Research on the Dynamic Relationship Between the Growth of Innovation Activity and Entrepreneurial Activity in China

Abstract

This study aims to empirically investigate the contemporaneous, bidirectional causal relationship between innovation and entrepreneurial activities in China by constructing a dynamic simultaneous equation system. Using panel data from 31 provincial administrative regions from 2000 to 2022, our empirical results demonstrate a robust two-way causal relationship: vigorous innovation activities significantly stimulate the emergence and subsequent growth of entrepreneurial ventures, while entrepreneurial dynamism similarly promotes regional innovation. These findings remain stable and consistent after rigorous robustness checks. Further, employing a Panel Vector Autoregression (PVAR) approach in extended analyses, we find clear evidence of a stable positive feedback loop between innovation and entrepreneurship, characterized by progressive and cumulative effects. Additionally, regional heterogeneity analysis indicates that macroeconomic disparities significantly influence the bidirectional relationship between innovation and entrepreneurship. Specifically, differences in regional resource endowments and economic conditions largely account for variations in innovation–entrepreneurship dynamics across regions. Consequently, local governments should tailor innovation and entrepreneurship policies to regional contexts to maximize economic outcomes effectively under China’s current development paradigm.

1. Introduction

Which comes first: entrepreneurship or innovation? In current policy frameworks and public discourse, innovation and entrepreneurship are closely intertwined and often discussed jointly. Numerous policy documents and media reports repeatedly emphasize innovation alongside entrepreneurship, implicitly acknowledging a strong and inherent connection between the two concepts. However, despite their interrelated nature, innovation and entrepreneurship may differ significantly regarding their practical importance and developmental impacts. Entrepreneurial activities, recognized as a crucial driving force behind China’s economic development, have consistently drawn substantial attention from policymakers and academia. Particularly under China’s robust policy initiatives advocating “Mass Entrepreneurship and Innovation”, entrepreneurial activities surged significantly alongside the rapid growth of the internet industry, contributing substantially to sustained high-speed economic growth.

In recent years, however, external shocks have profoundly impacted China’s macroeconomic environment, which includes the China–US trade conflicts, technological decoupling, and the COVID-19 pandemic. These events significantly altered entrepreneurial conditions, creating notable barriers to accessing entrepreneurial resources and adversely affecting the survival prospects of new ventures. Concurrently, the strategic importance of innovation, especially technology-driven innovation, has been increasingly emphasized as China transitions towards a high-quality, innovation-driven economic growth model. The Third Plenary Session communiqué of the 20th CPC Central Committee further underscored this strategic shift, explicitly calling for the establishment of novel institutional mechanisms promoting revolutionary technological breakthroughs and disruptive innovations, aimed at steering the orderly development of emerging industries. Simultaneously, entrepreneurship has been reaffirmed as a critical policy instrument for promoting high-quality employment, necessitating further investments to optimize the entrepreneurial ecosystem. Given these policy imperatives, clarifying the intrinsic interactive mechanisms between innovation and entrepreneurship is essential to identify targeted leverage points for enhancing innovation and entrepreneurial activities, thereby providing robust theoretical foundations and practical policy guidance.

Presently, extensive academic research explores the interrelationship between innovation and entrepreneurship [1,2,3,4,5,6,7]. However, existing studies primarily adopt a unidirectional perspective, either examining how entrepreneurial activities stimulate innovation or how innovation spurs entrepreneurial actions [1,4,8]. Although some literature acknowledges potential reciprocal interactions between innovation and entrepreneurship, current theoretical and empirical analyses typically reveal a temporal lag in these interactions [2,4,9,10]. Specifically, the positive effects are generally non-contemporaneous, whether innovation activities on entrepreneurial opportunities or vice versa, which often require substantial time (commonly over one year) to fully materialize. Additionally, certain studies highlight potential inhibitive effects, noting that intellectual property protections associated with innovation activities may constrain entrepreneurial opportunities [11], while the rapid growth of startups may diminish internal incentives for continuous innovation. Nonetheless, due to methodological constraints and limited generalizability, these findings have not been widely generalized. The prevailing consensus remains that innovation and entrepreneurship mutually reinforce each other [1,2,3].

Notably absent from the current literature is a systematic exploration of the contemporaneous bidirectional causal relationships between innovation and entrepreneurship. Moreover, no unified analytical framework has yet emerged to explicitly capture and dissect these dynamic interactions. Addressing this gap, the present study employs an advanced Panel Structural Vector Autoregressive (PVAR) model framework, extending traditional dynamic panel estimation methodologies via systems of linear dynamic equations. This approach seeks to elucidate the contemporaneous interactions and underlying mechanisms between innovation and entrepreneurial activities comprehensively. Specifically, the study not only investigates the lagged interactions and responses to shocks over time, but also explicitly examines contemporaneous mutual effects through refined dynamic panel techniques. Consequently, this methodological innovation enhances the explanatory power and accuracy in depicting the dynamic relationship between innovation and entrepreneurship.

The theoretical contributions of this study are threefold. Firstly, it empirically confirms the existence and significance of contemporaneous two-way causality between innovation and entrepreneurial activities in China and provides a detailed description of their dynamic relationship. Secondly, it systematically explores the underlying interaction mechanisms that facilitate the dynamic influences between innovation and entrepreneurship. Thirdly, acknowledging regional variations in macroeconomic conditions, this research further examines the heterogeneity in the innovation-entrepreneurship relationship across different provincial contexts in China. Practically, the study contributes by offering a more robust empirical foundation for enhancing China’s dual-innovation policy framework, providing valuable policy implications to governmental bodies for policy refinement and effective implementation of supporting measures.

The remainder of the study is structured as follows: Section 2 reviews the relevant literature on the relationship between innovation and entrepreneurship. Section 3 describes the empirical model specification and estimation methodology, also including variable selection and data sources and provides descriptive statistical analyses. Section 4 presents and interprets the empirical findings. Section 5 conducts extended analyses, further investigating the interactive mechanisms between innovation and entrepreneurship and assessing regional heterogeneity. Finally, Section 6 concludes by summarizing key findings and offering policy implications.

2. Literature Review and Hypotheses

Past studies have found that innovation and entrepreneurship are differentiated while interconnected. Innovation theory defines that any behavior that changes the wealth creation potential of existing resources can be called innovation. However, current academic research has not yet reached full agreement on the definition of “entrepreneurship”, but in recent years, the following two key points have been largely recognized: first, entrepreneurship is a process rather than an event; second, the core element of entrepreneurship is a series of responses to an opportunity [2,4]. Data from the Global Entrepreneurship Monitor suggests that not all entrepreneurial activity is accompanied by innovation, and that most innovations will not be realized through entrepreneurial means. In reality, however, the relationship between entrepreneurship and innovation is so strong that the public and policymakers often use the terms interchangeably, and entrepreneurship and innovation are often coupled to analyze the impact on economic activity [1,4,5,6].

2.1. Review of Research on Innovation for Entrepreneurship

In traditional research, innovation activities have been widely recognized as closely and positively correlated with entrepreneurial behaviors. Numerous studies explicitly position innovation as a prerequisite, core essence, and principal means underlying entrepreneurial processes [7,8]. Entrepreneurs establish startups by engaging in innovative actions and sustain their subsequent development through continuous innovation. Specifically, innovative activities drive entrepreneurial growth primarily through the following mechanisms:

First, innovation activities create entrepreneurial opportunities. Entrepreneurial opportunities refer to situations in which new products, services, or organizational methods are introduced into economic activities and markets [9]. Such opportunities typically emerge in response to evolving market conditions, shifting consumer demands, and structural changes within market environments. Innovation activities naturally satisfy the foundational conditions required for entrepreneurial opportunity creation. Outcomes of innovation often materialize as patents representing novel products, services, organizational structures, or production methods, which could effectively facilitate entrepreneurial opportunities by better fulfilling targeted consumer demands. Consequently, innovative behaviors extend existing market boundaries, creating additional economic activity spaces that encourage potential entrepreneurs to enter the market [10,11].

Second, innovation activities contribute substantially to the survival and sustained growth of startups. Innovation frequently involves developing, introducing, or refining products, processes, or business models. These activities enable startups and entrepreneurs to enhance performance and increase their market influence, thereby becoming crucial determinants for startups’ survival and long-term success [8,12]. Furthermore, different innovation modes significantly influence innovation outcomes and firm performance. Research and development (R&D) expenditures and investment activities, regarded as precursors to innovation, critically impact firms’ capabilities to develop new products and adopt innovative technologies that enhance productivity [13,14,15]. Additionally, proactive innovation, particularly in agile business model development, enables startups to flexibly configure, adapt, and reallocate internal and external resources and capabilities to achieve dynamic competitive advantages aligned with evolving customer and market demands. Moreover, innovation acquisition through external knowledge access or collaborative R&D partnerships helps entrepreneurs enhance absorptive capacity, strengthening their capabilities for subsequent innovation in products, processes, or business models, thus maintaining startups’ competitive positions and improving their sustainability [10].

Third, innovation activities facilitate the accumulation of essential entrepreneurial resources for entrepreneurs and startups. Throughout the entrepreneurial journey, entrepreneurs must integrate external resources with internally held assets to recognize and exploit entrepreneurial opportunities [11]. Innovative activities conducted before or during the early entrepreneurial phases typically yield novel products, services, or other unique assets, serving as critical initial resource endowments essential for initiating and supporting entrepreneurial ventures. In subsequent entrepreneurial phases, innovation-driven development of novel products, services, organizational structures, or processes can further enhance the resource base of startups, granting them assets characterized by rarity, uniqueness, and difficulty of imitation [12]. Such unique resource advantages enable startups to acquire external resources more efficiently, integrating them effectively with existing assets, thereby significantly increasing their survival prospects and enhancing subsequent growth potential [9].

Finally, innovation activities aid entrepreneurs and startups in formulating strategic orientations. Entrepreneurial strategy predominantly encompasses defining entrepreneurial orientation and guiding future business activities. Innovation-generated resources provide startups with initial endowments that determine their competitive advantages and strategic directions in subsequent operations. For example, innovations yielding novel products, services, or organizational methods typically orient startups towards expanding and capturing emerging markets. Conversely, innovations aimed at improving existing products, services, or processes can help startups reinforce their competitive positions within established markets [11].

In summary, innovation activities substantially shape the entrepreneurial process, from opportunity creation and resource accumulation to strategic positioning, significantly enhancing startups’ survival, adaptability, and long-term competitive advantage.

2.2. Review of Research on Entrepreneurship for Innovation

Existing research also emphasizes the critical role of entrepreneurship in fostering innovation. First, entrepreneurial activity is widely acknowledged as an essential catalyst for innovation due to the inherent connection between these two phenomena. Entrepreneurial activity typically involves the identification, exploitation, and realization of opportunities, where establishing legitimacy often constitutes a decisive factor for the survival and subsequent development of startups [16]. Innovation significantly contributes to legitimacy-building processes; startups differentiate their business models and products from established competitors through innovative approaches, thus circumventing early stage imitation traps and alleviating competitive pressures caused by normative institutional isomorphism. Consequently, entrepreneurial initiatives facilitate a strategic orientation toward innovation, effectively stimulating the proliferation of innovative activities [16,17].

Second, entrepreneurial firms must actively seize emerging industry opportunities, attract new customer segments, and penetrate new markets to achieve sustainable growth and profitability. For startups and entrepreneurs, proactive engagement in innovation represents a key strategic choice to secure first-mover advantages, facilitating rapid market entry, quicker profitability, and accelerated recovery of initial investments [17]. Hence, entrepreneurial strategies often prioritize active innovation, especially disruptive innovations. These innovations could significantly reshape existing market structures and business models. Empirical research across various global markets consistently supports this viewpoint, highlighting a strong positive correlation between entrepreneurial behavior and innovation outcomes [18].

Third, from a governmental policy perspective, innovation-driven entrepreneurship represents a critical engine for promoting economic growth, wealth accumulation, and employment creation. Encouraging entrepreneurial initiatives has become an indispensable policy measure to stimulate innovation. For entities or individuals engaging in innovative endeavors, securing resources during the initial stages of entrepreneurship is equally essential as finalizing innovation outcomes and realizing economic returns [19]. China’s current policy framework explicitly recognizes this reality. Accordingly, policy incentives for innovation not only involve talent cultivation and financial support for scientific research but also emphasize promoting the commercialization of innovation through entrepreneurship, thereby enhancing innovators’ ability to generate economic returns [20].

In summary, while innovation activities undoubtedly drive entrepreneurial behavior, the characteristics inherent in entrepreneurial processes also significantly incentivize innovation. This reciprocal influence implies a potential bidirectional causality between innovation and entrepreneurship. Thus, focusing solely on unidirectional causation may yield incomplete or even biased interpretations, whether from innovation to entrepreneurship or vice versa. Indeed, the underlying relationship between these two constructs is likely more complex than existing studies suggest.

Bidirectional causality between variables is frequently acknowledged in contemporary research [21,22,23,24]; however, scholars typically treat such causality as a source of endogeneity and attempt to mitigate its influence through instrumental variables, natural experiments, or other econometric techniques. Although these approaches rigorously establish unidirectional causation by ensuring exogeneity, they often fail to comprehensively portray the mutual feedback mechanisms, causal pathways, and dynamic interplay between variables. To address this limitation and elucidate the complete dynamic relationship between innovation and entrepreneurship in China, this study integrates both constructs into a unified analytical framework. Employing a dynamic panel methodology that explicitly considers contemporaneous and lagged interactions, this research systematically investigates potential bidirectional causal relationships between innovation and entrepreneurship [21]. Moreover, acknowledging regional heterogeneity in China’s economic landscape, this study further conducts supplementary analyses to explore provincial variations in innovation–entrepreneurship dynamics. Additionally, this paper employs the impulse–response function derived from a panel structural vector autoregression (PVAR) model, offering a precise depiction of dynamic interactions between innovation and entrepreneurship.

2.3. Variable Relationships and Hypotheses

This study focuses on the dynamic relationship between entrepreneurship and innovation activities, and firstly, we need to conduct a unit root test on the panel data to check the smoothness of the overall data. In order to make the test results more credible, this study will adopt the more common LLC test for homogeneous panel data, as well as the IPS test, Fisher–ADF test and LLC test for heterogeneous panel data to test the smoothness of the data. In addition, this study will also identify the long-term relationship between the variables through the cointegration test, and when the cointegration relationship between the variables is identified, the direction and type of causality between the variables will be further researched and discussed. This study focuses on the causal relationship between entrepreneurship and innovation activities, and the potential causal relationships include unidirectional, bidirectional, and no causal relationship, i.e., there may be positive or negative impacts, as well as long-term and short-term differences.

This study constructs a dynamic panel model including innovation, entrepreneurship and other potentially relevant macroeconomic control variables to investigate the dynamic relationship between innovation and entrepreneurial activities. This study examines the correlation between innovation and entrepreneurship within the same framework, taking into account the effects of the variables’ own lags while extending the classical dynamic panel estimation strategy to be compatible with the effects of contemporaneous bi-directional causality among the variables. In this study, while considering the two-way causality, we cannot ignore the dynamic impact of its own lag period, in order to capture the dynamic effects among system variables more effectively, therefore, we utilize the panel error correction model linkage equations expressed as follows:

$$\left\{\begin{array}{l}{entrepreneurship}_{i,t}={\beta }_0{entrepreneurship}_{i,t-1}+{\beta }_1{innovation}_{i,t}+\sum {Control}_{n,t}+v_i+e_{i,t}\\ {innovation}_{i,t}={\beta }_2{innovation}_{i,t-1}+{\beta }_3{entrepreneurship}_{i,t}+\sum {control}_{n,t}+w_i+{\mu }_{i,t}\end{array}\right..$$

(1)

Entrepreneurship_it and innovation_it represent the innovation activities in China as a whole (when i = 0) and in different provinces (when i > 0), and the development of innovation and entrepreneurship activities, e where entrepreneurship_it and innovation_it represent the development of innovation activities and entrepreneurial activities in China as a whole (when i = 0) and in different provinces (when i > 0), respectively, and e_i,t and μ_i,t are the unobservable perturbation terms in the two equations, respectively. The necessary control variables Control_n,t are also included in each equation, as well as v_i and w_i terms to represent individual fixed effects that do not vary over time. In this process, the coefficients β₀, β₁, β₂, and β₃ estimate the correlation between innovative and entrepreneurial activities. In order to analyze the bidirectional causality between innovation and entrepreneurial activities more precisely, this study differentially transforms the system of equations to eliminate the individual fixed effects and obtains a system of first-order differential linear contemporaneous dynamic simultaneous joint equations:

$$\left\{\begin{array}{l}∆{entrepreneurship}_{i,t}={\alpha }_0∆{innovation}_{i,t}+{\alpha }_1∆{entrepreneurship}_{i,t-1}+∆e_{i,t}\\ {∆innovation}_{i,t}={\alpha }_2∆{innovation}_{i,t-1}+{\alpha }_3∆{entrepreneurship}_{i,t}+∆{\mu }_{i,t}\end{array}\right.$$

(2)

In the formula, t represents the time range of variable taking values, and i refers to different provinces. When entrepreneurship_i,t and innovation_i,t are smooth and there is a cointegration relationship, the null hypothesis of Granger causality test is that innovation is a non-Granger cause of entrepreneurship or entrepreneurship is an innovation, at this time, α₀ = α₃ = 0. If the null hypothesis is valid, it means that no significant Granger causality between innovation and entrepreneurship and entrepreneurship and innovation exists. When only one of α₀ or α₃ is 0, it implies that there is unidirectional causality between innovation and entrepreneurial activities. When and only when α₀ or α₃ are not 0 and satisfy the requirement of significance, there is bidirectional causality between innovation and entrepreneurial activities, at this time, innovation and entrepreneurship are both caused by each other Granger and can play a predictive role for each other. At this time, the correlation between innovation and entrepreneurial activities is as follows (in Figure 1, note: “……” means the process from 2 to t − 2, the same as shown below):

On this basis, Hypothesis I is proposed: there is a bidirectional causal relationship between innovation and entrepreneurial activities, but there is only a contemporaneous effect between innovation and entrepreneurship, while the entrepreneurship_i,t−1 can only have an effect on innovation_i,t−1, or through the influence of entrepreneurship_i,t and eventually pass through to innovation_i,t.

Hypothesis 1 implies that innovation can only influence the occurrence of future entrepreneurial activity through state dependence, but not the likelihood of a shock between the variables occurring in the next period, while entrepreneurship influences the process of innovation. However, considering the complexity of the real situation, there may be a certain time gap and lag between the transformation of innovative activities into entrepreneurial projects and the process of innovation carried out by entrepreneurial firms. Therefore, considering the requirements of the System GMM, the Hypothesis that the perturbation term is uncorrelated with the sequence of lagged terms is further relaxed, so that the perturbation term of the equation is uncorrelated with the lagged term of the variable in the period t − 2 and later [25,26]. The correlation between innovation activity and entrepreneurial activity has also changed (in Figure 2):

On this basis, Hypothesis 2 is formulated: there is a bi-directional causality between innovation and entrepreneurial activity, when the variable’s period t − 2 and later can have an impact on period t through itself and the period t − 1 of the variable in the same period. The constraints of Hypothesis 2 are further relaxed and may apply to a wider range of situations in the case of compatibility with Hypothesis 1. However, if there is no serial correlation between the lagged and disturbed terms of the variables, i.e., when the pre-relaxation of Hypothesis 2 no longer holds, the results of Hypothesis 1 are more consistent and have higher convergence. Therefore, in this study, regression will be conducted based on hypothesis 1 and further verified by hypothesis 2 [27,28]. Also, in order to test the reasonableness of the instrumental variables and the serial correlation of the residual terms, Hansen’s test with the AR test will also be used to ensure the validity of the estimation results.

3. Data and Methods

3.1. Model Setting

In empirical studies analyzing the direction of causality between variables, the current common dynamic panel estimation method is the Generalized Method of Moments (GMM), which includes difference GMM and system GMM. The traditional difference GMM method requires that the perturbation term needs to be serially uncorrelated with the lagged term of the variable and thus cannot test the bidirectional causality between variables. In contrast, the system GMM approach relaxes this requirement, and in the case of panel data satisfying T ≥ 3 and a large N, after controlling for individual effects of variables and potentially relevant variables, the remainder of the disturbance term is random and the lagged terms of the explanatory variables are uncorrelated with it [22,23]. Therefore, the difference terms of the explanatory variables can be chosen as instrumental variables for their lagged terms and combined with individual difference equations to form a systematic GMM estimation method [24]. Under the premise that bi-directional causality holds, there is an interaction between innovation and entrepreneurial activities, and the results of any shocks to innovation will be transmitted to the final situation of entrepreneurial activities, while shocks to entrepreneurial activities will likewise have an impact on innovation. On this basis, in order to fully reveal the causal relationship between innovation and entrepreneurship in China, this study analyzes the potential bidirectional causality between the two based on an extended to dynamic side panel model, taking into account the effects of the lags of the variables themselves, and selecting the relevant data at the provincial level in China for testing.

3.2. Variable Selection

Core variables: Regional entrepreneurial activity and regional innovation activity. This study primarily focuses on identifying the dynamic relationship between regional entrepreneurial activity and regional innovation in China, emphasizing the coefficients reflecting mutual causality in regression models. To eliminate the potential effects of non-time-varying regional factors, such as administrative divisions, the linear dynamic equations system is differenced before estimation. Specifically, regional entrepreneurial activity is measured using the annual number of newly registered enterprises [5,6,7], which directly captures entrepreneurial initiation from inception [5,6,7,8]. The natural logarithm of new startup registrations in each province from 2000 to 2021 is employed to reflect regional variations and dynamic trends in entrepreneurial activity. Similarly, regional innovation intensity is typically represented by innovation outputs [6,7,8,9,20]. Hence, the number of annual patents granted is utilized as a proxy for regional innovation, and its logarithmic transformation captures dynamic regional differences in innovation intensity across the same period [7,19,20].

Control variables: To exclude potential confounding effects and enhance the robustness of empirical findings, this study incorporates several time-varying regional economic factors previously identified as influential for innovation and entrepreneurship. Prior research highlights market size and structure, regional economic development, government intervention, and financial development as significant determinants of innovation and entrepreneurial activities. Therefore, control variables were selected to comprehensively represent these influential factors.

Specifically, regional GDP per capita is adopted as a proxy for regional economic development levels, reflecting local economic conditions likely to affect entrepreneurial and innovative initiatives [29]. The ratio of government expenditure to regional GDP captures the degree of governmental intervention and market regulation [30]. Regional financial development is measured by the logarithm of total regional deposits and loans, indicating financial market depth and capital availability [30,31]. Lastly, regional human capital resources are approximated by the logarithmically transformed resident population size in each province, representing available human capital stocks [30,32].

3.3. Descriptive Statistics

Considering data availability and sample adequacy, this research covers a balanced panel dataset comprising 31 provincial administrative regions in China over a period of 21 years (2000–2021). Data utilized in this analysis are sourced from publicly available reports published by the National Bureau of Statistics of China (NBS) and the China Regional Economic Statistics Yearbook.

Table 1. Results of descriptive statistics.

Variable Name	Abbreviation	Variable Description	Mean	Standard Deviation
Entrepreneurship	ent	Regional level of entrepreneurship (logarithm of the number of regional new startups)	12.283	1.237
Innovation	pat	Regional level of innovation (logarithm of the number of new patents granted in the region)	9.072	1.973
Marketization degree	market	Ratio of government expenditure to GDP	0.827	0.059
Financial index	fin	Ratio of the value added of the regional financial sector’s GDP to the total GDP	0.058	0.032
GDP per capita	pgdp	Level of economic development (GDP per capita, logarithm of the GDP)	9.386	3.339
Population	peo	Permanent population of the region, reflecting the human resources of the region	8.091	0.859

summarizes descriptive statistics for all variables used in the empirical analysis. The standard deviations presented indicate relatively moderate dispersion, implying acceptable data variability and the absence of severe outliers, thus ensuring robustness of the subsequent econometric analysis. Prior to regression estimation and Granger causality tests, all variables underwent rigorous preprocessing, including handling of missing values, detection and removal of potential outliers, and appropriate data transformations.

4. Results and Analysis

4.1. Baseline Regression Results

The core analytical objective is to empirically assess the contemporaneous bidirectional causality between regional entrepreneurial and innovation activities. To adequately reflect dynamic interactions, the analysis incorporates lagged dependent variables. Consequently, this study employs stepwise regression techniques within a dynamic panel estimation framework to systematically explore mutual causation between entrepreneurship and innovation (summarized in

Table 2. Main model regression results.

	Hypothesis 1				Hypothesis 2
	(1)	(2)	(3)	(4)	(5)	(6)
	ent	pat	ent	pat	ent	pat
ent		0.881 *** (56.5)		0.151 *** (3.47)		0.119 ** (2.5)
L. ent	0.776 *** (17.84)		0.739 *** (15.76)		0.739 *** (15.63)
pat	0.118 *** (4.48)		0.121 *** (2.64)		0.107 * (1.84)
L.pat		0.223 *** (6.89)		0.842 *** (30.33)		0.835 *** (20.76)
Control Variable	NO	NO	YES	YES	YES	YES
AR (1)	(0.001)	(0.002)	(0.002)	(0.002)	(0.002)	(0.003)
AR (2)	(0.858)	(0.223)	(0.841)	(0.297)	(0.894)	(0.220)
Hansen J	30.88	30.84	30.03	30.67	29.94	30.61
	(1.000)	(1.000)	(1.000)	(1.000)	(1.000)	(1.000)
Observations	651	651	651	651	651	651

Note: *** p < 0.01, ** p < 0.05, * p < 0.1.

).

Empirical models are assessed using Hansen’s J-test to validate instrumental variables, yielding p-values consistently exceeding 0.1, thus indicating valid instrument selection. Additionally, residual serial correlation diagnostics confirm the appropriateness of model specification, as AR(1) tests reveal expected first-order correlation (p < 0.1), while AR(2) and AR(3) tests show no significantly higher-order correlation (p > 0.1).

Given these conditions, this paper adopts the System Generalized Method of Moments (System-GMM) estimator, jointly estimating level (Equation (2)) and differenced (Equation (3)) equation systems. The regression outcomes, summarized in Table 2, control for macroeconomic factors and indicate several key findings. First, lagged entrepreneurial and innovation activities exhibit significantly positive effects, demonstrating notable dynamic cumulative impacts within each respective domain. Second, contemporaneous interactions reveal significant mutual positive effects; specifically, a 1% increase in entrepreneurial activity (measured by newly registered enterprises) is associated with approximately a 0.881% rise in patent grants. Similarly, a contemporaneous 1% increase in patent grants stimulates entrepreneurial activity by approximately 0.118%. Inclusion of macroeconomic control variables further confirms these relationships, suggesting the robustness and stability of the identified bidirectional causality.

Empirical results affirm a robust and mutually reinforcing relationship between regional entrepreneurial and innovative activities in China. In practice, this interaction is evidenced by an increase in startup registrations fostering greater innovation, while higher innovation output simultaneously encourages entrepreneurial initiatives. Innovations enhance regional industrial potential, attracting new entrepreneurial entrants, while the daily operations of entrepreneurial ventures further facilitate the generation, application, and formalization of patentable innovations, forming a virtuous cycle. Thus, empirical evidence strongly supports contemporaneous bidirectional causality between innovation and entrepreneurship. To further substantiate these findings, this study conducts rigorous robustness checks employing sub-sample analyses and extends the analysis using impulse response functions within a Panel VAR (PVAR) framework to capture potential lagged impacts.

4.2. Robust Test

To test the reliability of the benchmark regression results, this study conducted a robust type test by sub-sample regression. Currently, China’s innovation patents are divided into invention patents, utility model patents and design patents, and the data show that invention patents and utility model patents accounted for nearly 75% of the total number of patents granted during 2000–2022, and similarly China’s tertiary industry entrepreneurial enterprises also accounted for 85% of the number of newly registered enterprises. Therefore, this study uses the sum of invention patents and utility model patents and the number of tertiary industry startups to replace the original innovation activity and entrepreneurial activity in this study, using the same method for the joint estimation and finds that the dynamic relationship between innovation and entrepreneurship still exists. This indicates that the replacement of core explanatory variables does not change the main conclusions of this paper (summarized in

Table 3. Results of Robust test.

	Patent Classification		Entrepreneurial Classification
	(1)	(2)	(3)	(4)
	ent	pat	ent	pat
ent		0.0785 *** (4.76)		0.0997 *** (5.89)
L. ent	0.9032 *** (28.71)		0.8220 *** (26.55)
pat	0.0451 *** (2.26)		0.1001 *** (4.51)
L. pat		0.6289801 *** (78.08)		0.8890 *** (47.75)
Control Variable	YES	YES	YES	YES
AR (1)	(0.001)	(0.002)	(0.001)	(0.001)
AR (2)	(0.649)	(0.760)	(0.858)	(0.821)
Hansen J	30.70	30.93	29.42	30.66
	(1.000)	(1.000)	(1.000)	(1.000)
Observations	651	651	651	651

Note: *** p < 0.01.

).

Further robustness verification addresses structural shifts associated with major economic events. Notably, the 2008 global financial crisis significantly reshaped China’s macroeconomic landscape, influencing domestic innovation and entrepreneurship trajectories. Therefore, this study analyzed two periods: from 2000 to 2008 and from 2009 to 2021. Results confirm the consistent presence of a stable dynamic relationship between innovation and entrepreneurship across both periods. Despite evident macroeconomic disturbances, the core findings regarding contemporaneous and dynamic bidirectional causality between entrepreneurial and innovative activities remain consistently significant, underscoring the resilience and reliability of the study’s primary conclusions (summarized in

Table 4. Results of Robust test.

	Before the Financial Crisis		After the Financial Crisis
	(1)	(2)	(3)	(4)
	ent	pat		ent
ent		0.0785 *** (4.76)		0.184 *** (0.045)
L. ent	0.9032 *** (28.71)		0.868 *** (0.044)
pat	0.0451 *** (2.26)		0.868 * (0.024)
L.pat		0.6289801 *** (78.08)		0.807 *** (0.025)
Control Variable	YES	YES	YES	YES
AR (1)	(0.001)	(0.002)	(0.001)	(0.001)
AR (2)	(0.649)	(0.760)	(0.253)	(0.023)
Hansen J	30.70	30.93	29.70	30.81
	(1.000)	(1.000)	(1.000)	(1.000)
Observations	651	651	651	651

Note: *** p < 0.01, * p < 0.1.

).

5. Extensional Research

To further illustrate the dynamic interplay between innovation and entrepreneurial activities, this study employs a Panel Vector Autoregression (PVAR) framework, incorporating innovation, entrepreneurship, and relevant macroeconomic control variables. The PVAR approach combines the strengths of traditional time-series models and panel data methods, effectively capturing individual heterogeneity among variables, dynamic interdependencies, and causal mechanisms, thereby enhancing the robustness and validity of estimation results [22]. Compared to standard dynamic panel approaches, the PVAR model explicitly captures dynamic responses of each variable to exogenous shocks within the system through orthogonalized impulse response functions, while simultaneously clarifying variable ordering by integrating Granger causality tests and assessments of variable exogeneity [21,30]. Following stationarity and cointegration tests, this study employs the same dataset to examine impulse responses, forecast error variance decompositions, and regional heterogeneity in causal dynamics between innovation and entrepreneurship.

5.1. Unit Root Test

Initially, to ensure reliability and avoid spurious relationships, unit root tests were performed on core variables, including innovation intensity, entrepreneurial activity, and macroeconomic control variables. Robustness was ensured by adopting commonly applied tests: LLC, IPS, and Fisher tests under fixed-effects with linear trend specifications. Results indicate non-stationarity of the original series at the 5% significance level. After applying first-order differencing, the null hypothesis of a unit root was consistently rejected at the 5% significance level, confirming stationarity in the transformed variables. Consequently, potential issues related to spurious regression or incorrect causality inference due to non-stationary processes were effectively mitigated (summarized in

Table 5. Results of unit root test.

Variable	Original Hypothesis (H0)	LLC Test	IPS Test	Fisher Test
Innovation	The panel includes the unit root process	−17.1439 (0.0000)	−2.7356 (0.0031)	4.6005 (0.0000)
Entrepreneurship	The panel includes the unit root process	−14.4566 (0.0000)	−12.8997 (0.0000)	1.5952 (0.0553)
Degree of marketization	The panel includes the unit root process	−16.5522 (0.0000)	−15.5481 (0.0000)	1.9560 (0.0252)
Financial Development Index	The panel includes the unit root process	−12.4255 (0.0000)	−10.8302 (0.0000)	2.8956 (0.0019)
GDP per capita	The panel includes the unit root process	−18.8833 (0.0000)	−19.4612 (0.0000)	2.8833 (0.0020)
Resident population	The panel includes the unit root process	−8.4499 (0.0000)	−6.7398 (0.0000)	2.8672 (0.0021)

).

Subsequently, panel cointegration tests (summarized in

Table 6. Results of cointegration test.

	Tranc	5% Critical Value	p Value	Max-Eigen	5% Critical Value	p Value
rank = 0	−3.537	−7.326	0.000	−12.621	−0.65	0.258
rank > 1	−20.355	−8.084	0.000	−13.679	−3.954	0.000

) confirmed the existence of cointegration relationships among differenced core variables at the 5% significance level, validating the appropriateness of subsequent causality analysis within the PVAR framework.

Based on the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and Hannan-Quinn Information Criterion (HQIC), an optimal lag order of two periods was selected for the PVAR model (

Table 7. Results of optimal lag order selection.

lag	AIC	BIC	HQIC
1	−15.9441	−14.4169	−15.3518
2	−17.4364 *	−15.593 *	−16.7198 *
3	−15.7862	−13.6007	−14.9347
4	−15.3163	−12.7589	−14.3175
5	−16.7076	−13.744	−15.5473
6	−17.2534	−13.844	−15.9151
7	−18.2599	−14.3584	−16.7243

Note: * mean the best ranking.

).

5.2. Impulse Response Analysis

The impulse response analysis examines how shocks to innovation and entrepreneurship affect each other dynamically. Utilizing the same dataset, the PVAR model incorporated 23 response periods and was simulated via 1000 bootstrap replications to produce impulse response functions at a 90% confidence interval. Figure 3 and Figure 4 illustrate impulse response trajectories under alternative variable orderings to address potential sensitivity to variable sequencing.

Figure 3 demonstrates that both entrepreneurship and innovation exhibit smooth autoregressive responses following their own shocks, gradually diminishing over subsequent periods. In Figure 3, the middle line is the impulse response estimates for a horizon of up t time, and the lines on both sides are the one-standard error confidence bands, while the lines in Figure 4 have the same meaning. Specifically, the figure shows that a 1% increase in entrepreneurial activity significantly enhances innovation activity, reaching its peak effect (approximately 0.05%) in the eighth period, after which the response decays steadily with increasing uncertainty. Correspondingly, innovation positively influences entrepreneurial growth: a 1% increase in innovation leads immediately (first period) to a peak entrepreneurial response of approximately 0.2%.

To verify the robustness of impulse responses against alternative variable sequencing, Figure 4 presents results after adjusting the order of variables. Autoregressive trajectories remain consistent with Figure 3. Under this scenario, innovation’s impulse on entrepreneurial activity reaches a slightly lower maximum effect (around 0.02%) at period six, with a more delayed peak compared to previous settings. Conversely, entrepreneurship’s impact on innovation activity slightly decreases in magnitude (maximum effect around 0.15%), though the response pattern remains consistent.

Thus, these analyses confirm the robust, contemporaneous bidirectional causality between innovation and entrepreneurial activities in China, reflecting a self-reinforcing dynamic feedback mechanism. Specifically, entrepreneurial dynamism fosters innovation outputs, while enhanced innovation further stimulates entrepreneurial activity, cumulatively reinforcing regional economic vitality [33].

5.3. Forecast Error Variance Decomposition

Forecast error variance decomposition quantifies the relative contribution of shocks to each variable from itself versus other variables within the PVAR system [30]. Table 7 summarizes the five-year forecast error variance decomposition of innovation and entrepreneurship. In year one, variation in entrepreneurial activity originates exclusively from its own shocks, but this self-explanatory power significantly diminishes to merely 1.6% by year five, while innovation’s explanatory power increases markedly, accounting for approximately 89.2%. These results suggest that entrepreneurial activities become progressively less self-determined, increasingly relying on innovative outcomes.

Conversely, variation in innovation activity initially arises entirely from its own shocks, decreasing to about 55.3% in year five, with entrepreneurial activity and other macroeconomic factors explaining about 5.3% and 39.4%, respectively (in

Table 8. Results of forecast error variance decomposition.

Variable	Forecast Period	Entrepreneurship	Innovation	Other Variables
	1	100.00%	0.00%	0.00%
	2	79.70%	20.10%	0.20%
Entrepreneurship	3	13.60%	84.90%	1.40%
	4	3.40%	89.20%	7.40%
	5	1.60%	80.10%	18.30%
	1	0.00%	100.00%	0.00%
	2	0.30%	94.60%	5.00%
Innovation	3	1.20%	85.20%	13.60%
	4	3.60%	63.40%	32.90%
	5	5.30%	55.30%	39.40%

). These findings align closely with impulse response results, reinforcing the existence of strong mutual influences and robust bidirectional causality between innovation and entrepreneurship. This dynamic implies innovation exerts a significantly stronger cumulative influence on entrepreneurial activity compared to the reverse scenario, corroborating the study’s primary empirical conclusions.

The results of the forecast error variance decomposition are similar to the results of the impulse response analysis of the PVAR model, with a strong correlation and correlation between innovation and entrepreneurial activities, and a significant bidirectional causal relationship between innovation and entrepreneurial activities. In line with the main effect of the study, the growth of innovation activity is driven by the growth of entrepreneurial enterprises, but also by the influence of the output of the previous innovation, and the regional macroeconomic factors will also have the corresponding promotion and influence. The contribution of innovation activity to entrepreneurial activity is even greater, to a much greater extent than the impact of prior entrepreneurial activity and other macroeconomic factors, which effectively complements the findings of the main effects.

5.4. Heterogeneity of Location Factors

The Granger causality test within the PVAR framework further explores regional heterogeneity regarding causal relationships between entrepreneurial and innovation activities across China’s 31 provinces (in

Table 9. Results of forecast error variance decomposition.

Region	Result	Obs/lags	chi2	Prob > chi2|
The two-way causality is significant
Heilongjiang	Entrepreneurship influences innovation	23	24.62	0.000
	Innovation influences entrepreneurship	2	11.3	0.000
Jilin	Entrepreneurship influences innovation	23	12.268	0.002
	Innovation influences entrepreneurship	2	16.105	0.000
Liaoning	Entrepreneurship influences innovation	23	15.879	0.000
	Innovation influences entrepreneurship	2	6.531	0.038
Qinghai	Entrepreneurship influences innovation	23	11.691	0.003
	Innovation influences entrepreneurship	2	4.823	0.090
Ningxia	Entrepreneurship influences innovation	23	−3.97	0.000
	Innovation influences entrepreneurship	2	1.91	0.057
Shaanxi	Entrepreneurship influences innovation	23	6.9321	0.031
	Innovation influences entrepreneurship	2	14.9	0.001
Tianjin	Entrepreneurship influences innovation	23	4.9347	0.085
	Innovation influences entrepreneurship	2	8.224	0.016
Xizang	Entrepreneurship influences innovation	23	5.0723	0.079
	Innovation influences entrepreneurship	2	10.205	0.006
Entrepreneurship affects innovation
Fujian	Entrepreneurship affects innovation	23	26.011	0.000
	Innovation does not affect entrepreneurship	2	2.287	0.319
Guangdong	Entrepreneurship affects innovation	23	20.839	0.000
	Innovation does not affect entrepreneurship	2	0.869	0.648
Jiangsu	Entrepreneurship affects innovation	23	14.721	0.001
	Innovation does not affect entrepreneurship	2	1.241	0.538
Zhejiang	Entrepreneurship affects innovation	23	21.865	0.000
	Innovation does not affect entrepreneurship	2	0.044	0.978
Innovation affects entrepreneurship
Beijing	Entrepreneurship does not affects innovation	23	0.204	0.903
	Innovation affect entrepreneurship	2	5.066	0.079
Guangxi	Entrepreneurship does not affects innovation	23	1.069	0.586
	Innovation affect entrepreneurship	2	8.445	0.015
Guizhou	Entrepreneurship does not affects innovation	23	1.710	0.425
	Innovation affect entrepreneurship	2	9.079	0.011
Hebei	Entrepreneurship does not affects innovation	23	0.899	0.638
	Innovation affect entrepreneurship	2	8.594	0.014
Henan	Entrepreneurship does not affects innovation	23	1.914	0.384
	Innovation affect entrepreneurship	2	45.183	0.000
Jiangxi	Entrepreneurship does not affects innovation	23	0.752	0.687
	Innovation affect entrepreneurship	2	13.156	0.001
Neimenggu	Entrepreneurship does not affects innovation	23	1.8924	0.388
	Innovation affect entrepreneurship	2	7.956	0.019
Shandong	Entrepreneurship does not affects innovation	23	1.582	0.453
	Innovation affect entrepreneurship	2	9.156	0.010
Shanxi	Entrepreneurship does not affects innovation	23	2.187	0.335
	Innovation affect entrepreneurship	2	4.833	0.089
Sichuan	Entrepreneurship does not affects innovation	23	0.09757	0.952
	Innovation affect entrepreneurship	2	6.8668	0.032
Xinjiang	Entrepreneurship does not affects innovation	23	0.724	0.696
	Innovation affect entrepreneurship	2	4.999	0.082
Yunnan	Entrepreneurship does not affects innovation	23	1.463	0.481
	Innovation affect entrepreneurship	2	13.524	0.001
The two-way causality is not significant
Anhui	Entrepreneurship does not affects innovation	23	0.148	0.929
	Innovation does not affect entrepreneurship	2	0.718	0.698
Gansu	Entrepreneurship does not affects innovation	23	2.899	0.235
	Innovation does not affect entrepreneurship	2	1.768	0.413
Hainan	Entrepreneurship does not affects innovation	23	0.713	0.700
	Innovation does not affect entrepreneurship	2	4.389	0.111
Hubei	Entrepreneurship does not affects innovation	23	0.015	0.992
	Innovation does not affect entrepreneurship	2	4.308	0.116
Hunan	Entrepreneurship does not affects innovation	23	3.936	0.140
	Innovation does not affect entrepreneurship	2	4.416	0.110
Shanghai	Entrepreneurship does not affects innovation	23	3.705	0.157
	Innovation does not affect entrepreneurship	2	0.025	0.987
Chongqing	Entrepreneurship does not affects innovation	23	0.49	0.783
	Innovation does not affect entrepreneurship	2	1.6218	0.444

). Results indicate significant bidirectional causality between entrepreneurship and innovation in eight provinces and autonomous regions, including Heilongjiang, Jilin, Liaoning, Qinghai, Ningxia, Shaanxi, Tianjin, and Tibet. In these regions, enhanced patent output significantly drives entrepreneurship, while entrepreneurial proliferation concurrently boosts regional innovation performance.

Unidirectional causality from innovation to entrepreneurship is observed in twelve provinces and regions: Guizhou, Henan, Hainan, Hebei, Beijing, Inner Mongolia, Shandong, Sichuan, Shanxi, Jiangxi, Yunnan, and Xinjiang. Here, increased patent activity substantially stimulates regional entrepreneurial growth, but entrepreneurship itself does not significantly spur innovation. Conversely, in economically developed provinces such as Fujian, Jiangsu, Guangdong, and Zhejiang, causality predominantly flows from entrepreneurship to innovation. Entrepreneurial growth in these regions significantly accelerates patenting activity, whereas innovation outputs exhibit limited feedback influence on entrepreneurship.

Finally, in provinces such as Anhui, Gansu, Hubei, Hunan, Shanghai, and Chongqing, no significant causality emerges in either direction. This lack of causal interaction can be attributed either to insufficient macroeconomic conditions, constraining innovation-entrepreneurship transformation processes, or to highly diversified innovation ecosystems where multiple stakeholders beyond entrepreneurial enterprises predominantly drive regional innovation, thereby diminishing the direct interdependence between entrepreneurship and innovation.

These findings underscore substantial regional heterogeneity in innovation–entrepreneurship dynamics, highlighting the necessity for region-specific policies to maximize dual-innovation potential and facilitate effective regional economic development strategies.

The above empirical findings indicate that the stability and significance of the bidirectional causality between innovation and entrepreneurial activities depend heavily on macroeconomic factors, including regional disparities in economic development, scientific research capacities, and the endowments of human and financial resources. Such macro-level conditions fundamentally determine the feasibility of innovation-led entrepreneurship and whether entrepreneurial ventures can accumulate adequate resources to foster continuous innovation.

Specifically, empirical analyses reveal robust bidirectional causality primarily in provinces such as Heilongjiang, Jilin, Liaoning, Qinghai, Ningxia Hui Autonomous Region, Shaanxi, Tianjin, and Tibet, where innovation consistently drives entrepreneurship, and entrepreneurship simultaneously promotes local innovation.

In contrast, in economically developed regions such as Fujian, Guangdong, Jiangsu, and Zhejiang, a unilateral causal relationship emerges predominantly from entrepreneurship to innovation. These provinces feature mature market economies with well-developed institutional frameworks that protect entrepreneurial enterprises and encourage innovation activities. Nevertheless, due to the well-established market environments, entrepreneurial behaviors in these regions are less reliant solely on innovative outputs and are often driven by imitation and profit-seeking opportunities derived from existing market mechanisms, institutional environments, and international trade dynamics [34]. Consequently, innovation-driven entrepreneurial growth is comparatively less pronounced.

Regions where innovation unilaterally drives entrepreneurship far outnumber those regions where entrepreneurship unilaterally stimulates innovation, and these regions are primarily located in North, Northwest, and Southwest China. These areas typically experience constrained market conditions, limited entrepreneurial resources, and insufficient incentives for startups to pursue active innovation independently. Innovation in these regions tends to originate from established firms, government institutions, or research universities, indicating a relatively limited impact of entrepreneurial activities on regional innovation growth [34,35].

Finally, in provinces where no significant causal relationship is identified, restrictive macroeconomic conditions result in an unstable relationship between entrepreneurship and innovation. The reasons usually include insufficient economic development, limited financial support, or inadequate innovation infrastructure. Additionally, in regions with abundant educational and research resources, such as Shanghai, Chongqing, Hubei, and Hunan, diverse actors beyond entrepreneurial ventures play dominant roles in innovation activities, thus diminishing the exclusive influence of entrepreneurship. The complexity and multiplicity of influencing factors further disrupt the stable interaction mechanism between innovation and entrepreneurial activities, resulting in non-significant or unstable causality.

6. Conclusions

Innovation and entrepreneurial activities have consistently served as pivotal contributors to China’s economic growth and industrial upgrading, both during previous high-speed economic expansion and the current transition towards high-quality development. Based on a comprehensive empirical analysis of panel data from 31 provincial-level administrative regions spanning 2000–2022, this study employs the System Generalized Method of Moments (System-GMM) approach within a dynamic panel model framework to systematically examine the interactive relationship between innovation and entrepreneurial activities.

Firstly, empirical results demonstrate a robust, positive, and bidirectional dynamic causal relationship between regional innovation and entrepreneurial activities. Specifically, increased entrepreneurial activity significantly enhances innovation outputs, while innovation activities similarly foster entrepreneurial growth. Robustness checks through subsample regressions further confirm the stability and consistency of these core findings. These outcomes strongly validate the rationale and necessity of China’s current dual-innovation (“Mass Entrepreneurship and Innovation”) policy system, emphasizing that innovation and entrepreneurship constitute inseparable components within China’s contemporary economic development framework. Given their inherent interdependence, isolated policy support targeting either innovation or entrepreneurship alone may prove insufficient. Therefore, governmental policies should more actively leverage entrepreneurial mechanisms to translate innovation outputs into practical applications, simultaneously encouraging innovation as a primary source of sustainable entrepreneurial opportunities.

Secondly, the variance decomposition and impulse-response analyses within the panel VAR (PVAR) framework indicate that the mutual interaction between innovation and entrepreneurship is more dynamically intensive than previously recognized. Specifically, innovation growth depends heavily on previous innovation outputs, entrepreneurial dynamics, and macroeconomic factors. Notably, innovation’s cumulative influence on entrepreneurship surpasses the impact of prior entrepreneurial activity, confirming existing findings regarding innovation’s role as a foundational resource and primary opportunity source for entrepreneurship. Given these findings, policy initiatives should prioritize support and subsidies targeting innovation processes, incentivizing entrepreneurs by enhancing market infrastructures, facilitating entrepreneurial opportunities, and ensuring resource availability for entrepreneurial ventures.

Thirdly, significant heterogeneity exists regarding innovation-entrepreneurship interactions across Chinese provinces, primarily due to variations in regional economic development, resource endowments, and macroeconomic contexts. Empirical evidence suggests regional governments should customize dual-innovation policies according to local characteristics. In innovation-driven regions, policies should focus on incentivizing startups to engage actively in innovation, including targeted financial assistance, tax incentives, and talent recruitment. Conversely, in entrepreneurship-driven areas, governments should facilitate the transformation of innovation outputs into viable entrepreneurial ventures through incubation mechanisms, fiscal policies, and industrial support measures. Finally, regions lacking significant innovation-entrepreneurship interactions must leverage comparative advantages, optimize existing industrial policies, and strategically accumulate resources to foster conducive innovation and entrepreneurship ecosystems. The insights from this research thus provide valuable theoretical guidance for tailored policy-making at the regional level.

Despite these contributions, this study has certain limitations. First, the analysis predominantly relies on Chinese domestic data post-2000, lacking comparative benchmarks from other major global economies. Due to the completeness and accessibility of the data, this study ignores relevant data from 2022 to the present and, therefore, fails to discuss the impact of other macro events, such as pandemics, wars, and economic recessions well. Second, while regional heterogeneity has been extensively addressed, the influence of industry-specific differences remains underexplored. Given that diverse production modes yield differential innovation demands and outputs, future studies should explicitly incorporate industrial variations. Finally, the distinction between opportunity-driven and necessity-driven entrepreneurship has not been clearly addressed. Recognizing that different entrepreneurial motivations significantly shape innovation activities, future research should systematically investigate these nuanced relationships to further enrich our understanding of the complex innovation-entrepreneurship nexus.