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Abstract

Using the panel data of China’s 286 prefecture-level cities from 2011 to 2019, this paper explores the causal relationship between digital economy and urban innovation ability by panel vector auto-regression (PVAR), examines the spatial and dynamic effects of digital economy on urban innovation ability by spatial dynamic panel Durbin (SDPD) model, and studies the nonlinear effects of digital economy on urban innovation ability under different external environments using threshold spatial dynamic panel (TSDP) model. The results show that: (a) The urban innovation ability has significant spatial dependence and presents a U-shaped evolution trend. (b) In the short term, the digital economy has a positive impact on urban innovation ability, both directly and indirectly; in the long term, only the indirect effect of the digital economy remains significantly positive. (c) In different external environments, the impact of digital economy on urban innovation ability is nonlinear and has significant external environmental threshold characteristics. Specifically, the digital economy is more conducive to the improvement of urban innovation ability with a moderate degree of marketization; the effect of digital economy empowering urban innovation ability is better in a good legal environment or technological environment.

Plain language summary

Facing the great changes in the world such as the COVID-19 epidemic and the Russian-Ukrainian war, the rise of digital economy has prompted cities in China to carry out digital transformation, creating favorable conditions for improving urban innovation ability. However, while using the digital economy as a new engine to promote high-quality economic development, problems such as development imbalance, governance dilemmas, and digital divide have gradually emerged. In the context of the “New Normal” of China, can digital economy supported by information technology become a new driving force for improving urban innovation ability? With the development of the Internet and information technology, the spatial mobility of innovation resources has become more frequent and convenient. Is there a certain spatial rule in the impact of the digital economy on urban innovation ability? Resource endowment, marketization process, financial and technological support may often differ among cities. Is the digital economy empowering urban innovation ability non-linear due to the differences in the external environment? Clarifying the above issues has important practical significance for grasping the “digital opportunities” in the digital economy era and effectively promoting urban innovation ability. Based on the panel data of 286 prefecture-level cities in China from 2011 to 2019, this paper explores the causal relationship between digital economy and urban innovation ability by Panel Vector Auto-Regression (PVAR), examines the spatial and dynamic impacts of digital economy on urban innovation ability by Spatial Dynamic Panel Durbin (SDPD) model, and analyzes the nonlinear impacts of digital economy on urban innovation ability under different external environments by Threshold Spatial Dynamic Panel (TSDP) model.

Keywords

digital economy nonlinear effect urban innovation ability threshold spatial dynamic panel model

Introduction

According to the data from the China National Intellectual Property Administration, China has ranked first in the world in 2019 with a total of 4.333 million patent applications (Dai & Chapman, 2022). However, among these patents, only 32% are invention patents known for their technical content, and the implementation rate and industrialization rate of effective invention patents are only 49.4% and 32.9%. This means that the process of innovation-driven and high-quality development is greatly hampered by China’s patents, which keep being in the embarrassing predicament of “higher quantity and lower quality” (Liang et al., 2021). At the same time, digital technologies, including blockchain, big data, Internet and Internet of Things, have become ubiquitous in both production and life, indicating the arrival of the digital era. As a result, the digital economy has emerged as a crucial driver of high-quality, innovation-driven development high-quality, innovation-driven development. (Ren & Li, 2022; Zhao et al., 2020). According to the White Paper on the Development of China’s Digital Economy published by the China Academy of Information and Communications Technology (CAICT), the total size of the Chinese digital economy was 31.3 trillion yuan in 2018, accounting for 34.8% of the country’s GDP; by 2020, this figure had increased to 39.2 trillion yuan, accounting for 38.6% of GDP. The growth of the digital economy has had a significant influence on a number of sectors and industries within China’s national economy.

Cities have evolved into the primary places for innovation output and digital economy resources as they serve as the spatial carriers of innovation activity and the digital economy (Li & Yang, 2019). The initiative to increase cities’ capacity for innovation is intricate and systematic, and its primary goal is to boost the innovation vitality of businesses and other types of organizations so that they can truly take the lead in driving innovation. China’s urban structure has been transformed by the growth of the digital economy, resulting in the emergence of new first-tier cities like Hangzhou and Chengdu. These cities are largely associated with the rise of the digital economy. Therefore, to build an innovative country, it is crucial to conform the general trend of digital economy development, consolidate the basic conditions of urban innovative development, break through the bottleneck limitation of transformation, and achieve high-quality economic development. Additionally, the dynamic system and growth trajectory of China’s urban innovation have been significantly impacted by the rapid expansion of the digital economy, creating new prospects for enhancing urban innovation ability. Digital economic resources are concentrated in urban regional space, and when they extend to other cities, they initially help the local economy grow quickly and with high quality. In conclusion, it is very sensible and crucial to investigate how the digital economy affects innovation by taking cities as the research object.

Facing the great changes in the world such as the COVID-19 epidemic and the Russian-Ukrainian war, the rise of digital economy has prompted cities in China to carry out digital transformation, creating favorable conditions for improving urban innovation ability. However, as the digital economy being a new engine to promote high-quality economic growth, issues including development imbalance, governance conundrums, and digital divide have gradually surfaced (Zhao et al., 2023). In the context of the “New Normal” of China, can the information economy-supported digital economy serve as a new engine for enhancing urban innovation ability? Due to the advancements in the Internet and information technology, the spatial mobility of innovation resources has become more frequent and convenient. Is there a certain geographical rule governing how the digital economy affects urban innovation ability? Resource endowment, marketization process, and financial and technological support may often differ among cities. Is it nonlinear for the digital economy to enable urban innovation due to various external environments? Answering the abovementioned questions is crucial for grasping the “digital opportunities” in the digital economy era and enhancing the ability to promote urban innovation effectively.

To this end, this paper measures the urban innovation ability of China’s 286 prefecture-level cities, explores the causal relationship between digital economy and urban innovation ability by using panel vector auto-regression (PVAR), examines the spatial and dynamic impacts of digital economy on urban innovation ability by using spatial dynamic panel Durbin (SDPD) model, and explores the nonlinear impacts of digital economy on urban innovation ability under different external environments by using threshold spatial dynamic panel (TSDP) model. The marginal contributions of this paper are as follows. First, based on the realistic background of China, this paper develops a reasonable and feasible analytical framework to discuss the causal relationship between digital economy and urban innovation ability, and reveals the spatial and non-linear effect of digital economy empowering urban innovation ability. This not only provides empirical evidence at the city level, but also makes up for the lack of quantitative analysis in this field. Second, this paper explores the potential non-linear impact of the digital economy on urban innovation capacity, which furthers the relevant research by integrating external environment elements into the research framework. Third, combined with the research findings, the policy recommendations concerning “how to use better the digital economy to foster urban innovation ability” are put forward from the perspectives of government agencies, industry stakeholders, and city planners.

Literature Review

Digital Economy

The concept of digital economy first appeared in Tapscott’s (1996) book The Digital Economy: Promise and Peril the Age of Networked Intelligence during the American New Economic Period (Liu et al., 2022). Information technology and e-commerce may be used to characterize the early digital economy (Brynjolfsson & Kahin, 2000). With the widespread adoption of digital technology across different sectors of economy and society, the concept of digital economy has increasingly surpassed its previous boundaries. It becomes a new economic structure resulting from digital technology, with the features of digitalization and informatization (Li et al., 2021). Although the definition of digital economy is still controversial among academics, it has become an important standard to define the digital economy by taking knowledge, information and other digitized data as key factors of production (Li et al., 2022). Measurement of digital economy is a crucial component of quantitative analysis of digital economy. However, as the digital economy involves various walks of life and is not limited by geography, it is challenging to precisely measure the digital economy (Wang et al., 2022). Researchers have attempted to measure the digital economy from different dimensions using various methods, which has somewhat enriched the measuring system of digital economy (Xu & Zhang, 2020). The current calculation methods are mainly divided into two categories: “direct method” and “comparison method.” The direct method is to measure or estimate the total size of digital economy in different countries or regions within a defined accounting scope (Barefoot et al., 2018). The comparison method is to integrate various dimensions and levels to quantify the indicators of digital economic growth in different regions, and finally obtain the relative level of digital economy among regions through analysis and comparison (Liu et al., 2020; Zhao et al., 2020). Limited by the availability of data, academics mostly use comparison method to measure digital economy (Li & Wang, 2022). Subsequently, some researchers have started a discussion about the impact of the digital economy on economic and social progress. (Chen et al., 2022). At the macro level, it primarily concerns the impact of digital economy on economic growth (Ozili, 2018; Qian et al., 2020; Zhang et al., 2019), industrial restructuring and upgrading (Bai et al., 2021; Liu & Chen, 2021), total factor productivity (Guo & Liang, 2021; Pan et al., 2022; Yang & Jiang, 2021), regional innovation efficiency (Wen et al., 2020), and eco-environmental governance (Aaron & Jason, 2016; Guo et al., 2022). At the micro level, it mainly involves the digital economy’s price addition to firms (Bai & Yu, 2021), firm technology diffusion (Dang et al., 2021), firm R&D innovation (Hu & Yu, 2022; Jiang & Pan, 2022), resource allocation efficiency (Thompson et al., 2014), management model change, etc. (Caputo et al., 2019; Qi & Xiao, 2020).

Urban Innovation Ability

In the past few years, there has been an increasing number of researches on urban innovation ability. One of the important reasons is that competition in regional economic is increasingly focused on the city level, and urban innovation abilities are regarded as the key to the transformation to new from old economic engines and the upgrading of economic internal driving force (Wang et al., 2020). Distinguished from the mere quantitative growth of urban innovation, innovation ability reflects breakthroughs in technological innovation (Zhang et al., 2020). Currently, research on urban innovation ability can be summarized into the following three major aspects. (a) In terms of the measurement of urban innovation ability, despite varying generalizations among researchers regarding the definition of urban innovation ability, there is an increasing convergence in the research on the measurement of it (Bai & Jiang, 2015). (b) In terms of the improvement path of urban innovation ability, urban innovation ability is not only regionally heterogeneous, but also has differentiated path dependence (Gu & Shen, 2018). (c) In terms of influencing factors of urban innovation ability, government expenditure (Lu & Liu, 2015), institutional supply (Jin et al., 2019), environmental regulation (Chen & Liu, 2019; Zhao & Sun, 2016), intellectual property protection (Deng et al., 2019; Zhang, 2019a), tax policy (Cappelen et al., 2012), and industrial agglomeration (Ning et al., 2016) and other factors can all have a significant impact on urban innovation ability.

Digital Economy and Urban Innovation Ability

Although the digital economy and urban innovation ability are different fields of research, they share a common constraint: technological innovation, which has led some researchers to combine the two for research (Ma & Zhu, 2022). Related research is still in infancy, so the literature is few and focuses on the following three aspects. (a) Scientific and technical innovation is utilized as a bridge to explore the evolution of urban innovation ability (Zhang, 2019b) and the mechanism of the digital economy on urban innovation ability (Ding, 2020) from a theoretical level. (b) The digitalization and informatization characteristics of digital economy are fully utilized to empirically investigate the influence of Internet technology (Yousaf et al., 2021) and digital finance (Tang et al., 2020; Yao & Yang, 2022) on urban innovation ability. (c) The evaluation index system for digital economy development constructed at the provincial level is applied to test the influence of digital economy development on regional innovation level (Li et al., 2022), regional innovation intensity (Ding et al., 2022), etc. However, few researches have explored the spatial spillover effects and nonlinear effects of digital economy affecting urban innovation ability (Huang et al., 2022).

In addition, the relevant studies have the following shortcomings. First, owing to the availability of data, most of the researches are based on the provincial or regional (including city clusters) level. Therefore, it is necessary to refine the scale of research more precisely on the digital economy. Second, recent empirical researches neglect the spatial correlation between the growth of digital economy and the innovation ability of cities, leading to some bias in the results of empirical model. Finally, recent researches have not sufficiently considered the external environment, ignoring its effects on the relationship between the digital economy and urban innovation ability, including the degree of marketization and property rights.

Temporal and Spatial Characteristics of Urban Innovation Ability in China

Urban innovation ability is the capability of a city to transform knowledge, information and other resources into new technologies, new products, new processes, and new services (Li et al., 2020). The research sample for this paper consists of 286 prefecture-level cities in China, spanning from 2011 to 2019. And the patent authorization score, as indicated by the Index of Regional Innovation and Entrepreneurship in China (IRIEC), is used as the proxy variable to measure urban innovation ability. Note that the patent authorization score includes the newly increased invention patents score (50% weight), the newly increased utility model patents score (30% weight), and the newly increased design patents score (20% weight). The IRIEC is constructed by the Center for Enterprise Research (CER) of Peking University (https://opendata.pku.edu.cn) as an objective, real-time and multi-dimensional index to reflect the temporal and spatial distribution of innovation and entrepreneurship activities, utilizing administrative business enterprise registration database in China from 1990 to 2019 in combination with big data from other sources. This index mainly focuses on three core elements, i.e., entrepreneurship, capital, and technology, using the number of new enterprises, outside direct investment, venture capital investment, number of patents granted, and trademark registration, which can effectively reflect the vitality and performance of innovation of prefecture-level cities in China (Cheng & Zheng, 2023).

Temporal Characteristics

The average values and the coefficients of variation for urban innovation ability in China from 2011 to 2019 are shown in Figure 1. From 2011 to 2019, the urban innovation ability grows on average from 5.594 to 7.211, with an average annual growth rate of 3.23%, showing a consistent upward trend during the period. The coefficient of variation of urban innovation ability shows a decreasing trend.

Figure 1.

Temporal characteristics of urban innovation ability.

Spatial Characteristics

Global Moran’s I is used to reveal the spatial autocorrelation of urban innovation ability (see Equation 1). According to LeSage (2014), the non-geo-spatial weight matrix cannot accurately quantify the spatial effects, and the simple spatial weight matrix should be constructed as much as possible to describe the spatial connection of geographical units (Zhang & Yang, 2016). Two of the geo-spatial weight matrices are chosen: matrix based on geographic adjacency weight ( $W^{A}$ ) and that based on geographic distance weight ( $W^{D}$ ). The latter uses the inverse of the squared centroid distance of each city to describe the level of connection between spatial units (Shang et al., 2022). Note that the squared centroid distance between cities is measured by R language based on the electronic map at a scale of 1:4,000,000 provided by the National Platform for common Geospatial Information Services (http://www.ngcc.cn/ngcc).

MoranI = \frac{\sum_{i = 1}^{n} \sum_{j = 1}^{n} W_{ij} (Inn o_{i} - \bar{Inno}) (Inn o_{j} - \bar{Inno})}{\sum_{i = 1}^{n} W_{ij} {(Inn o_{i} - \bar{Inno})}^{2}}

(1)

where $W_{ij}$ denotes the row-normalized spatial weight matrix, $\bar{Inno} = \frac{1}{n} \sum_{i = 1}^{n} Inn o_{i}$ , and $Inn o_{i}$ denotes the innovation ability of city $i$ .

As shown in Table 1, the spatial autocorrelation test for urban innovation ability is consistently significant, regardless of whether the geographic adjacency or geographic distance weight matrix is used. Additionally, Moran’s I under both weight matrices is positive. It indicates that from 2011 to 2019, there is a significant positive spatial autocorrelation of urban innovation ability in China. In other words, a city’s ability for innovation is influenced by the cities around it.

Table 1.

Results of Spatial Autocorrelation Test.

Year	Urban innovation ability
Year	$W^{A}$	$W^{D}$
2011	0.082***	0.112***
2012	0.078***	0.107***
2013	0.075***	0.106***
2014	0.076***	0.110***
2015	0.082***	0.123***
2016	0.084***	0.130***
2017	0.092***	0.142***
2018	0.095***	0.147***
2019	0.095***	0.141***

***

Indicates significant at the 1% statistical level.

Research Design

Methodology

First, the panel vector auto-regression (PVAR) model is used for clearly exploring the causal relationship between digital economy and urban innovation ability. In PVAR model (Equation 2), all variables are considered endogenous and interrelated, both dynamically and statically (Abrigo & Love, 2016). This model can not only effectively address the issue of variable endogeneity (Wu & Zhao, 2019) but also accurately describe the shock response and variance decomposition between digital economy and urban innovation ability.

Y_{it} = Y_{i, t - 1} A_{1} + Y_{i, t - 2} A_{2} + \dots + Y_{i, t - (p - 1)} A_{p - 1} + Y_{i, t - p} A_{p} + f_{i} + g_{t} + ε_{it}

(2)

where $Y_{it}$ denotes the explained variables, including $k = 2$ dimensional vectors (digital economy and urban innovation ability). $f_{i}$ is an unobserved an unobserved intercept effect. $g_{t}$ and $ε_{it}$ denote the time effect and the random error, respectively.

Second, we use spatial dynamic panel Durbin (SDPD) model to explore the spatial effect of digital economy on innovation ability (Equation 3). The introduction of both explained and explanatory variables with spatial lags can help to alleviate the issue of omitted variables and effectively extracts the spatial effects of explanatory variables (Fischer & Nijkamp, 2020; LeSage, 2014). The model is as follows:

\begin{matrix} Inn o_{it} = τ \cdot Inn o_{i, t - 1} + ρ \cdot \sum_{j = 1}^{286} W_{ij} Inn o_{it} + β \cdot Digi t_{it} \\ + θ \cdot \sum_{j = 1}^{286} W_{ij} Digi t_{it} + λ X + μ_{i} + υ_{t} + ε_{it} \end{matrix}

(3)

where $i$ and $t$ denote city and year, respectively, and $j (j \neq i)$ denotes surrounding city. $Inn o_{it}$ is the explained variable “urban innovation ability,” $Inn o_{i, t - 1}$ is the first-order lagged term of the explained variable. $Digi t_{it}$ is the core explanatory variable “digital economy.”

Third, the threshold spatial dynamic panel (TSDP) model is used to explore the possible asymmetric and nonlinear effects of digital economy on urban innovation ability. Equation 3 can explore the homogeneous spatial effect of digital economy on urban innovation ability. To delve deeper into the asymmetric and nonlinear impacts of digital economy, the TSDP proposed by Wu and Matsuda (2021) is employed. This model is inspired by the threshold non-dynamic panel with fixed effects, allowing parameters $β$ for regressors $Digi t_{it}$ to switch between two groups (Hansen, 1999). Take the TSDP with a single threshold as an example.

\begin{matrix} Inn o_{it} = τ \cdot Inn o_{i, t - 1} + ρ \cdot \sum_{j = 1}^{286} W_{ij} Inn o_{it} + β_{1} \cdot I (E n_{it} \leq γ) Digi t_{it} + β_{2} \cdot I (E n_{it} > γ) Digi t_{it} \\ + θ \cdot \sum_{j = 1}^{286} W_{ij} Digi t_{it} + λ X + μ_{i} + υ_{t} + ε_{it} \end{matrix}

(4)

where $E n_{it}$ represents the threshold variable, $γ$ stands for the threshold value. $β_{1}$ and $β_{2}$ are the response coefficients of digital economy (Zhao et al., 2023).

Data

The data are mainly from the Index of Regional Innovation and Entrepreneurship in China (IRIEC) constructed by the Center for Enterprise Research (CER) of Peking University (https://opendata.pku.edu.cn/), the Chinese Innovation Research Database (CIRD) provided by Chinese Research Data Services Platform (CNRDS, https://www.cnrds.com/), the Digital Inclusive Financial Index jointly published by Digital Finance Research Center of Peking University and Ant Financial Group (https://en.idf.pku.edu.cn/), and the “Internet Plus” Urban Digital Economy Development Index compiled by Tencent Research Institute. The marketization index stems from Wang et al. (2021). The number of intellectual property cases comes from “Peking University Legal Treasure database” (PKULAW.COM). The remaining indicators are derived from “China City Statistical Yearbook.”

Combining the availability of data and referring to (Deng & Zhang, 2022; Zhao et al., 2020), the index measurement of the digital economy is designed (Table 2). This measurement assesses the digital economy levels of 286 cities across two dimensions: digital industry and digital finance. The first dimension “digital industry” mainly involves digital industry infrastructure and digital industry economy. The former is calculated by Internet penetration rate, the scale of Internet employees and cell phone penetration rate; the latter is calculated by the volume of Internet business. The second dimension “digital finance” is based on the “Digital Inclusive Financial Index,” which focuses on “coverage breadth of digital finance,”“usage depth of digital finance,” and “digitalization level of finance” (Jiang et al., 2021).

Table 2.

Measurement of Digital Economy.

Fist level	Second level	Third level	Measurement	Attribute
Digital economy	Digital industry	Internet penetration rate	Internet users per 100 people	+
		Size of the Internet-related workforce	Computer services and software industry and other Internet-related employees accounted for the proportion of the urban unit employment population	+
		Cell phone penetration rate	Number of cell phone subscribers per 100 people	+
		Internet business volume	Total telecom services per capita	+
	Digital finance	Coverage breadth of digital finance	Breadth of inclusive financial coverage	+
		Usage depth of digital finance	Depth of inclusive financial usage	+
		Digitalization level of finance	Degree of digitalization of financial inclusion	+

Besides, this paper examines other significant factors, including control variables at city level and threshold variables that measure the external environments. The city-level control variables include GDP (Gdp), population density (Pop), education expenditure (Edu), and foreign direct investment (FDI). The external environment, as a Petri dish for innovation, is a significant factor to promote the urban innovation ability. Under the background of imperfect intellectual property protection system and obvious regional differences in China, external environmental factors such as the degree of marketization, the financial environment, and the technical environment may affect the relationship between digital economy and urban innovation ability (Zhao & Xu, 2023). The symbols and measurements of the main variables are summarized in Table 3. The descriptive statistics for the abovementioned variables are reported in Table 4.

Table 3.

Variable Definition.

Category	Variable	Symbol	Measurement
Core variable	Urban innovation ability	$Inno$	The index of the number of patents, the details are shown in IRIEC.
Core variable	Digital economy	$Digit$	See Table 2 for details.
Control variable	GDP	$Gdp$	Natural logarithm of GDP per capita.
	Population density	$Pop$	Natural logarithm of population density.
	Education expenditure	$Edu$	Local government expenditure on science and education/total fiscal expenditure.
	Foreign direct investment	$FDI$	Actual amount of foreign investment used × central parity rate of current year/GDP.
Threshold variable	Market environment	$Mkt$	First, referring to the calculation method of Wang et al. (2019), the marketization index at provincial level is matched to prefecture-level cities, and then the marketization index of each city from 2011 to 2016 is obtained. Second, referring to the method of Ma et al. (2015), the marketization index of each city from 2017 to 2019 is calculated.
	Legal environment	$Law$	Number of first instance IPR cases in prefecture-level cities (Zhuang et al., 2020). Note that this variable was processed by adding one and taking the natural logarithm.
	Technological environment	$Tech$	Logarithmic values of the number of people employed in scientific research and technical service industries (Han et al., 2021).
	Financial environment	$Fin$	The number of banks per 100 million yuan of GDP (Long et al., 2015).
	Policy environment	$Pol$	China’s Municipal Fiscal Transparency Index.

Table 4.

Descriptive Statistics.

Variable	Mean	Std	Med	Min	Max	Obs
$Inno$	6.556	1.574	6.421	2.014	11.316	2574
$Digit$	2.118	0.532	2.129	1.037	5.366	2574
$Gdp$	7.262	0.981	7.190	0.667	10.549	2574
$Pop$	5.751	0.883	5.881	2.925	7.336	2574
$Edu$	0.194	0.042	0.195	0.015	0.372	2574
$FDI$	0.156	6.048	0.013	0.000	352.562	2574
$Mkt$	6.895	1.683	6.780	2.330	11.400	2574
$Law$	3.040	2.271	2.944	0.000	9.571	2574
$Tech$	2.618	0.972	2.484	0.274	7.729	2574
$Fin$	0.451	0.426	0.360	0.098	9.384	2574
$Pol$	0.410	0.214	0.409	0.000	0.922	2574

Empirical Discussion

Causal Relationship

Since non-stationarity of the variables frequently leads to spurious regressions, results in biased or even invalid conclusions. To analysis the relationships between digital economy and urban innovation ability, the stationarity test must be conducted beforehand. As shown in Table 5, Levin-Lin-Chu test (LLC), Harris-Tzavalis test (HT), and Im-Pesaran-Shin test (IPS) are used to verify whether there are unit roots. The test results reject the assumption that the variables are non-stationary, suggesting that the two variables are stable and suitable to PVAR analysis.

Table 5.

Unit Root Test Results.

Variables	Test methods and statistics			Conclusions
Variables	LCC	HT	IPS	Conclusions
$Inno$	−16.145***	0.596***	−2.106**	Stable
$Digit$	−59.891***	1.746**	−4.204***	Stable

p < .05. ***p < .01.

According to the information criteria shown in Panel A of Table 6, the PVAR model with a lag order of 1 is established. Furthermore, the Granger causality test results are shown in Table 6 (Panel B). At a 1% level of significance, the initial hypothesis, the initial hypothesis “The change of $Digit$ is not the reason for the change of $Inno$ ” is rejected, indicating that the urban innovation ability should be explained variable while the digital economy should be explanatory variable. Panel C of Table 6 shows that both $L . Inno$ and $L . Digit$ may contribute to the development of urban innovation ability, and $L . Digit$ enhances significantly the digital economy. This finding also confirms that the urban innovation ability should be explained variable, which is affected by the digital economy.

Table 6.

Results of PVAR Model and Granger Test.

Panel A
Selection	AIC criterion	BIC criterion	QIC criterion
Lag order 1	−132.998	−246.297	−299.154
Lag order 2	23.281	−45.823	−14.108
Lag order 3	6.197	−37.281	5.005
Panel B
Granger test	Hypothesis		p Value
$Inno$	The change of Digit is not the reason for the change of Inno.		.000
$Digit$	The change of Inno is not the reason for the change of Digit.		.352
Panel C
		Explained variable
Explanatory variable		$Inno$ coefficient	$Digit$ coefficient
$L . Inno$		0.840*** (0.083)	0.015 (0.012)
$L . Digit$		0.216* (0.169)	0.447*** (0.128)

Note. Robust standard errors in parentheses.

p < .1. ***p < .01.

Spatial effect

Benchmark

The estimated results of SDPD using the explanatory variable of urban innovation ability are presented in Table 7. Referring to Elhorst (2014), some verifications such as LM tests, Wald tests, Hausman tests, are proceeded. Firstly, the Hausman test results for the model with two different spatial weights significantly reject the hypothesis of using a random effects model. Secondly, according to the LR statistics for time fixed effects and city fixed effects, using a two-way fixed effects model is demonstrably superior to a one-way fixed effects model. Thirdly, according to the results of Wald test and LR test, the SDPD with two-way fixed effects should be selected.

Table 7.

Estimated Results of SDPD.

Variable	Urban innovation ability
Variable	$W^{A}$	$W^{D}$
$Inn o_{i, t - 1}$	0.783*** (0.015)	0.776*** (0.015)
$Digi t_{it}$	0.156*** (0.037)	0.063* (0.035)
$W \times Inn o_{it}$	3.593*** (0.069)	0.122*** (0.028)
$W \times Digi t_{it}$	0.051*** (0.011)	0.029** (0.133)
Control variables	Yes	Yes
R-squared	0.71	0.76
\|Log-L\|	191.85	308.71
Observations	2574	2574
Hausman test	260.43***	337.59***
City FE	29.40***	165.31***
Year FE	29.16***	164.86***
Wald test	18.43***	25.32***
LR test	21.60***	42.87***

Note. Robust standard errors in parentheses.

p < .1. **p < .05. ***p < .01.

Lagging factors are introduced into the SDPD, so that the direct impact of the digital economy on urban innovation ability cannot be obtained from Table 7. Nevertheless, the results below are still informative. (a) The estimated coefficient of the time-lagged term of urban innovation ability ( $τ$ ) is significantly positive. It means that there is a path dependence of urban innovation ability, and early-stage progress in urban innovation can facilitate its future advancement. (b) The spatially lagged term of urban innovation ability ( $ρ$ ) has a positive and significant regression coefficient under both spatial weight matrices, but the coefficient estimated under the adjacency matrix is considerably higher than that under the distance matrix. It indicates that urban innovation ability in China is significantly influenced by spatial factors, and that innovation ability between adjacent cities has a stronger mutual driving effect. (c) The estimated coefficient of the digital economy ( $β$ ) remains consistently positive regardless of which spatial weight matrix is used. It indicates that the growth of the digital economy in Chinese cities has typically encouraged the enhancement of their own ability for innovation. (d) The estimated coefficient of the spatial lag term of digital economy ( $θ$ ) is significantly positive. It means that the digital economy can affect the urban innovation ability of neighboring cities through spatial effect.

Effect Decomposition

The results in Table 8 confirm that in the short term, the digital economy has a significantly positive impact on urban innovation ability in both direct and indirect ways, but in the long term, only the indirect effect remains significant. It suggests that the positive spillover effects of the digital economy are evident in the short term, not only within the local city but also in neighboring cities. In the long run, the growth of digital economy is more beneficial to the transfer and diffusion of innovation resources and frontier technologies outside the city, which significantly promotes the innovation ability of neighboring cities, but the positive spillover to the city will decay with time and has a certain timeliness.

Table 8.

Effect Decomposition of Digital Economy on Urban Innovation Ability.

			Urban innovation ability
Category		Formula	$W^{A}$	$W^{D}$
Short term	Direct	${[{[I - ρ W]}^{- 1} [β_{k} I_{N}]]}^{\bar{d}}$	0.1846*** (0.0528)	0.0650* (0.0342)
	Indirect	${[{[I - ρ W]}^{- 1} [β_{k} I_{N}]]}^{\bar{rsum}}$	0.2193*** (0.0471)	0.0466* (0.0223)
	Total	${[{[I - ρ W]}^{- 1} [β_{k} I_{N}]]}^{\bar{d}} + {[{[I - ρ W]}^{- 1} [β_{k} I_{N}]]}^{\bar{rsum}}$	0.4039*** (0.0309)	0.1116* (0.0589)
Long term	Direct	${[{[(1 - τ) I - ρ W]}^{- 1} [β_{k} I_{N}]]}^{\bar{d}}$	0.0087 (0.0081)	0.3093 (0.2583)
	Indirect	${[{[(1 - τ) I - ρ W]}^{- 1} [β_{k} I_{N}]]}^{\bar{rsum}}$	0.1552*** (0.0428)	0.8799* (0.4301)
	Total	${[{[(1 - τ) I - ρ W]}^{- 1} [β_{k} I_{N}]]}^{\bar{d}} + {[{[(1 - τ) I - ρ W]}^{- 1} [β_{k} I_{N}]]}^{\bar{rsum}}$	0.1639*** (0.0621)	1.1892* (0.5889)

Note. Robust standard errors in parentheses; $\bar{d}$ represents the mean of the diagonal elements of the matrix; $\bar{rsum}$ represents the mean of the row sums of non-diagonal elements of the matrix; $τ$ represents the coefficient of time lag.

p < .1. ***p < .01.

Robustness Check

In order to reduce the impact of statistical variable selection on estimate results, this paper conduct robustness tests by substituting the original statistical variables with comparable ones.

Explained Variable

We take the number of patent applications in each city as a proxy variable of urban innovation ability, then assigns 50%, 30% and 20% weights to invention patents, utility model patents and design patents respectively, and finally adopts the weighted number of patent applications as a measure of urban innovation ability. The estimated results after replacing the explained variables are show in Table 9, where the coefficients of the time and space lag items of urban innovation ability ( $τ$ and $ρ$ ), the estimated coefficients of the digital economy ( $β$ ) and its spatial lag item coefficient ( $θ$ ) are all significantly positive, indicating that the estimation results after replacing the explained variables are still robust.

Table 9.

Robustness Test: Replacement of Explained Variable.

Variable	Urban innovation ability
Variable	$W^{A}$	$W^{D}$
$Inn o_{i, t - 1}$	0.650*** (0.015)	0.723*** (0.016)
$Digi t_{it}$	1.811*** (0.069)	0.054*** (0.023)
$W \times Inn o_{it}$	1.692*** (0.034)	0.357*** (0.028)
$W \times Digi t_{it}$	0.009** (0.003)	0.093* (0.048)
Control variable	Yes	Yes
Hausman test	148.95***	145.46***
City FE	32.72***	157.38***
Year FE	45.79***	192.46***
Wald test	874.68***	3.66*
LR test	807.23***	5.97**
Observations	2574	2574
R-squared	0.91	0.93

Note. Robust standard errors in parentheses.

p < .1. **p < .05. ***p < .01.

Explanatory Variable

Referring to Wei (2022), this paper takes the “Internet Plus” Urban Digital Economy Development Index from 2014 to 2018 compiled by Tencent Research Institute as a proxy variable for the core explanatory variable to verify the robustness of empirical results. In Table 10, the estimated coefficients are all positive and significant, indicating that the estimates remain robust after replacing the explanatory variable.

Table 10.

Robustness Test: Replacement of Explanatory Variable.

Variable	Urban innovation ability
Variable	$W^{A}$	$W^{D}$
$Inn o_{i, t - 1}$	0.965*** (0.015)	0.777*** (0.015)
$Digi t_{it}$	0.296*** (0.038)	0.072** (0.035)
$W \times Inn o_{it}$	0.799*** (0.068)	0.124*** (0.017)
$W \times Digi t_{it}$	0.118*** (0.001)	0.027** (0.012)
Control variable	Yes	Yes
Hausman test	260.51***	341.29***
City FE	28.32***	149.27***
Year FE	28.09***	169.38***
Wald test	10789.10***	12.54**
LR test	222.61***	15.32***
Observations	1430	1430
R-squared	0.41	0.82

Note. Robust standard errors in parentheses.

p < .05. ***p < .01.

Nonlinear Effect

Using the Bootstrap method, the results of threshold test for each external environmental factor after sampling 300 times are compiled in Table 11. Specifically, the Bootstrap findings are significant for both the single threshold hypothesis and the double threshold hypothesis whether the market environment or policy environment is employed as the threshold variable, but the test results are not significant under the triple threshold hypothesis. It is confirmed that there are two significant thresholds for the market and policy environment. The Bootstrap findings for the single threshold hypothesis are significant when the regulatory environment, technical environment, or financial environment is utilized as the threshold variable, however the test results for the double threshold hypothesis are not significant. It indicates that there is only one significant threshold for legal environment, technological environment and financial environment. Based on the threshold estimations and their test results presented in Table 11, the market environment is classified as “high marketization ( $Mkt > 5.610$ ),”“moderate marketization ( $5.140 < Mkt \leq 5.610$ ),” and “low marketization ( $Mkt \leq 5.140$ )”; the legal environment is classified as “good legal environment ( $Law > 3.850$ )” and “poor legal environment ( $Law \leq 3.850$ )”; the technology environment is classified as “good technology environment ( $Tech > 1.378$ )” and “poor technology environment ( $Tech \leq 1.378$ )”; the financial environment is classified as “good financial environment ( $Fin > 0.241$ )” and “poor financial environment ( $Fin \leq 0.241$ )”; the policy environment is classified as “good policy environment ( $Pol > 0.658$ ),”“moderate policy environment ( $0.587 < Pol \leq 0.658$ )” and “poor policy environment ( $Pol \leq 0.587$ ).”

Table 11.

Threshold Test Result.

Threshold variable	Model	Threshold	MSE	F value	p Value	BS	Critical value
Threshold variable	Model	Threshold	MSE	F value	p Value	BS	1%	5%	10%
$Mkt$	Single	5.140	0.039	20.49**	.014	300	22.703	20.347	16.569
	Double	5.140	0.038	26.50*	.040	300	28.999	25.564	19.968
	Double	5.610	0.038	26.50*	.040	300	28.999	25.564	19.968
	Triple	5.140	0.038	15.51	.601	300	46.921	38.565	35.725
		5.610
		6.810
$Law$	Single	3.850	0.039	12.80*	.090	300	20.347	13.983	11.802
	Double	3.850	0.039	6.68	.290	300	19.657	15.193	10.964
	Double	5.946	0.039	6.68	.290	300	19.657	15.193	10.964
	Triple	—	—	—	—	—	—	—	—
$Tech$	Single	1.378	0.041	10.36*	.094	300	14.223	12.551	10.079
	Double	1.378	0.041	7.49	.340	300	16.911	14.485	13.086
	Double	2.331	0.041	7.49	.340	300	16.911	14.485	13.086
	Triple	—	—	—	—	—	—	—	—
$Fin$	Single	0.241	0.041	12.35*	.095	300	15.368	12.947	11.143
	Double	0.241	0.041	4.42	.600	300	14.951	11.108	9.978
	Double	0.663	0.041	4.42	.600	300	14.951	11.108	9.978
	Triple	—	—	—	—	—	—	—	—
$Pol$	Single	0.658	0.039	13.56**	.020	300	14.325	11.047	9.094
	Double	0.587	0.039	16.18**	.020	300	16.310	12.464	10.928
	Double	0.658	0.039	16.18**	.020	300	16.310	12.464	10.928
	Triple	0.354	0.039	4.94	.850	300	42.806	29.654	23.502
		0.587
		0.658

Note. “—” represents that it does not exist.

p < .1. **p < .05.

The estimated results of TSDP with different external environments as threshold variables are reported in Table 12. The results show that: (a) When the degree of marketization is either too high or too low, it becomes challenging for the digital economy to foster urban innovation ability. However, a moderate degree of marketization ( $5.140 < Mkt \leq 5.610$ ) can facilitate the promotion of urban innovation ability by the improvement of digital economy. The internal mechanism of the result may be that: when the degree of marketization is low, neighboring cities tend to have a stronger “siphon effect” on the city, causing the outflow of local innovation resources, thus weakening the incentives for urban innovation ability in the digital economy. Besides, a low degree of marketization can limit the leading role in the allocation of innovation resources, and even inhibit the improvement of urban innovation ability. However, a high degree of marketization can often strengthen the “diffusion effect” of the city to neighboring cities, pushing the innovation activities of the city to the neighboring cities, resulting in a stronger spatial (indirect) effect of the digital economy on the urban innovation ability and a weaker direct promotion effect on the city. (b) No matter how the legal environment is, digital economy is always beneficial to promote urban innovation ability, and it is more effective in a better legal environment. (c) A better technology environment can make the digital economy more effective in empowering urban innovation ability. The reason may be that scientific and technological talents can improve the ability of enterprises to absorb and imitate advanced technologies and to use them to promote innovation (Barcenilla et al., 2019). The empowerment of urban innovation abilities by the digital economy mainly relying on high-tech industries, which need to be realized through the deep integration of digital economy and traditional industries, so the dependence on scientific and technological talents and technological environment is more significant (Gu et al., 2016). (d) Compared with a good financial environment, the promotion effect of digital economy on urban innovation ability will be stronger in a poor financial environment. The reason may be that in a good financial environment, the development of urban innovation mostly relies on existing resource endowments, so the innovation path is easily restricted, which ultimately leads to limited breadth and depth of digital transformation. However, in a poor financial environment, the development of urban digital economy and innovation is not only no longer restricted by resource endowments, but also can be adjusted more effectively, so digital economy can promote the innovation ability of cities more strongly. (e) The policy environment can affect the promotion of digital economy on urban innovation ability. In cities with a moderate or even poor policy environment, it is often difficult for digital economy to effectively promote urban innovation ability. The explanation might be that under a favorable legislative climate, urban innovation can be more effectively penetrated by the digital economy, allowing for a more complete release of the digital economy dividend.

Table 12.

Estimated Results of TSDP.

	Threshold variable
	$Mkt$	$Law$	$Tech$	$Fin$	$Pol$
Threshold 1	5.140	3.850	1.367	0.241	0.587
Threshold 2	5.610				0.658
Digital economy
Low interval	−0.020 (0.166)	0.011* (0.006)	0.162 (0.189)	0.138*** (0.052)	0.409 (0.565)
Middle interval	0.294*** (0.173)				0.381 (0.576)
High interval	0.061 (0.174)	0.083* (0.041)	0.098* (0.047)	0.067* (0.037)	0.424* (0.231)
Proportion of low interval samples	15.61%	62.94%	5.93%	22.19%	63.79%
Proportion of high interval samples	79.52%	37.06%	94.07%	77.81%	21.52%
Control variable	Yes	Yes	Yes	Yes	Yes
Observations	2,574	2,574	2,574	2,574	2,574

Note. Robust standard errors in parentheses.

p < .1. ***p < .01.

Conclusion

The burgeoning development of digital economy in China is a new engine for boosting urban innovation ability and provides strong support for the promotion of innovation. Based on the panel data of 286 prefecture-level cities in China from 2011 to 2019, this paper explores the causal relationship between digital economy and urban innovation ability by PVAR, examines the spatial and dynamic impacts of digital economy on urban innovation ability by SDPD, and analyzes the nonlinear impacts of digital economy on urban innovation ability under different external environments by TSDP. It is found that: (a) The urban innovation ability has significant spatial dependence and presents a U-shaped evolution trend. (b) In the short term, the digital economy can empower urban innovation ability, and it is not only limited to its own city, but also has a significant impact on nearby cities. In the long run, the growth of digital economy can also promote neighboring cities’ ability for innovation, which is more beneficial to the transfer and diffusion of innovation resources and cutting-edge technologies to outside of the city. However, the positive spillover effect on the city itself decays with time, which has certain timeliness. (c) The impact of the digital economy on urban innovation ability varies in different external environments, showing obvious nonlinearity and significant external environmental threshold characteristics. Specifically, a moderate degree of marketization is beneficial to the digital economy in enhancing urban innovation ability; a better legal or technological environment also facilitates the digital economy in empowering urban innovation ability; in a poor financial environment, the digital economy has a stronger effect on promoting urban innovation ability; on the contrary, in a moderate or poor policy environment, it is challenging for digital economy to effectively promote urban innovation ability.

Based on the above findings, this paper provides recommendations on how government agencies, industry stakeholders, and city planners can leverage the digital economy to foster urban innovation ability.

First, for government agencies. The relationship between the digital economy and the capacity for urban innovation can be impacted by the external environment. Therefore, relevant government agencies should constantly improve the external environment such as technological environment, and create a good operating ecology where the digital economy can effectively foster urban innovation ability. While promoting the digital economy, the relevant government agencies should control a moderate level of marketization to realize the promoting effect of digital economy on urban innovation ability. Additionally, the relevant government agencies should try to establish a favorable policy implementation environment, improve the transparency of fiscal revenue and expenditure, introduce policies and regulations related to technological innovation, improve the system of laws and regulations and the supply system of intellectual property rights, and create a fair external environment in an all-round and multi-dimensional way, thus actively encouraging urban innovation activities. Besides, relevant government agencies should focus on the common growth of digital economy and urban innovation ability. In terms of digital infrastructure construction and provision of public goods, government agencies should constantly broaden the channels for all kinds of subjects (e.g., enterprises and universities) to participate in urban innovation and development, and strive to make more capable and willing innovative subjects participate in improving urban innovation ability through the mode of government purchasing services, so as to enhance the stickiness between innovative subjects and urban innovation and achieve the goal of common growth.

Second, for industry stakeholders. Industry stakeholders involve enterprises, investors and employees. Strengthening digital transformation, promoting the deep integration of digital economy and real economy, and improving their own innovation ability are the primary tasks of enterprises. Meanwhile, enterprises should actively strengthen the cooperation and coordination of digital economy, promote the transfer and diffusion of innovative resources and cutting-edge technologies, and share the “knowledge dividend” of digital economy. Additionally, enterprises should enhance the cultivation of talents in digital economy and invest in R&D, advocate and establish an innovative culture, and continuously improve their innovation ability and market competitiveness. As far as investors are concerned, they should comprehensively understand the urban innovation ability and the growth of digital economy, pay attention to the changes of external environment and the developing tendency of technology in order to formulate corresponding and reasonable investment strategies. Concerning employees, they should constantly improve their digital skills, master digital tools and technologies, and actively participate in digital innovation to better meet the needs of the digital era.

Third, for city planners. From the perspective of time and space, digital economy can foster urban ability for innovation. On the one hand, city planners should optimize the urban spatial layout and encourage digital business to gather in the city, which helps to fully exploit the contribution of the digital economy to fostering urban innovation ability. On the other hand, according to the spatial effect of the digital economy, city planners should enhance the cooperation between cities, break the administrative boundaries, attract multi-agents to participate in a wider range, and jointly promote the growth of the digital economy, so as to expand the spillover radius of the digital economy and achieve mutual benefit and “win-win” results. In addition, city planners should strengthen the construction of urban innovation ecosystem, provide better ecological environment and support for digital economy and innovation resources, in order to further promote the improvement of urban innovation ability.

This study still has some limitations which need to be further explored and improved in future studies. First, many other external environmental factors worth exploring. Due to the length of the paper, only five environmental factors, such as market environment and legal environment, are considered in this paper. And future research on the influence mechanisms of other elements of the external environment (such as the cultural environment) is possible. Second, due to the limited availability of data, the study on measuring urban innovation ability is still in the exploratory stage, and the choice of indicators for measuring the digital economy at the city level is limited. Therefore, we will further optimize and improve the measurement of these important indicators in future study.

Footnotes

Acknowledgements

The authors are grateful to Prof. Sebastien Menard for his helpful comments and contribution to this manuscript.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The research was funded by Shandong Provincial Natural Science Foundation [grant number ZR2023MG075 & ZR2024QE171], and Shandong Province Youth Innovation and Technology Support Program for Higher Education Institutions(2023KJ111).

ORCID iDs

Kai Zhao

Wanshu Wu

Data Availability Statement

Data available on request from the authors.

References

Aaron

Jason

(2016). The end of ownership: Personal property in the digital economy. The MIT Press.

Abrigo

M. R. M.

Love

(2016). Estimation of panel vector autoregression in Stata. The Stata Journal, 16(3), 778–804.

Bai

J. H.

Jiang

F. X.

(2015). Synergy innovation, spatial correlation and regional innovation performance. Economic Research Journal, 50(7), 174–187. (in Chinese)

Bai

P. W.

(2021). Digital economy development and firm’s markup: Theoretical mechanism and empirical facts. China Industrial Economics, 11, 59–77. (in Chinese)

Bai

X. J.

Song

Liao

S. N.

(2021). Can digital economy promote the transformation of China’s industrial structure? Based on the perspective of efficient technological progress. Journal of Xi’an Jiaotong University (Social Sciences), 41(6), 1–15. (in Chinese)

Barcenilla

Gimenez

Lopez-Pueyo

(2019). Differences in total factor productivity growth in the European union: The role of human capital by income level. Prague Economic Papers, 28(1), 70–85.

Barefoot

Curtis

Jolliff

Nicholson

J. R.

Omohundro

(2018, March 15). Defining and measuring the digital economy (Working Paper, pp. 1–24). Bureau of Economic Analysis, US Department of Commerce.

Brynjolfsson

Kahin

(2000). Understanding the digital economy: Data, tools, and research. MIT Press.

Cappelen

Raknerud

Rybalka

(2012). The effects of R&D tax credits on patenting and innovations. Research Policy, 41(2), 334–345.

10.

Caputo

Cillo

Candelo

Liu

Y. P.

(2019). Innovating through digital revolution: The role of soft skills and big data in increasing firm performance. Management Decision, 57(8), 2032–2051.

11.

Chen

X. H.

Yan

Chen

(2022). Can the digital economy promote FinTech development? Growth and Change, 53(1), 221–247.

12.

Chen

Y. K.

Liu

L. T.

(2019). Research on the influence of environmental regulation intensity and enterprise scale on the quality of technological innovation. Science & Technology Progress and Policy, 36(16), 84–90. (in Chinese)

13.

Cheng

Zheng

(2023). Does the digital economy promote coordinated urban–rural development? Evidence from China. Sustainability, 15(6), Article 5460.

14.

Dai

X. L.

Chapman

(2022). R&D tax incentives and innovation: Examining the role of programme design in China. Technovation, 113, Article 102419.

15.

Dang

X. S.

Shen

(2021). Digital economy, innovation milieu and cooperative innovation performance. Journal of Shanxi University of Finance and Economics, 43(11), 1–15. (in Chinese)

16.

Deng

Hong

Chen

Yang

(2019). Government R&D subsidies, intellectual property rights protection and innovation. Chinese Management Studies, 13(2), 363–378.

17.

Deng

R. R.

Zhang

A. X.

(2022). Research on the impact of urban digital economy development on environmental pollution and its mechanism. South China Journal of Economics, 2, 18–37.

18.

Ding

Liu

Zheng

(2022). Digital economy, technological innovation and high-quality economic development: Based on spatial effect and mediation effect. Sustainability, 14(1), Article 216.

19.

Ding

Z. F.

(2020). Research on the mechanism of digital economy driving high-quality economic development: A theoretical analysis framework. Modern Economic Research, 1, 85–92.

20.

Elhorst

J. P.

(2014). Spatial econometrics: From cross-sectional data to spatial panels. Springer.

21.

Fischer

M. M.

Nijkamp

(2020). Handbook of regional science. Springer.

22.

C. W.

Wang

J. Y.

L. L.

Pan

X. Y.

(2016). A research on S&T young talent service problem by taking Shanghai as an example. Science Research Management, 37(S1), 219–224. (in Chinese)

23.

W. N.

Shen

Y. M.

(2018). The evolution and scientific and technological innovation ability of central cities and the improving paths. Economic Geography, 38(2), 113–122. (in Chinese)

24.

Guo

B. N.

Wang

Zhang

(2022). Does digital economy improve urban air quality: Quasi natural experiment based on national Big Data comprehensive pilot zone. Journal of Guangdong University of Finance & Economics, 1, 58–74. (in Chinese)

25.

Guo

J. T.

Liang

(2021). The impact mechanism of the digital economy on China’s total factor productivity: An uplifting effect or restraining effect? South China Journal of Economics, 10, 9–27. (in Chinese)

26.

Han

Chen

Liang

L. L.

(2021). Digital economy, innovation environment and urban innovation capabilities. Science Research Management, 42(4), 35–45. (in Chinese)

27.

Hansen

B. E.

(1999). Threshold effects in non-dynamic panels: Estimation, testing and inference. Journal of Econometrics, 93, 345–368.

28.

Y. Z.

(2022). Digital economy and enterprise innovation: Breakthrough innovation or progressive innovation? Research on Financial and Economic Issues, 1, 42–51. (in Chinese)

29.

Huang

X. C.

Zhou

J. J.

Zhou

(2022). Digital economy’s spatial implications om urban innovation and its threshold: Evidence from China. Complexity, 2022, Article 3436741.

30.

Jiang

D. C.

Pan

X. W.

(2022). The effect of digital economy development on the enterprise innovative performance: Based on the empirical evidence of listed companies in China. Journal of Shanxi University (Philosophy and Social Science Edition), 45(1), 149–160. (in Chinese)

31.

Jiang

P. Y.

Z. H.

(2021). Intellectual property protection, digital economy and regional entrepreneurship activity. China Soft Science, 10, 171–181. (in Chinese)

32.

Jin

P. Z.

Yin

D. S.

Jin

(2019). Urban heterogeneity, institutional supply and innovation quality. The Journal of World Economy, 42(11), 99–123. (in Chinese)

33.

LeSage

J. P.

(2014). What regional scientists need to know about spatial econometrics. The Review of Regional Studies, 44(1), 13–32.

34.

Tian

X. L.

Zhang

S. D.

Zhao

H. P.

(2020). Evaluation of urban innovation ability and evolution of spatial and temporal pattern. Journal of Applied Statistics and Management, 39(1), 139–153. (in Chinese)

35.

Rao

Wan

L. Y.

(2022). The digital economy, enterprise digital transformation, and enterprise innovation. Managerial and Decision Economics, 43(7), 2875–2886.

36.

Yang

S. Y.

(2019). Has the pilot project of innovative cities increased the level of innovation? Economic Perspectives, 8, 70–85. (in Chinese)

37.

Z. G.

Wang

(2022). The dynamic impact of digital economy on carbon emission reduction: Evidence city-level empirical data in China. Journal of Cleaner Production, 351, Article 131570.

38.

Z. H. X.

N. Y.

Wen

H. W.

(2021). Digital economy and environmental quality: Evidence from 217 cities in China. Sustainability, 13, Article 8058.

39.

Liang

Qiao

S. P.

M. X.

(2021). Digital economy development, spatial spillover and innovation quality growth: The threshold effect test of market efficiency. Shanghai Journal of Economics, 9, 44–56. (in Chinese)

40.

Liu

Yang

Y. Y.

Zhang

S. F.

(2020). Research on the measurement and driving factors of China’s digital economy. Shanghai Journal of Economics, 6, 81–96. (in Chinese)

41.

Liu

Chen

X. D.

(2021). The effect of digital economy on industrial structure upgrade in China. Research on Economics and Management, 42(8), 15–29. (in Chinese)

42.

Liu

Yang

Y. L.

H. H.

Zhong

K. Y.

(2022). Digital economy development, industrial structure upgrading and green total factor productivity: Empirical evidence from China’s cities. International Journal of Environmental Research and Public Health, 19(4), Article 2414.

43.

Long

X. N.

Zhang

X. B.

(2015). Impact of industrial clusters on contract protection and financing. China Economic Quarterly, 14(4), 1563–1590. (in Chinese)

44.

S. F.

Liu

(2015). Fiscal expenditure and regional innovation quality: An empirical analysis based on provincial data in China. Journal of Macro-quality Research, 3(1), 93–101. (in Chinese)

45.

Zhu

(2022). Innovation in emerging economies: Research on the digital economy driving high-quality green development. Journal of Business Research, 145, 801–813.

46.

L. F.

Wang

L. L.

Zhang

(2015). Pecking order of mixed ownership: The logic of market. China Industrial Economics, 7, 5–20. (in Chinese)

47.

Ning

Wang

(2016). Urban innovation, regional externalities of foreign direct investment and industrial agglomeration: Evidence from Chinese cities. Research Policy, 45(4), 830–843.

48.

Ozili

P. K.

(2018). Impact of digital finance on financial inclusion and stability. Borsa Istanbul Review, 18(4), 329–340.

49.

Pan

Xie

Wang

(2022). Digital economy: An innovation driver for total factor productivity. Journal of Business Research, 139, 303–311.

50.

Y. D.

Xiao

(2020). Transformation of enterprise management in the era of digital economy. Management World, 6, 135–152. (in Chinese)

51.

Qian

H. Z.

Tao

Y. Q.

Cao

S. W.

Cao

Y. Y.

(2020). Theoretical and empirical analysis on the development of digital finance and economic growth in China. The Journal of Quantitative & Technical Economics, 37(6), 26–46. (in Chinese)

52.

Ren

B. P.

P. W.

(2022). The mechanism and path for the digital economy to cultivate new drivers of high-quality economic development in China. Journal of Shaanxi Normal University (Philosophy and Social Sciences Edition), 51(1), 121–132. (in Chinese)

53.

Shang

Jiang

Pan

X. F.

(2022). Does R&D element flow promote the spatial convergence of regional carbon efficiency? Journal of Environmental Management, 322(15), Article 116080.

54.

Tang

X. C.

Zhu

(2020). Digital finance and enterprise technology innovation: Structural feature, mechanism identification and effect difference under financial supervision. Management World, 36(5), 52–66. (in Chinese)

55.

Tapscott

(1996). The digital economy: Promise and peril in the age of networked intelligence. McGraw-Hill.

56.

Thompson

Williams

Thomas

(2014). Are UK SMEs with active web sites more likely to achieve both innovation and growth? Journal of Small Business & Enterprise Development, 20(4), 934–965.

57.

Wang

H. T.

X. H.

Ali

(2022). Spatial characteristics and driving factors toward the digital economy: Evidence from prefecture-level cities in China. The Journal of Asian Finance, Economics and Business, 9(2), 419–426.

58.

Wang

X. L.

Fan

L. P.

(2019). Marketization index of China’s provinces: NERI Report 2018. Social Science Academic Press (China). (in Chinese)

59.

Wang

X. Y.

Ren

Y. Z.

Zhang

L. L.

(2020). The influence of technological innovation ability of universities on regional economic growth: Take coastal provinces and cities for example. Journal of Coastal Research, 103, 112–116.

60.

Wang

X. L.

L. P.

Fan

(2021). Marketization Index of China’s Provinces: Neri Report 2021. Social Sciences Academic Press(China).

61.

Wei

Z. Y.

(2022). Research on the impact of the development of digital economy on the efficiency of resource allocation in manufacturing enterprises. The Journal of Quantitative & Technical Economics, 39(3), 66–85. (in Chinese)

62.

Wen

Yan

Z. J.

Cheng

(2020). Research on the effect of digital economy on upgrading innovation capacity—Based on provincial-level panel data. Reform of Economic System, 3, 31–38. (in Chinese)

63.

J. Y.

Matsuda

(2021). A threshold extension of spatial dynamic panel model with fixed effects. Journal of Spatial Econometrics, 2(3), 1–30.

64.

Zhao

(2019). Dynamic interaction between foreign direct investment and the new urbanization in China. Journal of Housing and the Built Environment, 34, 1107–1124.

65.

X. C.

Zhang

M. H.

(2020). Research on the scale measurement of China’s digital economy–Based on the perspective of international comparison. China Industrial Economics. 5, 23–41. (in Chinese)

66.

Yang

H. M.

Jiang

(2021). Digital economy, spatial effects and total factor productivity. Statistical Research, 38(4), 3–15. (in Chinese)

67.

Yao

Yang

(2022). Can digital finance boost SME innovation by easing financing constraints? Evidence from Chinese GEM-listed companies. PLOS ONE, 17(3), Article e0264647.

68.

Yousaf

Radulescu

Sinisi

C. I.

Serbanescu

Paunescu

L. M.

(2021). Towards sustainable digital innovation of SMEs from the developing countries in the context of the digital economy and frugal environment. Sustainability, 13(10), Article 5715.

69.

Zhang

Wan

G. H.

Zhang

J. J.

Z. Y.

(2019). Digital economy, financial inclusion, and inclusive growth. Economic Research Journal, 54(8), 71–86. (in Chinese)

70.

Zhang

Yang

(2016). Review and comment on the research of spatial econometrics. Industrial Economic Review, 7(1), 5–21. (in Chinese)

71.

Zhang

L. Z.

(2019a). Discussion on the relationship between IP protection and the capabilities and quality of regional innovation based on the provincial data from 2007 to 2017. Journal of International Economic Cooperation, 6, 43–52. (in Chinese)

72.

Zhang

X. W.

(2019b). Research on evolution of innovation model under the condition of digital economy. Economist, 7, 32–39. (in Chinese)

73.

Zhang

Z. Q.

Qiao

Y. D.

Liu

(2020). Study on the temporal and spatial agglomeration effect of innovation quality of Zhongguancun Science Park. Science & Technology Progress and Policy, 37(11), 51–59. (in Chinese)

74.

Zhao

S. X.

(2023). External environment, enterprise innovation and government subsidies. Statistics & Decision, 39(6), 167–172. (in Chinese)

75.

Zhao

Yang

(2023). Impacts of digital economy on urban entrepreneurial competencies: A spatial and nonlinear perspective. Sustainability, 15, Article 7900.

76.

Zhao

Zhang

Liang

S. K.

(2020). Digital economy, entrepreneurship, and high-quality economic development: Empirical evidence from urban China. Management World, 36(10), 65–76. (in Chinese)

77.

Zhao

Sun

(2016). The influence of Chinese environmental regulation on corporation innovation and competitiveness. Journal of cleaner production, 112, 1528–1536.

78.

Zhuang

J. Q.

Wang

Zhang

W. T.

(2020). Does strengthening the judicial protection of intellectual property contribute to corporate innovation? Evidences from the establishment of courts for intellectual property right cases. Contemporary Finance & Economics, 9, 16–27. (in Chinese)

Digital Economy and Urban Innovation Ability: From the Spatial Nonlinear Perspective

Abstract

Plain language summary

Keywords

Introduction

Literature Review

Digital Economy

Urban Innovation Ability

Digital Economy and Urban Innovation Ability

Temporal and Spatial Characteristics of Urban Innovation Ability in China

Temporal Characteristics

Spatial Characteristics

Research Design

Methodology

Data

Empirical Discussion

Causal Relationship

Spatial effect

Benchmark

Effect Decomposition

Robustness Check

Explained Variable

Explanatory Variable

Nonlinear Effect

Conclusion

Footnotes

Acknowledgements

Declaration of Conflicting Interests

Funding

ORCID iDs

Data Availability Statement

References