increase in the digital economy, the level of common prosperity development will increase by 0.102%. This demonstrates the existence of a threshold variable of digital technology educational attainment, i.e., digital technology educational attainment has different impacts on the driving effect of the digital economy at different levels. When the level of digital technology education is lower than the threshold, the digital economy has a weaker role in promoting common prosperity; when the level of digital technology education is higher than the threshold, the digital economy has a significantly stronger role in promoting common prosperity development, which indicates that increasing the level of digital technology education is an important way to achieve high-quality development of the digital economy and common prosperity.\u003c/p\u003e \u003c/div\u003e"},{"header":"4. Endogeneity test","content":"\u003cp\u003eThere may be an endogeneity problem between the digital economy index and the common prosperity development index, that is, there is not only a causal relationship between the two, but also a feedback relationship or interference from confounding factors. For example, the development of the digital economy may raise the income level of the population and the level of social welfare, thus raising the common prosperity Development Index; however, at the same time, the realization of common prosperity may also provide broader market space and stronger social support for the development of the digital economy, thus raising the Digital Economy Index. In addition, the relationship between the Digital Economy Index and the common prosperity Development Index may be affected by other variables, such as government policies, human capital, innovation capacity, institutional environment, and so on. In order to verify the reasonableness of the model setting, this paper conducts endogeneity test of the model from the perspectives of omitted explanatory variables test and instrumental variables respectively.\u003c/p\u003e \u003cdiv id=\"Sec23\" class=\"Section2\"\u003e \u003ch2\u003e4.1. Omitted explanatory variables test\u003c/h2\u003e \u003cp\u003eThe omission of important explanatory variables in the model setting process may cause bias in the regression results. In this paper, two methods, Ramsey RESET test and Selection-ratio test, are used respectively to test whether there is any omission of variables in the model setting. The results show that the Ramsey RESET test has a p-value of 0.227, which does not reject the original hypothesis - the regression model has no omitted variables or non-linear relationships, i.e., the model is correctly set up; the Selection-ratio test of\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\delta }\\)\u003c/span\u003e\u003c/span\u003e is greater than 1 regardless of the inclusion of control variables, proving that the variables in the model are reasonably controlled and the omitted variables are not enough to change the current results.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec24\" class=\"Section2\"\u003e \u003ch2\u003e4.2. Instrumental variables testing\u003c/h2\u003e \u003cp\u003eIn order to more robustly assess the driving effect of China's digital economy on the development of common prosperity, this paper uses the frequency of words related to the digital economy over the years as an instrumental variable, and the two-stage least squares (2SLS) method is used for the test. Firstly Eq.\u0026nbsp;(\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e) performs the first-stage regression, the\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{p}\\text{o}\\text{l}\\text{i}\\text{c}\\text{y}\\)\u003c/span\u003e\u003c/span\u003e represents the digital economy policy word frequency of province i in year t, and vector Z is a series of control variables; Eq.\u0026nbsp;(\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e) is the second-stage regression, in which\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\widehat{lndigital}}_{i,t}\\)\u003c/span\u003e\u003c/span\u003e is the fitted value of the digital economy index variables in the first stage. The estimation results are shown in Table\u0026nbsp;\u003cspan refid=\"Tab10\" class=\"InternalRef\"\u003e11\u003c/span\u003e.\u003cdiv id=\"Equc\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equc\" name=\"EquationSource\"\u003e\n$${lndigital}_{i,t}={\\gamma }_{0}+{\\gamma }_{1}{policy}_{i,t}+{\\gamma }_{2}{Z}_{i,t}+{\\mu }_{i}+{\\phi }_{t}+{\\epsilon }_{i,t}$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equd\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equd\" name=\"EquationSource\"\u003e\n$${index}_{i,t}={\\gamma }_{0}+{\\gamma }_{1}{\\widehat{lndigital}}_{i,t}+{\\gamma }_{2}{Z}_{i,t}+{\\mu }_{i}+{\\phi }_{t}+{\\epsilon }_{i,t}$$\u003c/div\u003e\u003c/div\u003e\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 11\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eInstrumental variable test results\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\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eexplanatory variable\u003c/p\u003e \u003c/th\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 \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePhase II\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePhase I\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\u003eIndex\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003elndigital\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({lndigital}_{i,t}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.474*\u003c/p\u003e \u003cp\u003e(0.286)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({policy}_{i,t}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.001**\u003c/p\u003e \u003cp\u003e(0.000)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003econtrol variable\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003econtainment\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003econtainment\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eProvince fixed effects\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003econtainment\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003econtainment\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eYear fixed effects\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003econtainment\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003econtainment\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePhase I F-value\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e76.77\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003esample size\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e330\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e330\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c3\" namest=\"c1\"\u003e \u003cp\u003eNote: ** and * indicate significant at 5% and 10% level respectively.\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\u003eTable\u0026nbsp;\u003cspan refid=\"Tab10\" class=\"InternalRef\"\u003e11\u003c/span\u003e reports the estimation results. In the first stage regression in Column (2), the regression result of the instrumental variable POLICY on the level of development of the digital economy is significantly positive, indicating that the enactment of policies related to the digital economy has a significant facilitating effect on the digital economy. In the second stage regression of Column (1), the promotion effect of digital economy on common prosperity is still significantly positive after adopting the instrumental variable, which is consistent with the results of the benchmark regression. In addition, the F-value of the first stage regression is 76.77, which is much larger than 10, which indicates that there is no weak instrumental variable problem, and the regression results are valid, i.e., there is no reverse causality problem between the digital economy index and the common prosperity, and the model is reasonable.\u003c/p\u003e \u003c/div\u003e"},{"header":"5. Robustness tests","content":"\u003cp\u003eIn order to further verify the stability of the research results, this paper further performs the following tests.\u003c/p\u003e \u003cdiv id=\"Sec26\" class=\"Section2\"\u003e \u003ch2\u003e5.1. Shrink-tailed regression.\u003c/h2\u003e \u003cp\u003eIn order to avoid the impact of data outliers on the regression results, this paper shrinks the core explanatory variables at the 1% level, and the regression results after shrinking are shown in column (1) of Table\u0026nbsp;\u003cspan refid=\"Tab11\" class=\"InternalRef\"\u003e12\u003c/span\u003e. The empirical results show that the regression coefficient of the digital economy index is still significantly positive and close to the benchmark regression coefficient, confirming the robustness of the empirical results of this paper.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec27\" class=\"Section2\"\u003e \u003ch2\u003e5.2. Replacement of variables.\u003c/h2\u003e \u003cp\u003eThis paper uses the digital economy index synthesized by principal component analysis to replace the core explanatory variables, and the regression results after replacement are shown in column (2) of Table\u0026nbsp;\u003cspan refid=\"Tab11\" class=\"InternalRef\"\u003e12\u003c/span\u003e, and the regression coefficient of digital economy is significantly positive, which verifies the reliability of the research results.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec28\" class=\"Section2\"\u003e \u003ch2\u003e5.3. Moving average processing.\u003c/h2\u003e \u003cp\u003eIn order to avoid the impact of panel data fluctuations on the analysis results, this paper adopts the moving average to smooth the data before conducting regression analysis. The results in column (3) of Table\u0026nbsp;\u003cspan refid=\"Tab11\" class=\"InternalRef\"\u003e12\u003c/span\u003e show that the regression coefficient of the smoothed digital economy is significantly positive, indicating that the regression results are robust.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab11\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 12\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eRobustness test results\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\u003evariant\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(1)\u003c/p\u003e \u003cp\u003ehave one's tail reduced\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e(2)\u003c/p\u003e \u003cp\u003eSubstitution of variables\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e(3)\u003c/p\u003e \u003cp\u003emoving average\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({lndigital}_{i,t}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.092***\u003c/p\u003e \u003cp\u003e(0.029)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.094***\u003c/p\u003e \u003cp\u003e(0.030)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.063**\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003econtrol variable\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003econtainment\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003econtainment\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003econtainment\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eProvince fixed effects\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003econtainment\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003econtainment\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003econtainment\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eYear fixed effects\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003econtainment\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003econtainment\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003econtainment\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003esample size\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e330\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e330\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e330\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({R}^{2}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.995\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.995\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.995\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"4\" nameend=\"c4\" namest=\"c1\"\u003e \u003cp\u003eNote: *** and ** indicate significant at 1% and 5% level respectively.\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. Conclusion","content":"\u003cp\u003eWith digital economy as the core explanatory variable, common prosperity development level as the explanatory variable, and total factor productivity as the moderating variable, this paper adopts the spatial Durbin model, and utilizes the panel data of 30 provincial-level administrative regions in China from 2012 to 2022 to empirically analyze, from the three aspects of the direct effect, the spatial spillover effect, and the marginal incremental effect (the threshold effect) of the digital economy in driving the development of common prosperity, the mechanism and path of the digital economy's impact on common prosperity. The study finds:\u003c/p\u003e \u003cp\u003eThe digital economy has a significant positive direct effect and spatial spillover effect on the development of common prosperity, and there is a marginal incremental effect, i.e., the higher the level of the digital economy, the greater the contribution to the development of common prosperity. This shows that the digital economy is not only a new driving force for economic growth, but also a new way to promote the common prosperity, through improving efficiency and quality, to promote economic and social development and improve people's lives; total factor productivity plays a positive moderating role in the relationship between the digital economy and the development of the common prosperity, i.e., the higher the total factor productivity, the stronger the role of the digital economy in promoting the development of the common prosperity. This suggests that total factor productivity is a key factor in the role of the digital economy in the common good, reflecting the innovative capacity and competitiveness of the digital economy and an important indicator of the quality of the digital economy.\u003c/p\u003e \u003cp\u003eThe level of digital technology education is an important threshold variable affecting the development of the digital economy on common prosperity, and when the level of digital technology education is higher than a certain level, the promotion of the digital economy on the development of common prosperity is significantly enhanced, which indicates that improving the level of digital technology education is an important way to achieve high-quality development of the digital economy and common prosperity, and is also a necessary condition for narrowing the digital divide and promoting digital inclusion.\u003c/p\u003e \u003cp\u003eBased on the findings of this paper, in order to better utilize the role of digital economy in promoting common prosperity, the top-level design of the digital economy should be strengthened, the development strategy of the digital economy should be improved, laws, regulations and standards related to the digital economy should be formulated, the security and stability of the digital economy should be safeguarded, and the in-depth fusion of the digital economy with the real economy should be promoted, so as to facilitate the transformation, upgrading and innovative development of the digital economy.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eDeclaration of Competing Interest\u003c/h2\u003e \u003cp\u003eThere\u0026rsquo;s no conflict of interest.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eFunding\u003c/h2\u003e \u003cp\u003eThere\u0026rsquo;s no funding.\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eL.L. and X.G. conceived the research idea and designed the empirical model. L.L. collected and processed the data, and performed the spatial econometric analysis. X.G. wrote the introduction, literature review, and conclusion sections. Both authors contributed to the discussion and interpretation of the results, and revised the manuscript. All authors read and approved the final version of the manuscript.\u003c/p\u003e\u003ch2\u003eData availability\u003c/h2\u003e \u003cp\u003eData will be made available on request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eChen X, Chen Y, Huang W et al (2023) A new Malmquist-type green total factor productivity measure: An application to China. Energy Econ 117:106408\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eFu L, Han X, Lv C et al (2023) Measurement and spatio-temporal heterogeneity analysis of the coupling coordinated development among the digital economy, technological innovation and ecological environment. Ecol Ind 151:110325\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHan L, Peng Y, Meng Q (2023) Digital financial inclusion, entrepreneurial activity and common prosperity - an empirical study based on inter-provincial panel data in China. Soft Sci 37(3):18\u0026ndash;24\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHou L, Tian C, Xiang R et al (2023) Research on the Impact Mechanism and Spatial Spillover Effect of Digital Economy on Rural Revitalization: An Empirical Study Based on China\u0026rsquo;s Provinces. Sustainability 15(15):11607\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eJiang Q, Li Y, Si H (2022) Digital Economy Development and the Urban\u0026ndash;Rural Income Gap: Intensifying or Reducing, Land, 11(11), 1980\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLi Y, Ke JS (2021) Three-level digital divide: Income growth and income distribution effects of the rural digital economy. Agric Technol Econ 8:119\u0026ndash;132\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLiu J, Man J, Cui B et al (2023) Coupling and Coordination between Digital Economy and Urban\u0026ndash;Rural Integration in China. Sustainability 15(9):7299\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMirdamad MG (2020) Innovative Tools for Investment Management in the Digital Economy: A Guide for Post-Socialist Countries. Mark Manage Innovations, (4), 1\u0026ndash;12\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eShen W, Xia W, Li S (2022) Dynamic coupling trajectory and spatial-temporal characteristics of high-quality economic development and the digital economy. Sustainability 14(8):4543\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSu J, Su K, Wang S (2021) Does the digital economy promote industrial structural upgrading?\u0026mdash;A test of mediating effects based on heterogeneous technological innovation. Sustainability 13(18):10105\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTao Z, Zhang Z, Shangkun L (2022) Digital economy, entrepreneurship, and high-quality economic development: Empirical evidence from urban China. Front Econ China 17(3):393\u0026ndash;414\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTu X, Yan J, Zheng J (2023) Does digital economy strengthen the income distribution effect of fiscal expenditure? Evidence from China. PLoS ONE, 18(8), e0290041\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eYang Q, Ma H, Wang Y et al (2022) Research on the influence mechanism of the digital economy on regional sustainable development. Procedia Comput Sci 202:178\u0026ndash;183\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhao T, Zhang Z, Liang SK (2020) Digital economy, entrepreneurial activity and high-quality development: Empirical evidence from Chinese cities. Manage world 36(10):65\u0026ndash;76\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhang Z, Tao Z, Shangkun L (2020) Digital economy, entrepreneurship, and high-quality economic development: Empirical evidence from urban China. Front Econ China 17(3):393\u0026ndash;414\u003c/span\u003e\u003c/li\u003e\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":"Digital economy, Marginal incremental effect, Common prosperity, Total factor productivity, Spatial Durbin modeling","lastPublishedDoi":"10.21203/rs.3.rs-3923573/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3923573/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eDigital economy is not only a new driving force for economic growth, but also a new way to promote common prosperity. This paper examines how digital economy affects common prosperity development in China, using spatial Durbin model and panel data of 30 provinces from 2012 to 2022 to empirically analyze the direct effect, spatial spillover effect, and marginal incremental effect of the digital economy in terms of driving the development of common prosperity. The research results show that the digital economy has a significant positive direct effect and spatial spillover effect on the development of common prosperity, and there is a marginal incremental effect, i.e., the higher the level of the digital economy, the greater the promotion of the development of common prosperity. Plus, total factor productivity enhances the relationship between digital economy and common prosperity. The paper reveals the mechanism and path of digital economy\u0026rsquo;s impact on common prosperity, and provides theoretical and policy implications for improving digital economy strategy and promoting high-quality development and common prosperity.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e","manuscriptTitle":"How does digital economy affect the development of common prosperity level?","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-02-07 10:52:52","doi":"10.21203/rs.3.rs-3923573/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":"f47d8ed6-3b35-4632-9f25-7be7ef1b2e6d","owner":[],"postedDate":"February 7th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-10-04T20:08:27+00:00","versionOfRecord":[],"versionCreatedAt":"2024-02-07 10:52:52","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-3923573","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3923573","identity":"rs-3923573","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}