The Impact of the Digital Economy on Innovation: New Evidence from Panel Threshold Model

: The digital economy has aroused widespread concern. This paper studies the impact of the digital economy on innovation using a panel threshold model. Taking 30 provinces, municipalities, and autonomous regions in China as the research object, the time span is from 2013 to 2019. The data are from the National Bureau of Statistics of China (NBSC), China National Intellectual Property Administration (CAIPA), the China Stock Market and Accounting Research (CSMAR), and the Ministry of Industry and Information Technology (MIIT)of China. Data analysis is performed with ArcGIS 10.2 and STATA 16 software. The inﬂuence mechanism of digital economy on innovation is innovatively analyzed from the aspects of innovation elements, innovation tools, innovation subjects, and innovation environment. A digital economy development level index system is constructed using the entropy method, and the development level of China’s digital economy in time and space is analyzed. On this basis, the nonlinear impact of digital economy on innovation, i.e., the threshold effect, is innovatively studied using the panel threshold model. It is found that China’s digital economy develops rapidly, but there is a serious spatial imbalance, and there are great differences in the different dimensions of the digital economy. At the same time, the impact of digital economy on innovation has a double threshold effect with industrial structure as the threshold variable and a single threshold effect with urbanization level as the threshold variable. Speciﬁcally, the promoting effect of digital economy on innovation increases with the optimization of industrial structure or the improvement of urbanization level. This study enriches the theoretical research on the impact of digital economy on innovation, and it has important support and reference value for China’s development of digital economy and improvement of innovation capacity.


Introduction
Digital technology has become an important driver of global economy development, and the digital economy has aroused widespread concern.The authoritative and representative definition of the digital economy is given by the United States (US), proposing that the digital economy includes infrastructure, e-commerce, and chargeable digital services [1].In 2019, the United Nations (UN) released its first study report about the digital economy, pointing out that the US and China play a leading role [2].The 2021 sustainable development goals (SDGs) report stated that fourth-generation Internet coverage doubled between 2015 and 2021, reaching 88% of the global population [3].UN pointed out that China and the US have the strongest participation in and ability to benefit from the digital economy [4].The Chinese president pointed out that "China attaches great importance to the development of digital economy, and is actively promoting digital industrialization and industrial digitalization, guiding the deep integration of digital economy and real economy, and promoting high-quality economic development" [5].In 2021, NBSC defined the digital economy [6].Governments and their research institutions have recognized the importance of developing the digital economy and have proposed its definition.Although there are some discrepancies in the definition, the basic characteristics of the digital economy can be summarized as an economic activity, which takes digital technology as the core power and takes data resources as the core production factors.
The United Nations sustainable development goal (SDG) 9 is to build risk-resilient infrastructure, promote inclusive and sustainable industries, and promote innovation [7].The 2021 sustainable development goals report stated that the COVID-19 pandemic has demonstrated the importance of scientific and technological innovation in building back better homes and achieving the SDGs [8].In the global innovation index report, China's ranking rose 10 places from 22nd in 2017 to 12th in 2021, ranking firmly at the top of the middle-income economies and one of the fastest-improving countries in the world [9].The Chinese president proposed the development of the digital economy as the main path for China's innovative growth [10].China is vigorously promoting innovation to promote the implementation of the sustainable development goals.As the world's second largest economy, China faces many problems in its economic and social development.However, the dynamic digital economy has given new impetus to China's innovative development.Mambetova et al. proposed that the digital economy provides a systematic method for the development of tourism information technology [11].Hojeghan and Esfangareh demonstrated the impact of the Internet and web technologies on tourism [12].The digital economy has not only affected and changed the traditional industrial organization and operation mode profoundly, but also restructured the market economic system, optimized the allocation of resources, promoted the cross-border integration of entrepreneurship and innovation between digital technology enterprises and traditional enterprises, and expanded the development space of the consumer market.These are the great innovative effects brought by the digital economy.The innovation in this paper is in the narrow sense and focuses on innovation output.
The digital economy and innovation have attracted wide attention from academia and industry.Sultana et al. proposed a systematic process for data-driven innovation [13].Wang and Cen proposed that digital economy promotes innovation efficiency [14].Most scholars agree that the digital economy has a positive influence on innovation.However, the current measurement standards of digital economy are not unified, the research on the impact of digital economy on innovation is not deep enough, and there is a lack of systematic analysis of the impact mechanism and whether the impact of digital economy on innovation will show a threshold effect.These problems will lead to the underestimation or overestimation of the development status of digital economy, which hinders the digital economy's drive for innovation.This is not conducive to innovation and SDGs.
The motivation of this research is to clarify the impact of the digital economy on innovation.This study attempts to provide reference for China to develop the digital economy, enhance innovation capacity, and achieve the SDGs.Research on the impact of digital economy on innovation should focus on the current situation of China's digital economy development, the influence mechanism of digital economy on innovation, and whether there is threshold effect.Aiming at the above problems, the impact mechanism of digital economy on innovation is explained systematically from the aspects of innovation factors, innovation tools, innovation subjects, and innovation environment.The digital economy development level index system is constructed using the entropy method from the digital economy infrastructure, digital economy industry support, and digital economy application level.ArcGIS 10.2 software is used to visualize and analyze the digital economic development level innovatively of China.The panel threshold model is adopted to analyze the threshold effect of digital economy on innovation innovatively by taking industrial structure and urbanization level as threshold variables.This study enriches the theory of digital economy driving innovation, as well as facilitates the digital economy in China, the construction of a modern economic system, and the integration of innovation and digital economy.The innovation of this research reflects the following points: firstly, the influence mechanism of digital economy on innovation is analyzed from the aspects of innovation factors, innovation tools, innovation subjects, and innovation environment; secondly, the panel threshold model is used to study the threshold effect of digital economy on innovation.

Literature Review
This paper reviews the relevant research results from the measurement of the digital economy, the measurement of innovation, and the impact of digital economy on innovation, which lays a certain theoretical foundation and reference for the study of the impact of digital economy on innovation.

Measurement of Digital Economy
The index system of digital economy and society constructed by the European Union includes network connectivity, human resources, network applications, digital technology integration, and digital public services [15].The NBSC did not measure the digital economy, instead simply providing a classification of digital economy industries [6].The China Academy of Information and Communication Technology (CAICT) calculated the scale of China's digital economy from digital industrialization and industrial digitization [16].
Benčič et al. believed that the competitiveness of the digital economy is based on the high integration of information and communications technology (ICT) and equipment [17].Krieva et al. found that factors such as the digital skill level and the information and communication infrastructure play a decisive role in Russia's digital economy [18].Domazet and Lazić proposed that ICT is a factor affecting the competitiveness of the digital economy [19].Suska proposed that e-commerce is one of the basic pillars of the digital economy, and Poland and other EU countries have made significant progress in digital development, but the development of the e-commerce market is still unbalanced among EU member states [20].Research institutions and scholars have carried out substantial research on the measurement of digital economy, which provides the corresponding theoretical and methodological basis for this paper.
When measuring the digital economy, scholars have a different understanding of the digital economy and different concerns, leading to large discrepancies in the measurement results.However, the measurement of the digital economy basically includes the digital economic infrastructure, digital technology, digital industry, and digital application, and it is recognized that information and communications technology, ICT industry, e-commerce, and other important factors influence the development of the digital economy.This paper constructs the digital economy development level index system from the perspectives of the digital economy infrastructure, digital economy industrial support, and digital economy application level, measures the digital economy, and conducts a spatiotemporal analysis.

Measure of Innovation
China established an innovation capability system to monitor the whole country and all provinces and regions [21].Gault combined the definition of innovation applicable to all economic sectors with system approach to develop a conceptual framework for the statistical measurement of innovation [22].Garcia-Granero et al. divided the 30 commonly used enterprise innovation indicators into four types of green innovation [23].Janger et al. proposed a broader set of innovation outcomes indicators, finding that the measurement results of this indicator are quite different in many countries [24].
Bittencourt et al. measured cluster innovation capability from the aspects of acquisition capability, diffusion capability, and knowledge management capability [25].Chen et al. measured and ranked the urban innovation capacity of Liaoning Province from three dimensions of innovation input, innovation output, and innovation environment [26].According to the theory of regional innovation, Shan used the analytic hierarchy process (AHP) to construct the evaluation system [27].Pei et al. proposed a model to evaluate urban innovation capability using machine learning [28].Aiming at the shortcomings of traditional regional innovation capability evaluation methods, Wang et al. proposed a method to evaluate innovation on the basis of the backpropagation neural network [29].
There have been a series of studies on innovation measurement.The relevant research of scholars can provide the corresponding theoretical and methodological support for the research on innovation measurement.When constructing the innovation level index system, scholars mainly used the synthetic index method or analytic hierarchy process to determine the index weight, but the focus of research differed, and there were great differences in the division of innovation dimensions.Some scholars also used machine learning and neural network methods to measure innovation.The innovation in this paper focuses on the innovation output level.The entropy method is applied to weight each index within the innovation level to calculate the innovation index.

The Impact of Digital Economy on Innovation
Syrova considered the possibility of improving the efficiency of innovative activity identification and risk management through digital technologies [30].Wen found that digital platform capability can promote innovation performance [31].Hakesbrink and Schroll demonstrated that the digital economy is one of the pioneers of open innovation [32].Ding et al. proposed that the digital economy promotes high-quality economic development through the mediating role of technological innovation [33].Veselovsky et al. studied the function of end-to-end technology in Russia's economic development and the promotion of corporate innovation activities [34].Yousaf et al. believed that digital orientation, the Internet of things, and digital platforms are important prerequisites for sustainable digital innovation [35].Li et al. proposed that the digital economy improves the green economy through technological innovation [36].
According to the above literature review, most of the existing studies focused on the impact of digital technologies and digital platforms on innovation.The impact mechanism of the digital economy on innovation is not clear, and the relevant theories are not sufficient.Therefore, it is extremely urgent to carry out empirical research on the impact of the digital economy on innovation.Unlike previous studies, this paper systematically explores the impact mechanism of digital economy on innovation, empirically analyzes the threshold effect of digital economy on innovation using the panel threshold model, and proposes that the impact of digital economy on innovation has the effect of industrial structure and urbanization level as the threshold.

Panel Threshold Model
In recent years, the panel threshold model has been used by many scholars to evaluate the effects.Akram and Rath studied the relationship between optimal government size and economic growth using the panel threshold model [37].Ostadzad used a fixedeffects panel threshold model to explore whether innovation has the same impact on CO 2 equivalent per capita in EU countries [38].Ouyang et al. studied the nonlinear effects of environmental regulation and economic growth on PM2.5 based on panel threshold analysis [39].Shao used a threshold model to explore the impact of marine growth and patents on pollution [40].Forson et al. analyzed the contribution of innovation to economic growth using the panel threshold model [41].Polemis and Stengos assessed the impact of competition on industrial toxic pollution using the panel threshold model [42].Molla and Rahaman studied the threshold effect of R & D expenditure on bank performance [43].Khan et al. conducted a threshold analysis of the economic freedom on finance in developing economies [44].The above scholars' application of the panel threshold model provides a basis for this empirical study.

Hypothesis Development
The improvement in innovation level is inseparable from the interaction among innovation factors, innovation subjects, innovation tools, and innovation environment.Thanks to that foundation, the influence mechanism is proposed, as shown in Figure 1.

Hypothesis Development
The improvement in innovation level is inseparable from the interaction among innovation factors, innovation subjects, innovation tools, and innovation environment.Thanks to that foundation, the influence mechanism is proposed, as shown in Figure 1. The development of the digital economy enriches the innovation elements.Under the support of the digital economy infrastructure and digital economy industry, more and more economic activities are transformed from a traditional economy to a digital economy, which promotes the rise in the digital economy application level.The rise in the digital economy application level generates massive data, and these massive data can be quickly transferred to the innovation subject through the digital economy infrastructure and digital economy industry support.Through the sifting, processing, and mining of data, these data are transformed into important resources for scientific and technological innovation and become new production factors, which further enrich the innovation elements. The digital economy makes innovation tools digital.With the development of the digital economy, such as the Internet of things, artificial intelligence, 5G, and metaverse, innovation subjects can rely on advanced digital technologies to carry out innovation activities.At the same time, information flow, capital flow, and technology flow are transmitted in a digital way, which improves the efficiency of innovation. The digital economy has eliminated the spatial and temporal distance of innovation subjects.With the evolution of the digital economy, an innovation network is established among innovation subjects, innovation resources and innovation elements are shared, and the goal of collaborative development and rift innovation integration among innovation subjects is realized.In this way, the R&D cycle is shortened, the R&D efficiency and resource allocation efficiency are improved, and the innovation efficiency is improved.Digital technology enhances the ability of the innovation subject to obtain real-time information and reduces the communication cost, information search cost, negotiation cost, and time cost, thereby reducing the innovation cost. The growth of the digital economy has optimized the environment for innovation.
The digital economy has given birth to the explosive growth of data.The rapid growth of massive data has put forward new requirements for economic activities, changed the development concept, products and services, business models, industrial forms, and factor allocation, and thoroughly optimized the internal and external environment of innovation, thus promoting the innovation level.

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The growth of the digital economy has optimized the environment for innovation.The digital economy has given birth to the explosive growth of data.The rapid growth of massive data has put forward new requirements for economic activities, changed the development concept, products and services, business models, industrial forms, and factor allocation, and thoroughly optimized the internal and external environment of innovation, thus promoting the innovation level.
Metcalfe's law points out that the square of the number of connected users in the system is equal to the benefit of the telecommunication network [45].Moore's law states that the performance of components and circuits available on a given number of integrated circuits will double every 18-24 months when the price is constant [46].The Davidow effect shows that enterprises must upgrade their products to survive in the industry if they want to dominate the market [47].Yang et al. (2021) believed that the digital economy follows Metcalfe's law, and they analyzed the promoting role of the digital economy in the poverty alleviation policy of high-quality cultural tourism on this basis [48].Qi and Xu put forward that, thanks to Moore's Law, the digital economy can develop rapidly; hence, it should have a new innovation direction in the post-Moore era [49].Considering that the digital economy conforms to the above rules, the impact of the digital economy on innovation may be nonlinear.Are Metcalfe's law and the Davidow effect also true in the digital economy driving innovation?Through mechanism analysis in Table 1, it can be known that the digital economy can comprehensively promote the overall rise in innovation level by enriching innovation resources, improving innovation efficiency, reducing innovation costs, and optimizing the innovation environment.As the digital economy booms, the marginal cost of digital economy infrastructure and digital economy industrial support continues to decrease, the level of digital application increases exponentially, and the benefit obtained by innovative subjects increases geometrically.Moreover, this effect is enhanced with digital economy development, such that the improvement in innovation level becomes more significant.That is, does the digital economy have a threshold effect on innovation?Further research is needed.

Method
Firstly, the digital economy development level index system is constructed, and the entropy method is used to determine the index weight.Then, the panel threshold model of digital economy and innovation is constructed.Lastly, the variables in the constructed model are determined.

Index Selection
The definitions of digital economy differ; however, it can be considered an economic activity with data resources as the production factor and digital technology as the core power, as explained in Section 1.The measurement-related research of the digital economy was outlined in Section 2. The measurement of the digital economy basically includes digital economic infrastructure, digital technology, digital industry, and digital application, mainly using the index system method.According to the characteristics of the digital economy and the research results of previous scholars, a two-level system is constructed from the digital economy infrastructure, digital economy industrial support, and digital economy application level.In accordance with the principles of comprehensiveness, hierarchy, comparability, scientificity, operability, fairness, and dynamism, and combined with the availability of data, a digital economy indicator system is constructed, as shown in Table 1.China's digital economy is analyzed spatiotemporally.The measurement results lay a foundation for the empirical analysis of the threshold effect of digital economy on innovation.
Digital infrastructure is the foundation of the digital economy, and the focus is to ensure economic growth on the basis of the development of high-tech digital infrastructure [50].Therefore, the number of Internet broadband access ports, Internet broadband access users, mobile phone switch capacity, number of business outlets, long-distance optical cable line length, etc. are measured with respect to the digital economy infrastructure.With the deepening of digitalization, it mainly relies on information transmission and software to enable people to use digital services and economic activities on the Internet.Al-Sartawi discussed the impact of artificial intelligence and computational intelligence from the aspects of economics, finance, sustainability, network security, and knowledge management [51].Shokiraliyevich explored the role of ICT in the digital economy [52].Therefore, the total amount of telecom business, relevant indicators of software enterprises, the number of websites owned by enterprises, and other indicators are used to express the digital economy industrial support.It is generally agreed that e-commerce should be included in digital economy accounting [53,54].Therefore, the digital economy application level is measured by the indicators closely related to e-commerce, such as express business volume, e-commerce purchase amount, sales volume of e-commerce, the number of enterprises with e-commerce transaction activities, and express business income.

Indicator Weight Determination
After constructing the digital economy development level index system, the weight of each index is determined.For the determination of index weight, the more commonly used methods are AHP, coefficient of variation, and entropy.The entropy method assigns weight to the index according to mathematical theory; thus, it can objectively reflect the information of the original data.
Tutak and Brodny adopted the entropy method to evaluate the maturity level of European business digitalization [55].Busu and Busu used an algorithm based on the entropy method to evaluate the circular economy process in the European Union (EU) [56].Zachary and Dobson took Sheffield City in the UK as an example and applied the entropy method to establish the urban diversity index, which provided a method for assessing the "mixture" of green and urban space in the process of urban expansion and development [57].Therefore, the entropy method is utilized to determine the index weight.
The traditional entropy method is more suitable for determining the index weight of cross-section data, whereas, for panel data, the traditional entropy method needs to be improved.One approach is to add weights over the study period.The principle is to measure the information difference of the sum.The other is to find a weight for each indicator of panel data every year, and then take the weighted average of the weights of each indicator for many years as the final weight.In order to ensure the consistency of index weights among different years and comparability among different years, the first treatment is adopted to improve the entropy method by adding time variables.The model is described below.
X represents the indicator variable, θ represents the year θ, i represents the province i, and j represents the indicator j.
The panel data are first normalized.
A θij = X θij /X max (positive indicator). (1) Because all indicators in the digital economy index system constructed are positive indicators, Equation (1) was used to normalize the panel data from 2013 to 2019.
The indicators are standardized.The variables are summed for the same province in different years.
The information entropy is calculated.
The index weight is calculated.
The comprehensive score of the digital economy development level is calculated.

Model
For exploring the nonlinearity of the impact of digital economy on innovation, the threshold model established by Hanse (1999) [58] was used for reference.Relevant studies have shown that it is appropriate to use threshold model to study the impact of digital economy on innovation [59,60].Panel threshold models can be divided into single-threshold panel models and multiple-threshold panel models.The single-threshold panel model and double-threshold panel model are often applied in economic empirical analysis.
The expression of the single-threshold panel model is shown in Equation (11).
The expression of the double-threshold panel model is shown in Equation (12).
In Equations ( 11) and ( 12), the dependent variable Y it represents innovation, δ 0 is a constant term, X is the core explanatory variable digital economic development level, θ represents the threshold variable, I represents an index function, and γ is the threshold value to be estimated.If θ satisfies the corresponding requirement of γ, it takes the value of 1; otherwise, it takes the value of 0. Z is the other control variable, i is the province, t is the time, µ i is the individual disturbance term, and ε it is the random disturbance term.
The basic steps of panel threshold model estimation are as follows: first, it is checked whether there is a threshold value; if not, it is terminated, indicating that it is not applicable to the threshold model.If a threshold exists, the threshold value is estimated.On the basis of the threshold value calculation, the different stages divided by the threshold value are regressed.Combined with the actual economic significance, the change of the coefficient in the threshold value is analyzed.
The principle of threshold value estimation is described below.
First, the threshold variable γ as a known variable is estimated using the least squares method to estimate; then, the minimum value of S1(γ) is determined, and the estimate value of the threshold value γ is obtained.
The statistic F is used to test whether there is a threshold value.
where σ 2 = S 1 /n(T − 1), S 0 is the sum of squares of OLS residuals when the threshold effect does not exist, S 1 is the sum of squared residuals in the presence of some threshold value, N is the number of samples, and T is the time.
The empirical distribution of F is obtained by taking the sample individuals as the population and conducting repeated sampling with retractions.Fj = F1, F2, . . .p-value = (number of times F j is greater than F 0 )/the sampling frequency. ( Generally speaking, when the p-value is less than 0.05, the null hypothesis is rejected, indicating that the threshold effect exists; otherwise, the null hypothesis is accepted, indicating that the threshold effect does not exist, and the next step cannot be carried out. Since the previously calculated γ is a point estimator, combined with LR statistics and Hansen's fixed usage data, as long as the calculated value of LR(γ) is in the non-rejection domain of the confidence interval, it meets the requirements.

Variables
Dependent variable.Innovation level.The innovation level is measured by the number of patents.Caragliu and Del Bo used the total number of patent applications submitted by cities to calculate urban innovation output [61].Argente et al. found that, although patents and citations could not measure R & D success or failure well, patents and citations were the essence of innovation [62].Mann and Loveridge agreed that patents can provide a reasonable measurement standard for the innovation activities of urban institutions [63].Zemtsov and Kotsemir applied data envelopment analysis (DEA) to evaluate the relationship between patent results and regional innovation system (RIS) resources [64].It can be seen that patent as a measure of innovation level has been recognized by many scholars.Therefore, the innovation output index system is constructed by the acceptance of invention, the acceptance of utility model, the acceptance of appearance design, design patent authorization, utility model patent authorization, invention patent authorization, technology market transaction volume, and new product sales revenue of industrial enterprises above the designated size.The entropy method is adopted to calculate the index weight, and the innovation level is calculated.
Core explanatory variable.Digital economy development level.According to the digital economy development level index system constructed in Table 1, the digital economy level is calculated using the entropy method.
Control variables.According to the Griliches-Jaffe knowledge production function, it can be seen that R & D personnel input and R & D capital input are two important factors affecting innovation [65].The positive correlation between innovation input and innovation performance has been recognized by scholars [66].Diebolt and Hippe believed that human capital should be a key factor in innovation and economic development [67].Raghupathi and Raghupathi analyzed the role of economic indicators in innovation at the national level [68].Therefore, R & D personnel input, R & D capital input, economic development level, and human capital reserve were selected as control variables.The R & D personnel input is represented by the full-time equivalent of R & D personnel.The R & D capital input is measured by the expenditure of R & D funds.The per capita GDP represents the regional economic development level within a certain period of time, and the average number of students per 100,000 population of ordinary colleges and universities is used to represent the human capital reserve.
Threshold variables.Relevant studies have shown that digital economy, innovation and industrial structure, and urbanization level have a certain relationship.Zhao proposed that the improvement of industrial institutions can promote the improvement in regional innovation efficiency and has a spatial spillover effect [69].Waldner found that the degree of business model innovation of enterprises affects innovation performance positively [70].Ciołek et al. studied the effect of urbanization degree on innovation activities at the regional level [71].Tripathi studied the impact of general urbanization and urbanization mode on different stages of regional innovation process, and found that general urbanization has accelerated each stage of the innovation process, while the impact of different urbanization modes on innovation varies with different stages [72].Therefore, the industrial structure and urbanization level were taken as threshold variables to conduct nonlinear analysis to explore the threshold effect of digital economy on innovation.
The threshold variables were set from the two aspects of industrial structure and urbanization level to explore the possible structural changes in the impact of digital economy on innovation.The proportion of added value of tertiary industry in GDP is used to express the industrial structure, and the proportion of urban population is used to express the urbanization level.The selection of variables is shown in Table 2.

Data Sources
Panel data of 30 provinces, municipalities, and autonomous regions in China (except Hong Kong, Macao, Taiwan, and Tibet) from 2013 to 2019 were selected for analysis.The data of the dependent variable came from the China Statistical Yearbook [73], China High-Tech Industry Statistical Yearbook [74], and public reports issued by CAIPA [75].The index variables in the digital economy development level index system were from the NBSC [73], CSMAR [76], and the MIIT [77].Specifically, indicators 2, 7, 10, 12, 13, and 14 in Table 1 were from CSMAR, indicators 8 and 9 were from the MIIT, and the remainder were from the NBSC.The threshold variable was from the NBSC [73], and the control variable was from China Statistical Yearbook [73].The logarithms of the control variables such as economic development level, R & D personnel input, R & D capital input, and human capital reserves were taken.

Results and Discussion
The digital economy and different dimensions of the digital economy in China were calculated according to the index weights calculated using the entropy method and the actual values of selected indicators.On this basis, the digital economy level was visualized using the GIS Natural Breaks (Jenks).GIS Natural Breaks (Jenks) is considered as an effective means of data visualization, which can show the spatial changes in data visually, and which has been adopted by many scholars [78,79].Therefore, the digital economy development level was graded using the GIS Natural Breaks (Jenks), and the data were visualized.The economic development of China was analyzed from two aspects of time and space.

The Overall Level of China's Digital Economy
In terms of time, the digital economy level increased significantly from 2013 to 2019.As shown in Figure 2, the overall digital economy level in China in 2013 was not high, and the digital economy in some provinces was outstanding, such as Guangdong, Jiangsu Province, Beijing, and Zhejiang, with the highest value only about 0.3.As shown in Figure 2, the digital economy in all administrative regions in China improved significantly in 2019, with Guangdong province rising to about 0.9, followed by Jiangsu, Zhejiang, Beijing, and Shandong, which reached about 0.5.Compared with the results of Fu et al.'s ranking of digital economy development in each province of China [80], this further shows that the digital economy development level index system is scientific and comparable.

Results and Discussion
The digital economy and different dimensions of the digital economy in China were calculated according to the index weights calculated using the entropy method and the actual values of selected indicators.On this basis, the digital economy level was visualized using the GIS Natural Breaks (Jenks).GIS Natural Breaks (Jenks) is considered as an effective means of data visualization, which can show the spatial changes in data visually, and which has been adopted by many scholars [78,79].Therefore, the digital economy development level was graded using the GIS Natural Breaks (Jenks), and the data were visualized.The economic development of China was analyzed from two aspects of time and space.

The Overall Level of China's Digital Economy
In terms of time, the digital economy level increased significantly from 2013 to 2019.As shown in Figure 2, the overall digital economy level in China in 2013 was not high, and the digital economy in some provinces was outstanding, such as Guangdong, Jiangsu Province, Beijing, and Zhejiang, with the highest value only about 0.3.As shown in Figure 2, the digital economy in all administrative regions in China improved significantly in 2019, with Guangdong province rising to about 0.9, followed by Jiangsu, Zhejiang, Beijing, and Shandong, which reached about 0.5.Compared with the results of Fu et al.'s ranking of digital economy development in each province of China [80], this further shows that the digital economy development level index system is scientific and comparable.In terms of space, China's digital economy development has already formed space correlation.As shown in Figure 2a, the provinces with good digital economy development in 2013 were randomly distributed across China, being relatively discrete.The two provinces with the highest levels of digital economy development were distant, namely, Guangdong and Jiangsu.Beijing, Zhejiang, Shandong, Shanghai, Liaoning, and Sichuan, which had lower levels than Guangdong and Jiangsu, are also scattered across China.As can be seen in Figure 2b, China's digital economy development formed a continuous state in 2019, with the provinces located in the central region of China in particular entering the 0.1-0.4echelon.Comparing Figure 2a,b, the digital economy showed a trend of gradually improving from north to south and from west to east, which indicates that the development level of China's digital economy was improving on a whole, but there were problems of unbalanced spatial development.The results of this study are similar to those of In terms of space, China's digital economy development has already formed space correlation.As shown in Figure 2a, the provinces with good digital economy development in 2013 were randomly distributed across China, being relatively discrete.The two provinces with the highest levels of digital economy development were distant, namely, Guangdong and Jiangsu.Beijing, Zhejiang, Shandong, Shanghai, Liaoning, and Sichuan, which had lower levels than Guangdong and Jiangsu, are also scattered across China.As can be seen in Figure 2b, China's digital economy development formed a continuous state in 2019, with the provinces located in the central region of China in particular entering the 0.1-0.4echelon.Comparing Figure 2a,b, the digital economy showed a trend of gradually improving from north to south and from west to east, which indicates that the development level of China's digital economy was improving on a whole, but there were problems of unbalanced spatial development.The results of this study are similar to those of some scholars [81,82], further showing that the index system constructed in Table 1 is scientific.

The Development Level of China's Digital Economy Different Dimensions
On the basis of the analysis of the overall level of digital economy development in China, the digital economy infrastructure, digital economy industrial support, and digital economy application level in China were analyzed.Jiang and Murmann compared ecommerce and Internet-based services in the digital economy, arguing that China still lags behind the US in terms of Internet penetration, but China has built a mobile-first, fiber-intensive, and inclusive digital infrastructure [83].As shown in Figure 3, the different dimensions of digital economy in the same province were quite different.Guangdong, Sichuan, and Jiangsu had the best development in terms of digital economy infrastructure in 2019, ranking 0.7-1.Zhejiang, Shandong, Henan, Hebei, Hunan, and Anhui were in the second tier of digital economy infrastructure, at 0.4 to 0.7.Guangdong, Jiangsu, Beijing, Shandong, Shanghai, and Zhejiang had the best development in terms of the digital economy industrial support, while Sichuan, Fujian, Hubei, Liaoning, Chongqing, Shaanxi, Henan, Anhui, Hunan, and Hebei were in the second tier.Guangdong was the most developed province in the digital economy application level, while Zhejiang, Shanghai, Beijing, Jiangsu, Shandong, Fujian, Sichuan, Anhui, Hubei, Henan, and Hunan were in the second tier.Although the digital economy was obviously improved, the various dimensions of digital economy in the province were not balanced, and there were big disparities.some scholars [81,82], further showing that the index system constructed in Table 1 is scientific.

The Development Level of China's Digital Economy Different Dimensions
On the basis of the analysis of the overall level of digital economy development in China, the digital economy infrastructure, digital economy industrial support, and digital economy application level in China were analyzed.Jiang and Murmann compared e-commerce and Internet-based services in the digital economy, arguing that China still lags behind the US in terms of Internet penetration, but China has built a mobile-first, fiberintensive, and inclusive digital infrastructure [83].As shown in Figure 3, the different dimensions of digital economy in the same province were quite different.Guangdong, Sichuan, and Jiangsu had the best development in terms of digital economy infrastructure in 2019, ranking 0.7-1.Zhejiang, Shandong, Henan, Hebei, Hunan, and Anhui were in the second tier of digital economy infrastructure, at 0.4 to 0.7.Guangdong, Jiangsu, Beijing, Shandong, Shanghai, and Zhejiang had the best development in terms of the digital economy industrial support, while Sichuan, Fujian, Hubei, Liaoning, Chongqing, Shaanxi, Henan, Anhui, Hunan, and Hebei were in the second tier.Guangdong was the most developed province in the digital economy application level, while Zhejiang, Shanghai, Beijing, Jiangsu, Shandong, Fujian, Sichuan, Anhui, Hubei, Henan, and Hunan were in the second tier.Although the digital economy was obviously improved, the various dimensions of digital economy in the province were not balanced, and there were big disparities.According to the characteristics of the digital economy and considering the availability of data, a digital economy index system was constructed, and the index weight was determined using the entropy method.The digital economy level in China was measured.
On this basis, the development level of China's digital economy was analyzed from two aspects of time and space, and the measurement results were compared with others.This verifies the accuracy of the measurement results of the digital economy development level and lays a foundation for empirical research on the threshold effect of digital economy on innovation.

Threshold Existence Test
The industrial structure and urbanization level were taken as the threshold variables, and the innovation index was taken as the dependent variable to analyze the threshold effect of digital economy on innovation.The bootstrap method was used to repeat sampling 500 times to obtain the threshold effect test results, as shown in Table 3.The threshold effect of digital economy on innovation with industrial structure as the threshold variable was tested.As can be seen in Table 3, when the industrial structure was the threshold variable, the F-statistics of the single-threshold and double-threshold tests were 152.110 and 62.360, respectively, with p-values of 0.000, indicating a double-threshold effect of the digital economy's impact on innovation.
When the threshold variable was urbanization level, the single-threshold and doublethreshold effects of digital economy on regional innovation were tested.As shown in Table 3, when the threshold variable was urbanization level, the F-statistics corresponding to the single-threshold and double-threshold effect test of digital economy on innovation were 152.520 and 23.600, respectively, and the corresponding p-values were 0.000 and 0.164.According to the p-value, there is a single-threshold effect of digital economy on innovation with urbanization level as the threshold variable, which passes the significance test at the level of 1%, but there is no double-threshold effect.

Estimation of Threshold Value
The results of the threshold existence test manifested that the impact of digital economy on innovation is nonlinear.Specifically, the influence of digital economy on innovation had the nonlinear characteristic of a double threshold with industrial structure as the threshold variable.The impact of digital economy on innovation had a single threshold nonlinear feature with urbanization level as the threshold variable.
After determining the threshold effect of the digital economy on innovation with industrial structure and urbanization level as threshold variables, the threshold values of industrial structure and urbanization level were estimated.As illustrated in Table 4, when the threshold variable was industrial structure, the estimated values of the double threshold were 52.400 and 54.500.Therefore, when the threshold variable was industrial structure, it is appropriate to use the double-threshold panel model to analyze the impact of digital economy on innovation.As shown in Table 4, when the threshold variable was urbanization level, the single-threshold estimate value was 70.610.Therefore, when the threshold variable was urbanization level, it is appropriate to use the single-threshold panel model to analyze the impact of digital economy on innovation.

Analysis of Threshold Regression Results
According to the estimation result of threshold value, the threshold effect of digital economy on innovation was analyzed.In Table 5, models (1) and ( 2) are the regression results of the impact of digital economy on innovation with industrial structure and urbanization level as the threshold variables, respectively.According to model (1) in Table 5, when the industrial structure was less than 52.4%, the influence coefficient of digital economy on innovation was 0.083; for 52.4% < industrial structure ≤ 54.5%, the influence coefficient was 0.112; when the industrial structure was higher than 54.5%, the coefficient of digital economy was 0.161.These influence coefficients were all significant at the 1% level.It can be seen that with the improvement in industrial structure, the impact of digital economy on innovation was gradually enhanced.This illustrates that innovation promoted by the digital economy has obvious faults in China.When the industrial structure index is not high, the driving effect of digital economy on innovation is very small.When the industrial structure index reaches a relatively high level, the digital economy releases its driving effect on innovation.The reason may be that, when the industrial structure level is low, the development level of digital economy itself is not high; thus, it cannot play a driving role in innovation.When the industrial structure level is high, the integration of the digital economy and traditional industries is closer, the level of digitalization and informatization is high, and the innovation resources are richer.Furthermore, a high industrial structure promotes the flow of innovation factors [84], thus driving the improvement of innovation level.In addition, the optimization of the industrial structure, especially the development of the tertiary industry, provides a better platform for the digital economy to drive innovation.
According to model (2) in Table 5, digital economy has a significant nonlinear and differentiated impact on innovation, which is affected by the level of urbanization.When urbanization was less than 70.61%, the coefficient of the digital economy's impact on innovation was 0.120, passing the significance test at the 1% level.When the urbanization level was greater than 70.61%, the impact coefficient was 0.176, which also passed the significance test at the 1% level.This manifests that the driving force of the digital economy for innovation requires a high level of urbanization.In order for the digital economy to play the role in promoting innovation, it is not enough to develop the digital economy; it is also necessary to improve the level of urbanization.An increase in urbanization level represents an increase in the agglomeration level of manpower, capital, and technology, which provides the soil for innovation, thereby stimulating the driving effect of digital economy on innovation.
Relying on the Hanse threshold model, this paper analyzed the threshold effect of the digital economy on innovation with industrial structure and urbanization level as the threshold variables.It was found that digital economy has a double-threshold effect with industrial structure as the threshold variable and a single-threshold effect with urbanization level as the threshold variable on innovation.With the increase in industrial structure index and urbanization level index, the actuating effect of the digital economy on regional innovation would also rise.

Endogeneity Discussion and Robustness Tests
In the model part of this paper, the possible endogeneity problems were preprocessed accordingly.Considering the endogeneity problems brought about by the omitted variables to model estimation, the possible omitted variables were controlled for in the model.For example, factors affecting innovation such as R & D personnel input, R & D capital input, economic development level, and human capital reserve were taken into account in the model.
The endogeneity issue was solved by using the dynamic panel threshold model for re-estimation.To address the endogeneity of the threshold model, Caner and Hansen proposed the two-stage least squares (2SLS) and generalized method of moment (GMM) estimation methods for threshold parameters for cross-sectional data containing endogenous explanatory variables and exogenous threshold variables [85].In order to solve the endogeneity in the static threshold panel regression model, Seo and Shin extended the model to the dynamic panel threshold model (DPTM) [86].The DPTM was used to reduce the endogeneity problem caused by model setting bias.Compared with the regression results, the estimation results based on the DPTM did not change significantly, further indicating the validity of the research conclusions of this paper.
To further enhance the robustness of the research results, a robustness test was conducted on the sample data.The modified sample size method was used to check the robustness.The development level of different regions in China is quite different.The selected sample was simplified, and four autonomous regions in the sample were eliminated.The new panel data samples were obtained, and the model was re-estimated to eliminate as best as possible the adverse effects brought about by the outliers and non-randomness of the sample data on the results of the econometric regression.Compared with the regression results above, there was no noticeable change in the estimation results based on the reduced sample, further indicating the robustness of the research results.

Conclusions
The research aim was to explore whether the impact of the digital economy on innovation has nonlinear features.The following goals were targeted to address this aim: to determine the development status of China's digital economy, the influencing mechanism of digital economy on innovation, and whether the digital economy has a threshold effect on innovation.Some conclusions were drawn.Firstly, although the digital economy overall level in China is increasing gradually, there are serious problems such as unbalanced development and large differences in the development level of different dimensions of the digital economy in the same region.Secondly, the digital economy has a double-threshold effect with industrial structure as the threshold and a single-threshold effect with urbanization level as the threshold.With the adjustment of industrial structure and urbanization, the influence coefficient of digital economy on innovation increases.
The theoretical significance of this research is reflected in it enriching the relevant theories of digital economy measurement; the study on the threshold effect of digital economy on innovation also addresses gaps in the theory of the nonlinear influence of digital economy on innovation.The practical significance is that it provides a basis and reference for relevant administrative departments in China to formulate policies to unleash the vitality of innovation driven by the digital economy, while also contributing to sustainable development.
Combining the above research results, some suggestions for China are proposed.While vigorously developing the digital economy, it is indispensable to formulate targeted and differentiated development strategies for the digital economy.Relevant departments could increase the investment in digital economy infrastructure and increase the digital economy industrial support in the central and western regions, so as to promote the digital economy application level.In view of the impact of digital economy on innovation, it was found to be affected by the threshold effect of industrial structure and urbanization level.The integration of digital economy and traditional industries should be strengthened to further optimize the industrial structure.Meanwhile, the process of urbanization should be actively promoted, and good circumstances for the digital economy to drive innovation development should be created, so as to fully release the driving role of the digital economy in innovation.
Due to limited knowledge and ability, there were still some shortcomings in the research.In analyzing the endogeneity of the impact of digital economy on innovation, the DPTM was adopted.At present, the discussion on the endogeneity of the panel threshold model is relatively concordant in adopting the dynamic panel threshold model, as proposed by Seo and Shin [86].However, this method is aimed at a single threshold in the dynamic panel threshold model.Therefore, when discussing the endogeneity problem, this paper discussed the endogeneity of a single threshold.A better way to test the endogeneity problem of a two-threshold static panel threshold model deserves further attention.

Figure 1 .
Figure 1.The influence mechanism of digital economy on innovation.

Figure 1 .
Figure 1.The influence mechanism of digital economy on innovation.•Thedevelopment of the digital economy enriches the innovation elements.Under the support of the digital economy infrastructure and digital economy industry, more and more economic activities are transformed from a traditional economy to a digital economy, which promotes the rise in the digital economy application level.The rise in the digital economy application level generates massive data, and these massive data can be quickly transferred to the innovation subject through the digital economy infrastructure and digital economy industry support.Through the sifting, processing, and mining of data, these data are transformed into important resources for scientific and technological innovation and become new production factors, which further enrich the innovation elements.• The digital economy makes innovation tools digital.With the development of the digital economy, such as the Internet of things, artificial intelligence, 5G, and metaverse, innovation subjects can rely on advanced digital technologies to carry out innovation activities.At the same time, information flow, capital flow, and technology flow are transmitted in a digital way, which improves the efficiency of innovation.• The digital economy has eliminated the spatial and temporal distance of innovation subjects.With the evolution of the digital economy, an innovation network is established among innovation subjects, innovation resources and innovation elements are shared, and the goal of collaborative development and rift innovation integration among innovation subjects is realized.In this way, the R & D cycle is shortened, the R & D efficiency and resource allocation efficiency are improved, and the innovation efficiency is improved.Digital technology enhances the ability of the innovation subject to obtain real-time information and reduces the communication cost, information search cost, negotiation cost, and time cost, thereby reducing the innovation cost.•Thegrowth of the digital economy has optimized the environment for innovation.The digital economy has given birth to the explosive growth of data.The rapid growth of massive data has put forward new requirements for economic activities, changed the development concept, products and services, business models, industrial forms, and factor allocation, and thoroughly optimized the internal and external environment of innovation, thus promoting the innovation level.

Figure 2 .
Figure 2. Digital economy development level change: (a)digital economy development level in 2013; (b) digital economy development level in 2019.

Figure 2 .
Figure 2. Digital economy development level change: (a) digital economy development level in 2013; (b) digital economy development level in 2019.

Figure 3 .
Figure 3. Development level in different dimensions of digital economy in 2019: (a) digital economy infrastructure; (b) digital economy industrial support; (c) digital economy application level.

Table 1 .
Digital economy development level index system.

Table 4 .
Threshold estimates and confidence intervals.

Table 5 .
Threshold effect regression results.