The impact of public policy on enterprise innovation performance: Panel data on financial subsidy policy

Abstract

This study examined the impact of government subsidies on enterprise innovation performance in China. The fixed effects model was used for empirical analysis, utilizing panel data from 17,670 observations of 3703 listed A-share companies between 2012 and 2022, and the findings indicate that government subsidies significantly enhance enterprise innovation performance, with R&D investment serving as a partial mediator. The enterprise scale, ownership nature, and regional economic differences influenced the effectiveness of the subsidy. Larger enterprises benefit more than SMEs; non-state-owned enterprises show stronger innovation incentives and the incentive effects are more pronounced in the central and western regions than in the eastern regions. This study recommends increasing government subsidies, particularly for SMEs in the central and western regions, by optimizing subsidy methods, enhancing targeting, and refining subsidy evaluation mechanisms. Therefore, enterprise managers should focus on strategic planning and continuous innovation to drive sustainable economic development. This study contributes to the theoretical understanding of subsidy policy impacts and offers practical policy insights for enhancing innovation performance in enterprises.

1. Introduction

The United Nations (2016) mentioned in its 17 sustainable development goals that the power of innovation lies in its ability to unleash economic vitality and enhance economic competitiveness, thereby fostering job creation and income generation [1]. Moreover, it plays a pivotal role in the introduction and dissemination of novel technologies, facilitation of international trade, and enhancement of resource utilization efficiency. Most studies have considered innovation essential in promoting economic sustainable development (Aghion et al., 2014) [2]. Innovation, as a national strategy, will increasingly become an important driving force for economic development. Therefore, numerous nations have instituted government subsidy policies to encourage enterprises' sustainable innovation, which is an efficient practice (Castellacci & Lie, 2015) [3]. A study by Block and Keller (2009) analyzed the relevant data of 100 enterprises that have won relevant awards for innovation and found that about 90 % have received government subsidies. Nevertheless, it is worth noting that innovation activities have high risks, and innovation results have spillover effects, affecting enterprises' enthusiasm for innovation [4]. The government should establish suitable policies to facilitate the business endeavors of enterprises (Batrancea et al., 2022) [5]. Reasonable public policies can achieve high-quality innovation and drive the sustainable development of enterprises (Pu et al., 2023) [6]. The 18th National Congress of the Communist Party of China convened in 2012, prioritized innovation as the primary objective for national development and increased policy support for enterprise innovation. Under the influence of these changes, China's economic development has entered a “new normal” mode. This mode is characterized by a significant elevation in the status of scientific and technological innovation, transitioning from imitation to independent innovation and achieving a shift from “following” the economy to “leading” social development. Traditional industries face a series of problems, such as overcapacity, declining added value, resource wastage, and severe environmental pollution. Emerging industries, including high-end information technology, clean energy, high-end industrial equipment manufacturing, and medical treatment, are leading the direction of future industrial development.

To adapt to this transformation, enterprises must establish a competitive advantage by cultivating innovative abilities. The corporate objective is to synergize research and development (R&D) activities with innovation (Valaskova et al., 2022) [7]. The government is the most important external support force that can effectively intervene in and regulate the market and support enterprises’ innovation activities by strengthening the innovation network at the national level (Johnson, 1982) [8]. Judging from international experience, government policy supports R&D mainly in the following aspects: direct subsidies for projects, tax relief or preferential treatment for the investigation and development investment of enterprises, protection of the intellectual nature of enterprise ownership, and other policy-based support means, including financing and support for human resources training. Direct subsidies and tax exemptions are the two most important policy instruments (González & Pazó, 2008) [9]. Against the backdrop of a transitional economy, the Chinese government has continuously increased its economic policy of subsidies in recent decades. The most direct effects on enterprises are the sharing of R&D expenditures and the reduction of market risk. Government R&D subsidies are an important source of funding for corporate innovation (Liu et al., 2021) [10]. Therefore, studying the effect of government subsidy policies on enterprise innovation during this period is of great practical significance and research value.

Academic circles have different views on the effects of government subsidies on enterprise innovation. One view holds that government subsidies can solve the market failure dilemma, encourage enterprises to engage in external fundamental and constructive R&D, form internationally competitive patents for innovation, and impact enterprises' innovative output (Brenner & Putelko, 2019; Mei & Luo,2020) [11,12]. Another point of view is that the lack of regulatory mechanisms for government subsidies will distort factor prices, making the enterprises’ motivation to invest in R&D weakened, and “rent-seeking” behavior occurs, ignoring the real R&D needs of enterprises, resulting in the “crowding-out effect” (Boeing et al., 2016; Barrachina & Moreno, 2024)) [13,14]. This conclusion has been confirmed by previous studies of late-developing industrialized countries such as Thailand and South Korea (Mani,2004; Wong,2001) [15,16].

From the enterprise standpoint, the engine for improving R&D capability is R&D investment, which is closely related to the number of patents obtained by enterprises (Mueller, 1966) [17], thus further promoting innovation benefits. However, the question of whether government subsidies encourage enterprises remains controversial. To invest in innovation. About 60 % of the studies conclude that government subsidies can increase enterprises’ investment in R&D, and nearly 40 % support the conclusion that government subsidies have little effect or a detrimental impact on them (Zúñiga-Vicente et al., 2014) [18]. Nevertheless, from a systematic perspective of the innovation process, R&D innovation is more professional and complex than other innovations. Some scholars believe that in socialist countries, state-owned enterprises have natural privileges in receiving government subsidies (Hou &Li, 2023) [19]. However, improvements in innovation performance have not been significant (Ma et al., 2023) [20]. Others believe that state-owned enterprises outperform innovation (Feng & Wang, 2023) [21]. Similarly, the repercussions of different enterprises using government subsidies to improve innovation performance differ because of the different scales of the enterprises. Some believe that small- and medium-scale enterprises (SMEs) benefit more (Bronzini & Piselli, 2016) [22], while others believe that large-scale enterprises benefit more (Zheng & Zhang, 2019) [23]. The degree of development, competition, management levels, internal governance, and demand for innovation vary among enterprises in different regions of China. This leads to variations in the efficacy of government subsidies.

Academic discussions on the impact of government subsidies on corporate innovation have revealed two primary perspectives: positive and negative. Subsidies can address market failures by providing financial support for companies engaging in research and development (R&D), particularly for those unable to bear the costs themselves. Such support can lead to significant advances in innovation and competitive patent creation. However, inadequate regulation may result in inefficiency, as companies might engage in “rent-seeking” behavior, focusing on obtaining funds rather than on genuine innovation, thereby reducing their motivation for spontaneous innovation. Therefore, the impact of subsidies is conditional. Economic policies and regulatory frameworks play crucial roles in determining the effectiveness of subsidies, and more subsidies do not necessarily lead to increased R&D investment. Although government subsidies have the potential to promote corporate innovation, their effectiveness depends on the characteristics of enterprises and the regional context.

Despite the existing literature exploring the impact of government subsidies on innovation performance from various perspectives, the research conclusions remain contradictory, and a comprehensive discussion of the mechanisms involved is still lacking. Different development periods, economic regions, and company sizes or types may yield different results, and the influencing mechanisms are not singular. These aspects require further investigation. Therefore, this study aims to investigate and understand the complex impact mechanisms during the specific period of the “new normal” and to design subsidy policies tailored to specific needs and conditions. This study used a dataset consisting of 17,670 panel data points from 3703 Listed A-share enterprises (Shanghai and Shenzhen, China) spanning the period from 2012 to 2022. Building upon this premise, research hypotheses were established using the subsidy policy-investment-innovation path.” In this study, we construct a two-way fixed effects model to test this mechanism. Specifically, a regression analysis was used to test the authenticity of this path, particularly to determine whether there is a mediating effect of R&D investment within the total industry sample. Group regression was also used to test the change in this relationship for different enterprise scales, ownership characteristics, and economic regions. In this study, the endogeneity and robustness were tested to ensure the reliability of the research results.

This study makes three contributions. First, it employs a substantial amount of industry-wide data to conduct a comprehensive and rigorous empirical analysis of the effect of government subsidies on enterprise innovation performance. Second, it delves deeply into the intermediary effect of R&D investment and the moderating effect of enterprise scale to elucidate the underlying influence mechanisms. Third, this study examines the differential effects of enterprise ownership type and economic region. This study effectively addresses these theoretical gaps, making significant contributions to the formulation and adjustment of public innovation policies.

The results show that government subsidies can significantly improve enterprises’ innovation performance, which is more evident in non-eastern regions and state-owned enterprises. R&D investment has a mediating effect, and enterprise-scale innovation has a moderating effect.

2. Literature review and hypotheses

2.1. Government subsidy and enterprise innovation performance

There have been many studies on this relationship, but no consistent conclusions have been reached. Through their research on the biotechnology industry, Kang and Park (2012) and Hall and Bagchi-Sen (2007) conclude that government assistance can enhance enterprises' innovation performance [24,25]. Unsal and Houston (2024) arrived at the same conclusion [26]. Hewitt-Dundas and Roper (2010) researched Irish enterprises through the instrumental variable method. They discovered that public innovation assistance plays a vital role in boosting innovation, mainly in encouraging enterprises to innovate new products and improve product quality effects [27]. Liu et al. (2021) believe that both pre- and post-subsidies can positively affect enterprises' innovation performance, but pre-subsidies have a stronger effect [10]. Nevertheless, other scholars arrived at the opposite conclusion (Link & Scott, 2009; Catozzella & Vivarelli, 2016) [28,29]. In an imperfect market, enterprises engaging in scientific and technological innovation face high risks, increased uncertainty, and higher investment costs. If there are sufficient incentives or clear expectations, enterprises will invest sufficiently; their enthusiasm for R&D will decrease, and a lack of innovation will impede technological advancement and productivity improvements. Government subsidies have also effectively fostered enterprise innovation. Blank and Stigler (1957) were the first to investigate their impact. They believed that market failure increases the risk of R&D innovation among enterprises. If enterprises can obtain government incentives or have certain expectations, their enthusiasm for and efficiency of R&D activities will improve significantly. The incentive mechanism between them is as follows [30]: First, the government provides R&D funding support to enterprises, which improves enterprise resources for innovation, solves financing difficulties, reduces risks, stimulates motivation for innovation, and improves the probability of success of innovation projects (Howell,2017) [31]. Second, government subsidies can provide external investors with valuable investment signals and encourage subsidized enterprises to attract more external investment to enhance innovation performance (Zhang & Li,2017) [32]. Therefore, obtaining government subsidies positively affects enterprises’ innovation performance (Yaghi & Tomaszewski,2024) [33]. Based on the above viewpoints, hypothesis H1 is proposed as follows.

H1

Government subsidies have the potential to positively influence enterprises' innovation performance by serving as incentives.

2.2. Mediating effect of Enterprise's R&D investment

The impact of government subsidies on enterprises' innovation performance may manifest indirectly, and R&D investment plays a vital role (Li et al., 2023) [34]. Government investment in R&D personnel training, R&D funds, and patent subsidy policies will further promote enterprises' R&D investments and ultimately affect innovation performance by effectively using R&D resources. Government subsidies promote enterprises' R&D investments (Chung & Ahn,2023; Carboni,2011) [35,36]. Given China's current circumstances, government subsidies serve as an essential source of enterprise innovation in R&D. It can send a good message to the outside world, reduce the risk perception of outside investors, attract foreign capital investment, reduce corporate financing constraints, and help enterprises overcome difficulties, thereby encouraging them to increase their R&D expenditures (Špetlík & Čadil, 2023) [37]. A favorable association has been observed between the level of R&D investments made by enterprises and their subsequent success in terms of innovation (Scherer, 1965; Griliches, 1998) [38,39]. Mei and Luo (2020) explored their interactions by constructing a model for the mediating effect [12]. The empirical test results indicate that these two concepts are positively correlated and that R&D expenditures are a conduit between them. Therefore, Hypothesis H2 is proposed.

H2

Government subsidies impact innovation performance through the mediating effect of R&D investment.

2.3. Differences in incentive effect of government subsidy caused by heterogeneity of enterprise scale

The extant body of scholarly work has examined the relationship between enterprise scale and government subsidies. It is generally agreed that subsidies have different effects on enterprises at different scales (Dvoulety et al., 2021) [40]; however, the specific conclusions differ. Shefer and Frenkel (2005) consider minor enterprises highly innovative [41]. Bronzini and Piselli (2016) found that government subsidies benefit small- and medium-scale enterprises (SMEs) in northern Italy far more than huge enterprises [22]. However, Schumpeter (1934) argued that large companies possess distinct advantages in terms of accumulating innovation elements, undertaking innovation risks, and reaping benefits. They serve as the primary driving forces of technological innovation [42]. Due to the differences in micro-characteristics of the enterprises, the external and internal factors of the enterprise's innovation motivation are different, presenting different technological innovation modes, and these factors have different effects on innovation incentives, thus making the effects of innovation incentives different. The innovation strategies of SMEs are more flexible. However, from the resource acquisition perspective, large-scale enterprises have apparent advantages over SMEs in terms of innovative resources. Resource advantages are irreplaceable in the Chinese economy and play a pronounced role. Therefore, hypothesis H3 is proposed.

H3

The incentive effect of government subsidies on enterprises' innovation performance varies with the scale of the enterprises. Compared with SMEs, large-scale enterprises have more incentive effects. The enterprise scale has a positive moderating effect.

2.4. Differences in incentive effects of heterogeneity of nature of enterprise ownership on government subsidies

Existing literature on this subject is controversial. With the advancement of market-oriented reforms, enterprises with different types of ownership have distinct resources, operational goals, financial constraints, and varying impacts on government subsidies. State-owned enterprises have an advantage over non-state-owned enterprises in acquiring the resources needed to provide R&D subsidies (Wu,2017) [43]. However, Xu et al.(2021) argue that private enterprises can obtain higher returns from R&D investment than most state-owned enterprises because excessive subsidies to state-owned enterprises will plunge the government subsidy policy into the North paradox [44]. They are more likely to spend their time and resources on impactful (rent-seeking) activities than on productive ones (Du & Mickiewicz, 2016) [45]. Generally, non-state-owned enterprises have a more innovative spirit and more adaptable management structures. Most studies believe that there is significant promotion of both types of enterprises. Based on a literature review, this study posits that non-state-owned enterprises (SOEs) are more adaptable. Therefore, hypothesis H4 is proposed.

H4

Variations exist in the influence of government subsidies on the innovation level of enterprises with distinct ownership characteristics. Non-state-owned enterprises demonstrate a more pronounced incentive effect.

2.5. Influence of regional heterogeneity

Different regions in China have varying levels of enterprise development, competition, management, internal governance, and innovation demand, which results in varying effects of government subsidies (Shao & Wang,2023) [46]. Zhang et al. (2023) studied the impact of the Green Credit Policy (GCP) on corporate exploratory innovation. They concluded that this impact varies across different regions, with a more pronounced effect observed in the central regions [47]. In the past few years, the institutional environment in the central and western regions has made significant progress, and the government's service consciousness has greatly improved. The state has provided significant policy support for the development of this region, which will help improve the utilization rate of subsidies and thus improve innovation performance. After years of development, the economic scale of subsidies and enterprise innovation in the eastern region has become relatively large. This law diminishes the marginal effect. Therefore, regions with low innovation abilities benefit the most from subsidies (Broekel, 2015) [48]. Therefore, hypothesis H5 was proposed.

H5

The impact of government subsidies on enterprises' innovation performance varies across regions, with the central and western regions exhibiting stronger incentive effects than the eastern region.

Fig. 1 illustrates the theoretical framework of the model used in this study.

Fig. 1.

Theoretical model.

3. Methodology

3.1. Data origin

The sample comprises A-share listed companies in Shenzhen and Shanghai, China, spanning the research period from 2012 to 2022. To prevent empirical conclusions from being skewed by negative information such as incomplete or inaccurate disclosures, data from ST, ∗ST, financial industry enterprises, and companies with missing variables for the current year were excluded. Additionally, the main continuous variables were winsorized at the 1 % level at both ends to mitigate the impact of outliers.

Government subsidy data were obtained from the CSMAR database, patent data from the CNRDS database, and enterprise R&D investment data from the Chico database; annual reports supplemented missing information. Government subsidy information for listed companies has been disclosed under the subject of “non-operating income” in their annual reports. According to the above standards and screening methods, this study retained 17,670 data points from 3703 enterprises, as shown in Table 1.

Table 1.

Sample list.

Year	total	Shenzhen SE.	Shanghai SE	Large	SME	Eastern	Non-eastern	State-owned	Non-state owned
2012	1252	892	360	1059	193	819	433	416	836
2013	1324	916	408	1174	150	871	453	448	876
2014	1449	1008	441	1304	145	973	476	460	989
2015	1670	1158	512	1501	169	1133	537	490	1180
2016	1826	1251	575	1635	191	1240	586	508	1318
2017	1658	1193	465	1497	161	1171	487	403	1255
2018	1761	1131	630	1634	127	1218	543	502	1259
2019	1564	933	631	1453	111	1083	481	489	1075
2020	1331	794	537	1210	121	907	424	412	919
2021	1553	805	748	1450	103	1045	508	512	1041
2022	2282	1308	974	2097	185	1656	626	580	1702
Total	17670	11389	6281	16014	1656	12116	5554	5220	12450

3.2. Description of variables

• (1)Dependent variable: Quantity of patent authorization (patent). Extant scholarly works on identifying and evaluating key performance indicators for enterprise innovation are usually expressed in terms of patent achievements, number of patent authorizations, or applications received. The predominant emphasis in the published literature pertains to quantifying patent authorization by enterprises (Dohse et al., 2023) [49]. As the number of patent authorizations can be used to measure the technological innovation of an enterprise's resource expenditure and utilization efficiency and can more accurately reflect the actual innovation capability of enterprises (Zhang et al., 2024) [50], this study chooses it (patent) as an alternative indicator. It is represented by In(Patent+1). In addition, to better reflect the level of enterprise technological innovation performance, In this paper, the quantity of patent applications (Patent^a) is also used as a substitute variable of the model to improve the robustness of the research conclusion (Kijek et al., 2020) [51].
• (2)Independent variables: Government subsidies. The data comes from all levels of sub-subjects of “government subsidies” in financial statements.
• (3)Mediator variables: Enterprise R&D investment. This study defines direct R&D capital investment by drawing on existing research. Drawing from the actual circumstances of the enterprise, this study takes the logarithm of total investment in R&D″ as a measure of R&D investment intensity (Yin et al., 2023) [52].
• (4)Control variables: ①Age, is expressed by subtracting the founded year from the current Year; ②Return on Equity (Roe), which indicates an enterprise's capacity to generate revenue with its capital, expressed as net profit at the end of the year as compared with shareholders' Equity (Kasasbeh, 2021) [53]; ③The Profit status of the enterprise (profit), existing Research indicates a favorable relationship between an enterprise's profitability and its economic performance, based on the ratio of total profit to primary enterprise revenue; ④Debt-to-asset ratio (Lev), which is the external market investors' evaluation of their credit ability. The lower the debt-to-assets ratio, the smaller the financing constraints the enterprise faces (Söderblom et al., 2015).⑤Ratio of the largest shareholder (Crl), which is generally considered that the degree of Equity or concentration of Equity has an impact on the innovation-decision of enterprises. The ratio of independent directors(Indr) is thought to affect enterprise regulation and transparency and benefit corporate governance. Dual function(dual) can affect the level of corporate governance and thus affect innovation.
• (5)Moderator variables: enterprise scale (size). The division of enterprise-scale is based on the “Standard Provisions on the Classification of Small and Medium-scale Enterprise (SME)” published in 2017 by the Information Technology and Industry Ministry, which classifies enterprises with less than 1000 employees or an operating income of less than 400,000,000 yuan as SME, except for large-scale enterprises.
• (6)Grouping variables: ownership nature (Soe) and economic region (Dist). Ownership nature (Soe) is a virtual variable set to one for state-owned enterprises and zero for non-state-owned enterprises. The document Classification Method for east, west, central, and northeast regions, published by the National Bureau of Statistics of China in 2011, divides the economic regions into eastern (value 1) and non-eastern (central and western) areas (value 0). Table 2 lists the specific variables.

Table 2.

Variable definition.

Var type	Var name	Var	Explain
Dependent variable	Enterprise innovation performance	Patent	In(Patent+1)
		Patenta	In(Patenta+1)
Independent variable	Government subsidy	Sub	In(Sub+1)
Mediator variable	R&D investment	RD	In(Total of R&D investment)
Moderator variable	Enterprise scale	Size	Set the value to 1 for large and 0 for SME sizes
Grouping variable	Ownership nature	Soe	State is 1, non-state is 0
	Economic region	Dist	The eastern coastal area is 1; otherwise, 0.
Control variable	Age of Enterprise	Age	The year minus the Start-up year
	Debt-to-asset ratio	Lev	Total liabilities/Total assets
	Return on Equity	Roe	Net profit/Equity
	Enterprise profitability	Profit	Total profit/income
	Ratio of the largest shareholder	Cr1	Largest shareholder shares/total shares
	Ratio of independent directors	Indr	Independent Directors/all directors
	Dual function	Dual	Chairman and general manager concurrently 1, otherwise 0

3.3. Model Construction

3.3.1. Selection of baseline model

Before commencing the empirical analysis, it is imperative to select an appropriate model using a standard procedure.

The first step involved conducting unit root and cointegration tests. The purpose of the unit root test is to ascertain the stationarity of the time-series data, whereas the cointegration test aims to verify stability and prevent spurious regression. However, these tests require stringent implementation conditions. Generally, large cross-sectional dimensions (N) and time dimensions (T) are required: at least N > 300, T > 100(Kao,1999) [54], or T > 150 (Westerlund,2004) [55]. In cases where N is large but T is small, concerns regarding pseudo-regression in panel data are often insignificant (Philips & Moon, 2000) [56]. The panel data in this study are unbalanced, with a large N and small T (T = 11). This is not a simple time-series model; thus, there is no need to conduct unit root and cointegration tests. Moreover, the results obtained from statistical tools, such as the KAO, Pedroni, and Westerlund tests, also support the conclusion that these tests are not applicable.

The second step was to carry out the F-Test and the Hausman Test (Table 3).

Table 3.

F-test and the Hausman test.

Method	Statistic	P-value	Inspection conclusion
F-Test	11.120	0.000	The fixed effect model is better than the mixed OLS model.
Hausman Test	950.74	0.000	The fixed effect model is better than the random effect model.

The Hausman test is primarily used to determine whether to choose a fixed effects model (FEM) or a random effects model (REM). If the Hausman test result is significant (p-value <0.05), it indicates that individual effects are correlated with the explanatory variables. In this case, the fixed effects model should be selected, as it more effectively handles this correlation. Conversely, if the result is not significant, the random effects model is more appropriate.

The F-test is used to decide between the fixed effects model and the ordinary least squares (OLS) model. If the F-test result is significant (p-value <0.05), it suggests that individual effects are significant, and the fixed effects model should be used, as the OLS model cannot capture these individual differences. If the F-test result is not significant, it indicates that individual effects are not significant, and the OLS model can be chosen, as individual differences have minimal impact on the results.

The fixed effect model is finally selected as the baseline model.

3.3.2. Baseline fixed effect model

To examine H1, we first construct a baseline fixed-effects model (1):

$$\text{Paten}{\mathrm{t}}_{\text{it}}={\mathrm{\beta }}_1\text{Su}{\mathrm{b}}_{\text{it}}+{\mathrm{\gamma }}_1\text{Ag}{\mathrm{e}}_{\text{it}}+{\mathrm{\gamma }}_2\text{Le}{\mathrm{v}}_{\text{it}}+{\mathrm{\gamma }}_3\text{Ro}{\mathrm{e}}_{\text{it}}+{\mathrm{\gamma }}_4\text{Profi}{\mathrm{t}}_{\text{it}}+{\mathrm{\gamma }}_5\text{Cr}{1}_{\text{it}}+{\mathrm{\gamma }}_6{\text{Indr}}_{\text{it}}+{\mathrm{\gamma }}_7{\text{Dual}}_{\text{it}}+{\mathrm{\epsilon }}_{\text{it}}+\sum \text{Frim}+\sum \text{Year}+\mathrm{c}$$ (1)

If β1 is positive and statistically significant, this suggests that government subsidies have a motivating impact on the innovative performance of enterprises. Contrarily, the β1 is negative and statistically significant, indicating that it has an extrusion effect. If β1 is not significant, there is no evidence of influence between the two. Model (1) was used for robustness testing.

3.3.3. Mediating effect model

The traditional method for detecting the mediating effect is the step-by-step method (Baron & Kenny, 1986) [57], but it has been proven to have many disadvantages. Iacobucci et al. (2007) proposed an enhanced BK method to facilitate intermediate effect analysis through structural equation modeling (SEM) [58]. Rosak-Szyrocka and Tiwari (2023) further used SEM to test sustainable development in University 4.0 during the era of the ultra-smart society [59].In recent years, scholars have suggested replacing the Sobel test with bootstrapping because of its higher statistical power and avoidance of assumptions regarding a normal symmetric distribution (Kenny, 2016) [60]. An alternative approach that shows promise for the self-help method is the Monte Carlo approach (Jose,2013) [61]. Government subsidy is x, innovation performance is y, and R&D investment is m. Fig. 1 depicts this model.

This study employed a modified stepping method (Wen & Ye, 2014) [62] and structural equality modeling to examine the mediating effect. We hope to obtain comprehensive results in future studies.

Step 1

(Fig. 2 step 1) tests the relationship between the independent variable $\text{Su}{\mathrm{b}}_{\text{it}}$ and and dependent variables $\text{Paten}{\mathrm{t}}_{\text{it}}$. Equation (1) was established as follows:

$$\text{Paten}{\mathrm{t}}_{\text{it}}={\mathrm{\beta }}_1\text{Su}{\mathrm{b}}_{\text{it}}+{\mathrm{\gamma }}_1\text{Ag}{\mathrm{e}}_{\text{it}}+{\mathrm{\gamma }}_2\text{Le}{\mathrm{v}}_{\text{it}}+{\mathrm{\gamma }}_3\text{Ro}{\mathrm{e}}_{\text{it}}+{\mathrm{\gamma }}_4\text{Profi}{\mathrm{t}}_{\text{it}}+{\mathrm{\gamma }}_5\text{Cr}{1}_{\text{it}}+{\mathrm{\gamma }}_6{\text{Indr}}_{\text{it}}+{\mathrm{\gamma }}_7{\text{Dual}}_{\text{it}}+{\mathrm{\epsilon }}_{\text{it}}+\sum \text{Frim}+\sum \text{Year}+\mathrm{c}$$ (1)

If c $\left({\mathrm{\beta }}_1\right)$ is significant, there is the possibility of a mediating effect, and the step 2 is carried out.

Step 2

The relationship between the independent variables $\text{Su}{\mathrm{b}}_{\text{it}}$ and Mediator variables ${\text{RD}}_{\text{it}}$ is tested (Fig. 2 step 2).Equation (2) is established.

$${\text{RD}}_{\text{it}}={\mathrm{\beta }}_2\text{Su}{\mathrm{b}}_{\text{it}}+{\mathrm{\gamma }}_1\text{Ag}{\mathrm{e}}_{\text{it}}+{\mathrm{\gamma }}_2\text{Le}{\mathrm{v}}_{\text{it}}+{\mathrm{\gamma }}_3\text{Ro}{\mathrm{e}}_{\text{it}}+{\mathrm{\gamma }}_4\text{Profi}{\mathrm{t}}_{\text{it}}+{\mathrm{\gamma }}_5\text{Cr}{1}_{\text{it}}+{\mathrm{\gamma }}_6{\text{Indr}}_{\text{it}}+{\mathrm{\gamma }}_7{\text{Dual}}_{\text{it}}+{\mathrm{\epsilon }}_{\text{it}}+\sum \text{Frim}+\sum \text{Year}+\mathrm{c}$$ (2)

$\text{Su}{\mathrm{b}}_{\text{it}}$, ${\text{RD}}_{\text{it}}$ and $\text{paten}{\mathrm{t}}_{\text{it}}$ are regressed simultaneously to detect the indirect effects of independent and dependent variables, and the association between the mediator and dependent variables is also examined. Equation (3) is established as follows:

$$\text{Paten}{\mathrm{t}}_{\text{it}}={\mathrm{\beta }}_3\text{Su}{\mathrm{b}}_{\text{it}}+{\mathrm{\beta }}_4\mathrm{R}{\mathrm{D}}_{\text{it}}+{\mathrm{\gamma }}_1\text{Ag}{\mathrm{e}}_{\text{it}}+{\mathrm{\gamma }}_2\text{Le}{\mathrm{v}}_{\text{it}}+{\mathrm{\gamma }}_3\text{Ro}{\mathrm{e}}_{\text{it}}+{\mathrm{\gamma }}_4\text{Profi}{\mathrm{t}}_{\text{it}}+\text{Cr}{1}_{\text{it}}+{\mathrm{\gamma }}_6{\text{Indr}}_{\text{it}}+{\mathrm{\gamma }}_7{\text{Dual}}_{\text{it}}+{\mathrm{\epsilon }}_{\text{it}}+\sum \text{Frim}+\sum \text{Year}+\mathrm{c}$$ (3)

Fig. 2.

Diagrammatic representation of mediating effect.

If both a $\left({\mathrm{\beta }}_2\right)$ and b $\left({\mathrm{\beta }}_4\right)$ are significant, indirect effects can be observed. Then, proceed directly to the step 3 to verify c’ (Fig. 2 step3, ${\mathrm{\beta }}_3$).The bootstrap test should be taken if at least one of them is not statistically significant. If the test passes, an indirect effect exists; otherwise, there is no mediating effect.

Step 3

If c’ (β3) is significant, indicates that there is a direct effect, enter the fifth step, and if it is not apparent, it is a complete mediating effect.

Step 4

The same sign for a,b and c’ represents a partial mediating effect, with the effect value ab/c. Otherwise, it indicates a masking effect (Fig. 2 step4).

The following is the SEM method.

Step 1

Fit the model (Fig. 2 step4) by SEM to estimate the direct and mediating effect coefficients simultaneously.

If the two variables were not statistically significant, there was no evidence of a mediating role, and the research was terminated. If ab demonstrates statistical significance, it indicates the presence of a mediating function, and further research can be pursued.

Step 2

Calculate the Sobel Z-value to assess the magnitude of the mediating effect relative to the direct effect.

If the z-value is statistically significant, whereas the direct effect c’ is not, it indicates complete mediation. If both the z-value and direct effect c’ are statistically significant, this suggests partial mediation. In cases where the z value is not significant but c’ is, partial mediation with a direct effect exists. Finally, if neither the z-value nor the direct effect c’ is significant, it implies partial mediation without a direct effect.

3.3.4. Moderating effect model

The moderator variable ${\mathrm{mod}}_{\text{it}}$ is multiplied by the independent variable $\text{Su}{\mathrm{b}}_{\text{it}}$ to construct the interaction term $\text{Su}{\mathrm{b}}_{\text{it}}\ast {\mathrm{mod}}_{\text{it}}$. The interaction and moderator variables were added to the regression model to obtain a moderating effect model. It was constructed as follows:

$$\text{Paten}{\mathrm{t}}_{\text{it}}={\mathrm{\beta }}_5\text{Su}{\mathrm{b}}_{\text{it}}+{\mathrm{\beta }}_6{\mathrm{mod}}_{\text{it}}+{\mathrm{\beta }}_7\text{Su}{\mathrm{b}}_{\text{it}}\ast {\mathrm{mod}}_{\text{it}}+{\mathrm{\gamma }}_1\text{Ag}{\mathrm{e}}_{\text{it}}+{\mathrm{\gamma }}_2\text{Le}{\mathrm{v}}_{\text{it}}+{\mathrm{\gamma }}_3\text{Ro}{\mathrm{e}}_{\text{it}}+{\mathrm{\gamma }}_4\text{Profi}{\mathrm{t}}_{\text{it}}+{\mathrm{\gamma }}_5\text{Cr}{1}_{\text{it}}+{\mathrm{\gamma }}_6{\text{Indr}}_{\text{it}}+{\mathrm{\gamma }}_7{\text{Dual}}_{\text{it}}+{\mathrm{\epsilon }}_{\text{it}}+\sum \text{Frim}+\sum \text{Year}+\mathrm{c}$$ (4)

Equation (4) can be used to verify H3: Given that the interaction coefficient ${\mathrm{\beta }}_7$ is statistically significant, it indicates the existence of a regulation effect, and the symbol represents the direction of the regulation effect. As the scale of the enterprise is set as a categorical variable, we can also use group regression based on the baseline model to further explain and verify the moderating effect. This grouping regression method can also be used to verify H4 and H5:

In all the models above, i symbolizes the individual enterprise, and t denotes the time of the year. $\mathrm{\beta }$ and $\mathrm{\gamma }$ represent the fitting coefficients of the equation. For each variable in the model, ${\mathrm{\epsilon }}_{\text{it}}$ is the random error term; $\sum \text{Frim}$ represents the individual-fixed effect; $\sum \text{year}$ is the Time-fixed effect, and the intercept term is $\mathrm{c}$.

4. Result

4.1. Descriptive analysis

Before conducting the formal empirical analysis, it is necessary to summarize the general situation of the data. Descriptive statistics were calculated for each significant variable. Table 4 presents the study's results.

Table 4.

Descriptive statistics.

Var	Obs	Mean	SD	Min	Median	Max	Skewness	Kurtosis
Patent	17670	2.794	1.464	0.000	2.890	6.368	−0.050	2.638
Sub	17670	14.331	1.794	8.641	14.508	18.160	−0.622	3.659
RD	17670	17.958	1.369	14.110	17.916	21.633	0.038	3.456
Soe	17670	0.295	0.456	0.000	0.000	1.000	0.897	1.804
Size	17670	0.906	0.291	0.000	1.000	1.000	−2.788	8.774
Dist	17670	0.686	0.464	0.000	1.000	1.000	−0.800	1.640
Age	17670	18.511	5.719	7.000	18.000	36.000	0.473	3.194
Lev	17670	38.790	19.391	4.992	37.611	86.681	0.307	2.343
Roe	17670	6.783	12.010	−55.843	7.429	35.058	−2.139	12.309
Profit	17670	8.224	16.110	−71.417	8.003	50.007	−1.593	10.515
Cr1	17670	33.263	14.138	8.650	31.080	70.760	0.524	2.691
Indr	17670	0.376	0.053	0.333	0.357	0.571	1.219	4.315
Dual	17670	0.319	0.466	0.000	0.000	1.000	0.777	1.604

As Table 4 illustrates. The Patent variable has a minimum value of 0, a maximum value of 6.368, and a standard deviation of 1.464, signifying that there is still potential for enhancement in the overall innovation performance level of enterprises in China and the level of innovation performance differs significantly among various enterprises, even some enterprises have no innovation output. The sub-variable had a minimum value of 8.641, a maximum value of 18.160, and a standard deviation of 1.794. This gap is also relatively large. Nevertheless, we can also see that all the sample enterprises have received more or less government subsidies, which is a common phenomenon. This also reflects strong support from the state of enterprises in recent years. The median value of RD is 17.916, the average is 17.958, and the minimum and maximum values are 14.110 and 21.633, respectively. Enterprises’ level of R&D investment is generally high, and the difference is relatively small. The skewness of all variables has an absolute value of less than 3, and the kurtosis has an absolute value of less than 10 (with slightly higher values for Profit and Roe), indicating that the data do not strictly adhere to a normal distribution. However, this is considered acceptable for normality (Kline, 2023) [63].

In general, after eliminating missing values, the sample size of all variables remained the same, and the Obs was 17670. The range of all variables is defined as the disparity between the maximum and minimum values that are significantly reduced after the tail reduction and logarithmic processes, and there is no extreme value. The descriptive statistics of these data were summarized, and the data were suitable for modeling and regression.

4.2. Correlation analysis

Before establishing the regression model, the correlation coefficient matrices were used to verify the correlations between the variables (Table 5).

Table 5.

Correlation.

Var	Patent	Sub	RD	Soe	Size	Dist	Age
Patent	1
Sub	0.355∗∗∗	1
RD	0.548∗∗∗	0.464∗∗∗	1
Soe	0.123∗∗∗	0.079∗∗∗	0.120∗∗∗	1
Size	0.192∗∗∗	0.138∗∗∗	0.294∗∗∗	0.133∗∗∗	1
Dist	0.025∗∗∗	0.024∗∗∗	0.095∗∗∗	−0.198∗∗∗	0.009	1
Age	0.125∗∗∗	0.065∗∗∗	0.135∗∗∗	0.211∗∗∗	0.132∗∗∗	−0.003	1
Lev	0.235∗∗∗	0.118∗∗∗	0.230∗∗∗	0.311∗∗∗	0.284∗∗∗	−0.115∗∗∗	0.167∗∗∗
Roe	0.055∗∗∗	0.044∗∗∗	0.135∗∗∗	−0.092∗∗∗	0.078∗∗∗	0.064∗∗∗	−0.055∗∗∗
Profit	−0.040∗∗∗	−0.013∗	0.019∗∗	−0.114∗∗∗	−0.014∗	0.051∗∗∗	−0.067∗∗∗
Cr1	0.027∗∗∗	−0.023∗∗∗	0.012	0.183∗∗∗	0.028∗∗∗	−0.006	−0.096∗∗∗
Indr	−0.007	−0.004	0.005	−0.066∗∗∗	−0.052∗∗∗	0.027∗∗∗	−0.021∗∗∗
Dual	−0.054∗∗∗	−0.041∗∗∗	−0.053∗∗∗	−0.306∗∗∗	−0.084∗∗∗	0.109∗∗∗	−0.105∗∗∗
	Lev	Roe	Profit	Cr1	Indr	Dual
Lev	1
Roe	−0.231∗∗∗	1
Profit	−0.385∗∗∗	0.765∗∗∗	1
Cr1	0.023∗∗∗	0.124∗∗∗	0.097∗∗∗	1
Indr	−0.021∗∗∗	−0.016∗∗	−0.009	0.047∗∗∗	1
Dual	−0.143∗∗∗	0.038∗∗∗	0.057∗∗∗	−0.011	0.115∗∗∗	1

∗p < 0.1″, "∗∗p < 0.05″, "∗∗∗p < 0.01.

The correlation coefficient between sub-and Patent was 0.355 and significant (p < 0.01). This demonstrates that the empirical evidence solely examining the association between government subsidies and enterprise innovation supports the view that there is a close relationship between them, aligning with the anticipated outcome of Hypothesis H1. There is a strong positive correlation between R&D investment (RD) and patent acquisition at a significance level of 1 %. This suggests that more investment in R&D leads to higher levels of innovation performance within an organization. The variables Sub and RD have a strong positive correlation at the 1 % significance level, suggesting that the more subsidies, the more investment. The variables in the grouping and most control variables exhibit a significant positive correlation with patents, except for Profit and Dual patents, which display a negative correlation. In addition, Indr did not show a significant relationship. Conducting a correlation analysis is an initial step in examining the association between variables; however, it is essential to further investigate the precise relationship by integrating the findings of the regression analysis.

Table 6 examines multicollinearity in the variables through tolerance and variance inflation factor (VIF). All variables have a VIF value below 10, with an average VIF value of only 1.450. The tolerance for each variable exceeds 0.1. This indicates the absence of significant multicollinearity issues among the variables, making it appropriate for modeling and regression analyses.

Table 6.

VIF test.

Variable	VIF	Tolerance
Sub	1.280	0.782
RD	1.460	0.683
Soe	1.330	0.751
Size	1.180	0.845
Dist	1.070	0.934
Age	1.100	0.911
Lev	1.450	0.688
Roe	2.550	0.393
Profit	2.720	0.368
Cr1	1.090	0.921
Indr	1.020	0.979
Dual	1.120	0.889
Mean VIF	1.450

4.3. Regression analysis

4.3.1. Impact of government subsidy on enterprise innovation performance

The two-way fixed-effects model can better control endophytism by managing the time-fixed effect as well as the individual fixed effect, thus improving the interpretation and prediction ability of the model. The results of the regression analysis in column (1) of Table 7 were used to test Hypothesis H1. The coefficient of determination (R2) for the regression model was 0.227, indicating acceptable predictive capability. Based on the results of the significance tests, most variables in the model were statistically significant. This demonstrated the satisfactory overall performance of the regression model. The coefficient of Sub is 0.049 and is significant(P < 0.01), indicating that government subsidies can improve the innovation performance of enterprises. Thus, hypothesis H1 was established.

Table 7.

Grouping regression of stock market.

Var	(1)	(2)
		Shanghai	Shenzhen
	Patent	Patent	Patent
Sub	0.049c	0.034c	0.057c
	(8.161)	(3.438)	(7.506)
Age	−0.023	0.036	−0.053
	(-0.571)	(0.639)	(-1.103)
Lev	0.006c	0.004b	0.007c
	(5.306)	(2.187)	(4.792)
Roe	0.001	−0.000	0.002
	(1.063)	(-0.081)	(1.298)
Profit	−0.000	0.001	−0.000
	(-0.053)	(0.334)	(-0.411)
Cr1	−0.001	−0.001	−0.002
	(-0.668)	(-0.226)	(-0.669)
Indr	−0.758c	−0.704	−0.801c
	(-3.014)	(-1.630)	(-2.593)
Dual	0.055a	0.078	0.045
	(1.960)	(1.563)	(1.334)
_cons	1.782c	1.328a	2.039c
	(3.188)	(1.671)	(3.035)
Firm	Yes	Yes	Yes
Year	Yes	Yes	Yes
N	17670	6281	11389
R2	0.227	0.226	0.229

t statistics in parentheses.

^ap < 0.1.

^bp < 0.05.

^cp < 0.01.

We employ Model (4) to conduct a regression analysis between the Shanghai and Shenzhen stock exchanges to further validate this finding. (Table 7, column (2)).

Group regression shows that on the Shanghai Stock Exchange, the coefficient of Sub is 0.034 and significant (p < 0.01), whereas on the Shenzhen Stock Exchange, it is 0.057 and significant (p < 0.01). R-square was higher than 0.2. Overall, a strong positive association exists between government subsidies and enterprise innovation performance on the Shanghai and Shenzhen stock exchanges. This result further verifies hypothesis H1.

4.3.2. Mediating effect of R&D investment

To verify H2, Wen and Ye's (2014) methods and SEM were used to test the mediating effect.

The results of Wen and Ye (2014) are presented (Table 8)

Table 8.

Mediating effect of RD.

Var	(1)	(2)	(3)
	Patent	RD	Patent
Sub	0.049c	0.064c	0.028c
	(8.161)	(13.254)	(4.854)
RD			0.325c
			(16.009)
Age	−0.023	−0.021	−0.016
	(-0.571)	(-0.677)	(-0.456)
Lev	0.006c	0.006c	0.004c
	(5.306)	(6.791)	(3.601)
Roe	0.001	0.005c	−0.000
	(1.063)	(4.272)	(-0.350)
Profit	−0.000	0.000	−0.000
	(-0.053)	(0.549)	(-0.232)
Cr1	−0.001	−0.002	−0.001
	(-0.668)	(-1.110)	(-0.384)
Indr	−0.758c	−0.644c	−0.548b
	(-3.014)	(-3.301)	(-2.265)
Dual	0.055a	0.000	0.055b
	(1.960)	(0.020)	(2.052)
_cons	1.782c	16.621c	−3.625c
	(3.188)	(37.996)	(-5.983)
Firm	Yes	Yes	Yes
Year	Yes	Yes	Yes
N	17670	17670	17670
R2	0.227	0.425	0.265

t statistics in parentheses.

^ap < 0.1.

^bp < 0.05.

^cp < 0.01.

In Table 8,c = 0.049∗∗∗, indicating that government subsidies have a significant positive influence on enterprise innovation performance. a = 0.064∗∗∗, signifying that government subsidies have a significant positive effect on enterprises' R&D investment. b = 0.325∗∗∗, suggesting that R&D investment has a significant positive effect on innovation performance. This relationship is validated through both Sobel (Table 10) and Bootstrap (Table 9) tests, clearly demonstrating the presence of an indirect effect between government subsidies and enterprise innovation performance. Furthermore, c’ = 0.028∗∗∗ indicates a certain direct effect between these two variables. Therefore, R&D investment partially mediates the relationship between government subsidies and innovation performance. Thus, hypothesis H2 is confirmed. This indicates that government subsidies not only directly impact innovation performance but also indirectly enhance it by increasing R&D investment. This multilevel impact mechanism demonstrates the complexity and profound effects of policy interventions. Therefore, governments should consider the crucial role of R&D investment in this pathway when formulating subsidy policies. SEM (Table 11) was used to verify the relationship between the main variables (without the addition of control variables), and the results confirmed the existence of a partial mediating effect.

Table 10.

Sobel test.

Name	Est	Std_err	Z	P > z
Sobel	0.149	0.007	21.816	0.000
Aroian	0.149	0.007	21.811	0.000
Goodman	0.149	0.007	21.822	0.000

Table 9.

Bootstrap test.

	Observed coefficient	Bootstrap std. err.	Z	P > z	Normal-based [95 % conf.interval]
_bs_1	0.166	0.004	40.630	0.000	0.158	0.174
_bs_2	0.115	0.006	19.360	0.000	0.103	0.127

Table 11.

SEM mediation effect.

Estimates	Delta	Sobel	Monte Carlo
Indirect effect	0.185	0.185	0.185
Std. Err.	0.004	0.004	0.004
Z-value	49.136	49.136	49.103
P-value	0.000	0.000	0.000
Conf. Interval	0.178, 0.192	0.178, 0.192	0.178, 0.192

4.3.3. Heterogeneity analysis

The grouping regression method was employed to examine the heterogeneity in the impact of government subsidies on enterprise innovation performance across different enterprise scales, nature of ownership, and economic regions. The necessity of the heterogeneity analysis was assessed by conducting a t-test on the data, and the results are presented in Table 12. This indicates that there are significant differences in the Sub and Patent variables, as well as in most control variables. Therefore, it is important to conduct a heterogeneity analysis.

Table 12.

T-test of heterogeneity.

Var	Soe = 0		Soe = 1		mean-diff	Size = 0		Size = 1		Mean-diff	Dist = 0		Dist = 1		Mean-diff
	obs	mean	obs	mean		obs	mean	obs	mean		obs	mean	obs	mean
Patent	12450	2.678	5220	3.072	−0.394∗∗∗	1656	1.919	16014	2.885	−0.966∗∗∗	5554	2.741	12116	2.819	−0.077∗∗∗
Sub	12450	14.239	5220	14.551	−0.312∗∗∗	1656	13.559	16014	14.411	−0.852∗∗∗	5554	14.267	12116	14.361	−0.094∗∗∗
Age	12450	17.730	5220	20.373	−2.643∗∗∗	1656	16.158	16014	18.754	−2.597∗∗∗	5554	18.536	12116	18.499	0.036
Lev	12450	34.881	5220	48.115	−13.234∗∗∗	1656	21.636	16014	40.564	−18.928∗∗∗	5554	42.079	12116	37.283	4.796∗∗∗
Roe	12450	7.500	5220	5.072	2.427∗∗∗	1656	3.878	16014	7.083	−3.205∗∗∗	5554	5.652	12116	7.301	−1.649∗∗∗
Profit	12450	9.413	5220	5.388	4.025∗∗∗	1656	8.912	16014	8.153	0.760∗	5554	7.018	12116	8.777	−1.759∗∗∗
Cr1	12450	31.591	5220	37.252	−5.662∗∗∗	1656	32.027	16014	33.391	−1.364∗∗∗	5554	33.393	12116	33.204	0.189
Indr	12450	0.378	5220	0.371	0.008∗∗∗	1656	0.385	16014	0.375	0.009∗∗∗	5554	0.374	12116	0.377	−0.003∗∗∗
Dual	12450	0.411	5220	0.098	0.313∗∗∗	1656	0.440	16014	0.306	0.134∗∗∗	5554	0.244	12116	0.353	−0.109∗∗∗

Firstly, the Positive Moderating Effect of the Enterprise Scale.

Table 13 shows the results of the heterogeneity analysis, in which (1), (2), and (3) show grouped regressions of scale, ownership, and economic region, respectively.

Table 13.

Regression analysis of heterogeneity.

(1)				(2)				(3)
Var	Size = 1	Size = 0	All sample	Var Name	Soe = 1	Soe = 0	All sample	Var Name	Dist = 1	Dist = 0	All sample
	Patent	Patent	Patent		Patent	Patent	Patent		Patent	Patent	Patent
Sub	0.047c	0.018	0.019	Sub	0.038c	0.048c	0.048c	Sub	0.044c	0.058c	0.058c
	(7.290)	(1.057)	(1.164)		(3.355)	(6.908)	(6.967)		(6.285)	(5.116)	(5.138)
Age	−0.024	0.218	−0.022	Age	0.052	−0.081	−0.023	Age	−0.049	0.031	−0.024
	(-0.564)	(1.503)	(-0.539)		(1.098)	(-1.589)	(-0.565)		(-1.196)	(0.365)	(-0.590)
Lev	0.005c	0.003	0.005c	Lev	0.005c	0.006c	0.006c	Lev	0.005c	0.007c	0.006c
	(4.762)	(0.769)	(4.667)		(2.602)	(4.646)	(5.334)		(3.848)	(3.642)	(5.307)
Roe	0.001	−0.001	0.001	Roe	0.000	0.002	0.001	Roe	0.002	0.001	0.001
	(1.015)	(-0.150)	(0.952)		(0.284)	(0.900)	(1.026)		(1.061)	(0.404)	(1.062)
Profit	−0.000	−0.002	−0.000	Profit	0.001	−0.001	−0.000	Profit	−0.001	0.002	−0.000
	(-0.261)	(-0.825)	(-0.259)		(0.429)	(-0.713)	(-0.061)		(-0.951)	(1.203)	(-0.056)
Cr1	−0.003	0.017b	−0.001	Cr1	0.000	−0.003	−0.002	Cr1	−0.004	0.003	−0.002
	(-1.122)	(2.299)	(-0.535)		(0.061)	(-1.071)	(-0.716)		(-1.361)	(0.661)	(-0.686)
Indr	−0.579b	−1.050	−0.754c	Indr	−0.454	−0.832b	−0.769c	Indr	−0.670b	−0.853b	−0.758c
	(-2.192)	(-1.106)	(-3.004)		(-1.134)	(-2.539)	(-3.061)		(-2.116)	(-2.070)	(-3.018)
Dual	0.046	0.029	0.056b	Dual	0.063	0.046	0.054a	Dual	0.054	0.058	0.055b
	(1.532)	(0.328)	(1.997)		(1.165)	(1.371)	(1.908)		(1.557)	(1.168)	(1.965)
Size			−0.255	Soe			−0.111
			(-1.055)				(-0.551)
Sub_Size			0.032a	Sub_Soe			0.003	Sub_Dist			−0.013
			(1.861)				(0.249)				(-1.010)
_cons	1.893c	−1.482	2.043c	_cons	0.826	2.510c	1.822c	_cons	2.296c	0.725	1.798c
	(3.110)	(-0.844)	(3.404)		(1.033)	(3.807)	(3.261)		(3.953)	(0.626)	(3.223)
Firm	Yes	Yes	Yes	Firm	Yes	Yes	Yes	Firm	Yes	Yes	Yes
Year	Yes	Yes	Yes	Year	Yes	Yes	Yes	Year	Yes	Yes	Yes
N	16014	1656	17670	N	5220	12450	17670	N	12116	5554	17670
R2	0.228	0.069	0.229	R2	0.266	0.208	0.227	R2	0.231	0.223	0.227
Chow test statistics	30.05				14.87				7.45
P-Value	0.00				0.00				0.00

t statistics in parentheses.

^ap < 0.1.

^bp < 0.05.

^cp < 0.01.

(1) represents the outcome of the heterogeneity analysis at the enterprise scale. We categorized the data into two groups based on the criteria explained in Section 3.2: large enterprises and small to medium-sized enterprises. According to the test method described in section 3.3.4, we initially observed the interaction sub_size, which exhibited a significant value of 0.032 (P < 0.1) in the regression analysis conducted on the entire sample. Additionally, we found that the sub-variable exerted a substantial influence on the patent variable within the large-scale enterprise group (0.047∗∗∗). In contrast, its significance was not observed within either the small- or medium-scale groups or the all-sample group (0.018, 0.019). This indicates that government subsidies can significantly promote an increase in innovation performance in large-scale enterprises, but no corresponding evidence can be found in small and medium-sized enterprises. Simultaneously, the interaction item sub-size symbol was positive and significant (P < 0.1), indicating that the scale of the enterprise plays a positive moderating role. As enterprise scale in this study is treated as a category variable, referring to the practice of many scholars, this type of large-scale group is particularly significant in this study. In contrast, it is not significant in small- and medium-sized enterprise groups. Meanwhile, the sub-coefficient of the large-scale group was much higher than that of the other groups (0.047 > 0.018). Moreover, the intergroup coefficient test (Chow test p-value = 0) passed. This can still be considered a moderating effect (Jose. et al., 2013; Cleary, 1999) [61,64]. Therefore, H3 was simultaneously confirmed using two different methods.

Second, the heterogeneous analysis of the Nature of Enterprise Ownership and Economic Region.

As shown in (2) of Table 13, the coefficient (Sub) for the state-owned enterprise sample is 0.038 and significant(p < 0.01), whereas it is 0.048 and significant(p < 0.01) for the sample of non-state-owned enterprises. The regression coefficients between different samples cannot be compared directly, and a coefficient test between groups is required. Referring to the practice of Cleary (1999) [64], this study conducted a Chow test on the coefficients between the two groups, with P-value = 0.00, which passed the test. Therefore, the coefficients are compared. Government subsidies substantially enhance the innovation performances of both state-owned and non-state-owned firms. Conversely, the significance of non-state-owned enterprises was more pronounced(0.048 > 0.038). Thus, H4 was established. The lack of significance in the interaction Sub_Soe implies that the nature of enterprise ownership cannot be strictly considered a moderating variable.

The economic regions in (3) are analyzed, and a conclusion is drawn using the same method and criteria. Government subsidies can significantly improve the innovation performance of enterprises in any region. By contrast, the western region had a more significant promotional effect (0.058∗∗∗ > 0.044∗∗∗). Thus, H4 was established.

4.4. Endogeneity and robustness testing

4.4.1. Endogeneity test

First, the bidirectional fixed effects model employed in this study is a widely used approach to address endogeneity issues in panel data analyses. Incorporating individual and time-fixed effects allows for the control of unforeseeable factors and enhances the accuracy and reliability of the estimation results. This model effectively handles endogenous problems arising from variables that vary across time and individuals (Antonakis et al., 2019) [65,66].

Additionally, this study acknowledges the potential existence of a two-way causal relationship between enterprises’ innovation performance and government subsidies. To address endogeneity concerns, we employ the instrumental variable method by utilizing the lagged values of the sub-variables as instruments to construct a 2SLS regression model (Bellemare et al., 2017) [67]. Although lagging variables cannot completely resolve reverse causation issues, they can help alleviate them to some extent. Furthermore, we conducted an under-identification test and a weak identification test to verify the suitability of the instrumental variables. The detection results, along with those from the 2SLS regression, are presented in column (1) of Table 14. The coefficient of L-Sub in the first step was 0.047, which was statistically significant (P < 0.01). Similarly, in the second step, the coefficient of Sub was estimated to be 0.439, which is statistically significant (P < 0.01). These findings are consistent with the baseline model and successfully pass the endogeneity test.

Table 14.

Endogeneity and robust testing.

Var	(1) 2SLS		(2)	(3) Panel Tobit
	Patent	Patent	Patenta	Patent
	First	Second
L.Sub	0.047c
	(6.670)
Sub		0.439c	0.056c	0.086c
		(36.020)	(8.924)	(17.071)
Age	−0.041	−0.002	−0.068	0.016c
	(-0.662)	(-0.816)	(-1.422)	(4.339)
Lev	0.005c	0.013c	0.005c	0.009c
	(3.791)	(18.500)	(4.388)	(14.083)
Roe	0.002	0.016c	0.002	0.004c
	(1.602)	(8.976)	(1.362)	(4.110)
Profit	−0.000	−0.006c	0.002a	−0.002b
	(-0.420)	(-4.579)	(1.888)	(-1.986)
Cr1	−0.002	0.004c	−0.002	0.000
	(-0.619)	(4.610)	(-0.717)	(0.211)
Indr	−0.601b	−0.440a	−0.685c	−0.559c
	(-2.096)	(-1.929)	(-2.584)	(-2.914)
Dual	0.044	−0.056b	0.066b	0.024
	(1.296)	(-2.110)	(2.259)	(1.124)
_cons	2.423c	−3.585c	2.571c	0.270b
	(2.616)	(-17.259)	(3.908)	(2.192)
Firm	Yes	Yes	Yes	Yes
Year	Yes	Yes	Yes	Yes
N	12267	12267	17670	17670
R2	0.179	0.167	0.173	/
Underidentification test		0.000	/
Weak identification test		4599.259	/

t statistics in parentheses.

^ap < 0.1.

^bp < 0.05.

^cp < 0.01.

4.4.2. Robustness test

The robustness of this study was tested using two methodologies: replacing the dependent variable (Table 14 (2) Columns) and replacing the model (Table 14 (3) columns). This study continues previous research and uses the number of patent applications instead of the above dependent variables for regression (Dohse et al., 2023) [49]. Considering that the dependent variable in this study is non-negative and the left side of the data is truncated at zero, it is suitable to establish a Tobit model regression. This study establishes a Tobit model with zero truncation on the left-hand side for a robustness test. The results remained unchanged compared to the baseline regression. Upon modifying the dependent variables, the coefficient of determination for the sub-variables was 0.056, which was statistically significant (P < 0.01). After adjusting for the model, it was 0.086, which remained statistically significant (p < 0.01). These findings indicate that our model and research outcomes were reliable.

4.5. Discussion

The results in Table 7 verify H1. This aligns with the findings of Unsal and Houston (2024) and other researchers who believe that government subjects can greatly enhance the growth of innovation output in enterprises and improve enterprise innovation performance [26]. This suggests that government intervention in supporting enterprises' innovation activities is effective and provides a theoretical foundation for the government's formulation and implementation of innovation policies. Liu et al. (2021) also held this view, but the subtle difference lies in the detailed study of Liu et al.’s work on the difference in the degree of influence of ex-ante subsidies and ex-post subsidies [10]. This will help policymakers optimize the types of subsidies, thus promoting enterprise innovation more effectively. However, this is inconsistent with the conclusion of Catozzella and Vivarelli (2016) that government subsidies negatively affect enterprise performance through crowding-out effects [29]. The possible reason is that the government subsidy is affected by many factors: different enterprise scales, different industries, different ownership, different development times, different mechanisms of government subsidies, different Research focuses, and different selection of indicators will lead to different results. Government subsidies can increase enterprises' confidence in engaging in innovation activities and provide enterprises with funding sources to engage in innovation activities, reducing the cost and unknown risks of enterprises' innovation activities so that enterprises can carry out more innovation activities. This demonstrates the necessity of meticulously crafting subsidy policies to prevent wastage and inefficient resource utilization and to ensure that subsidies are effectively utilized to enhance enterprises' innovation capacity. Wen and Ye (2014) and SEM were used to confirm the mediating effect of H2 on R&D investment; this result further confirms the findings of most scholars (Zúñiga-Vicente et al., 2014) [18]. Government subsidies encourage enterprises to increase their R&D investment (Hussinger, 2008), and increasing an enterprise's R&D investment can improve innovation performance [68]. This highlights the indirect effects of subsidy policies and prompts policymakers to focus on long-term subsidy mechanisms. However, Scott (2000) believes that there is a crowding-out effect [69]. This may be due to differences in the selected samples. This provides important insights into designing effective subsidy policies and ensuring that subsidies can promote innovation. Therefore, this result expands research on the mediating effect of R&D investment in the entire industry sample. The results in Table 13 verify hypothesis H3. This study used two methods to test the moderating effect of enterprise scale. The interaction term test and grouping regression + Chow test confirm the existence of a moderating effect of enterprise scale. In addition, there are many studies on the heterogeneity of enterprise scale, but few have set enterprise scale as a fixed variable to investigate the moderating effect. This study expands research in this field to a certain extent. Table 13 further verifies hypotheses H4 and H5. Evidence suggests that government subsidies substantially enhance the innovation performance of both state-owned and non-state-owned enterprises. This finding was consistent with the mainstream perspective. In contrast, the role of non-state-owned enterprises is greater (0.048 > 0.038; the Chow test passed). This may be because, in the non-monopoly market, non-state-owned enterprises have a stronger ability to innovate and perform more prominently (Wu.,2017) [43]. The result in (3) shows that the incentive effect of government subsidies has regional differences and that the effect in the central and western regions is stronger than that in the eastern region. This could be due to policy differences or enterprise growth. With economic development, regional enterprises are more likely to make considerable progress. This finding is partly inconsistent with the conclusion of Shao and Wang's (2023) conclusion [46], mainly because of the different periods of panel data choice. This suggests that policymakers should consider the heterogeneity of enterprise scale, nature of property rights, and region when designing subsidy policies and adjust subsidy policies to maximize their effect. The results presented in Table 14 demonstrate the successful passing of both endogeneity and robustness tests, thereby significantly reinforcing the findings of this study. However, it is worth noting that the coefficient of determination R appears to be relatively low, which can potentially be attributed to the characteristics associated with unbalanced panel data as well as the substantial sample size – a common occurrence within the realm of finance and accounting research. In conjunction with the outcomes derived from the F-test, we firmly believe that this regression result has considerable significance.

In summary, this study posits that government subsidy policies positively influence corporate innovation performance by increasing R&D investment, with firm size playing a positive moderating role. Liu et al. (2021) also discussed this mechanism, emphasizing the significant impact of government subsidy policies on enterprise innovation performance [10]. In contrast, they delved deeply into the moderating roles of marketization and anti-corruption in this process. In his study on the UK, Pless (2019) broadly concurs but suggests that subsidies are complementary for small enterprises and substitutive for large enterprises, which contrasts with the conclusions of this study [70]. Zhang et al. (2021) also agree with this impact mechanism but use equity concentration as a mediating variable, finding that the positive impact is more pronounced in companies with low equity concentrations [71]. Other scholars have treated government subsidies as a moderating variable, asserting that R&D investment enhances corporate innovation performance, with government subsidies positively moderating this relationship (Shuang,2020) [72]. These differences in findings are primarily due to variations in the sample selection and research variables, indicating that the impact mechanisms of government subsidies on corporate innovation performance are not singular and offer numerous research possibilities. This underscores the potential of this topic to yield significant insights. The empirical results of this study have important economic significance for government subsidies to support enterprise innovation, optimize resource allocation, promote regional development, and enhance enterprise confidence.

The novelty of this study lies in several aspects: First, it examines the impact of policies on enterprise innovation, an area yet to be explored by previous Research. This contributes to filling this gap in the existing literature. Second, it presents a comprehensive analysis of all industries, which facilitates the formulation and adjustment of macroeconomic policies by the government. This broad perspective is also innovative, as limited studies have been conducted from a holistic viewpoint. Additionally, to ensure greater accuracy in our analysis, we employed a robust sample selection process along with a fixed-effects model to effectively control for endogeneity among the variables. Finally, various robustness testing methods were used to demonstrate the reliability and validity of our research findings. Although this study primarily focuses on data from China, its concepts and methodology can also be applied to other markets, particularly emerging markets that share similar economic characteristics.

This study had some limitations. First, the alternative variables must be considered. For instance, while this study employs the number of patents applied for and authorized by enterprises as an alternative variable to measure innovation performance, others may consider the output value of new products as a more suitable alternative variable. Second, this study focuses solely on examining the impact of government subsidies on enterprise innovation performance. However, numerous other variables can also influence it, such as management team structure, innovation willingness, political environment, and utilization of digital technology. A more comprehensive consideration of these factors will contribute to the formulation and implementation of effective government subsidy policies. Third, the scope of application of the conclusions is limited. The research subject of This study focuses on A-share listed enterprises and companies with sufficient sample size and representativeness. However, it should be noted that unlisted enterprises and listed enterprises may differ in terms of organization, production, and operation, as well as marketing and sales. Therefore, the conclusions drawn from this paper may not apply to unlisted enterprises. Similarly, although we believe that the methodology designed in this study is reproducible, our findings may not apply to other countries. Finally, this is an overall study of the whole industry, and the conclusion is general and may be different in different industries.

Henceforth, there are three potential avenues for future development in this Research.

• 1)Expanding the scope of the sample by incorporating relevant data from other countries, particularly emerging markets, thereby verifying these findings and enriching the conclusions derived from this Research.
• 2)Additional effective alternative variables should be considered to enhance the study further.
• 3)Considering the influence of more variables, more control variables can be added to improve the accuracy of the prediction of the research model.
• 4)The Research conducted in various industries can yield more comprehensive findings, thus contributing significantly to the field.

5. Conclusions and policy implications

5.1. Conclusion

The primary findings can be summarized as follows. (1) Government subsidies can improve the innovation performance of enterprises and promote sustainable development. This indicates that the government's policy tool of encouraging enterprise innovation through subsidies was effective. (2) R&D investment had a mediating effect. Therefore, the effectiveness of a government subsidy policy largely depends on whether it can increase enterprise R&D investment. (3) Enterprise scale has a specific positive moderating effect. Government subsidies to large-scale enterprises have a greater positive impact on innovation performance. (4) The nature of enterprise ownership and economic region affects the promoting effect of government subsidies on enterprise innovation performance. Regardless of enterprise ownership, increasing government subsidies can significantly improve innovation performance. There is little difference between the two, and the effect is slightly stronger for non-state-owned enterprises. Regardless of the economic region, government subsidies and innovation performance are significantly positively correlated, with the central and western regions performing the best.

5.2. Policy implications

The current government subsidy policy significantly impacts enterprise innovation performance, which is in line with policy expectations. Public policies should support innovation. At the micro level, they should be constantly adjusted and improved to better serve enterprises and national strategies. The specific points are as follows.

5.2.1. Continue to increase the number of government subsidies and expand the ways of subsidies

The government should thoroughly investigate the innovation input, supply and demand, and innovation quality of enterprises and provide adequate financial support under the framework of laws and market rules. Possible methods include increasing the amount of direct subsidies, improving the rewards for scientific and technological talent and enterprises’ scientific and technological achievements, and providing more tax incentives to innovative enterprises.

5.2.2. Adjust and optimize government subsidy policies and improve the pertinence of government subsidies

The government should implement differentiated subsidies for heterogeneous enterprise scales. First, we continued to increase the extent and magnitude of the subsidies. For large enterprises, appropriately increasing the support for SMEs, giving full play to the guiding and driving role of government subsidies in the capital market, improving financing channels and innovative service systems for enterprises, and achieving the best allocation of market resources. At present, government support for SMEs is insufficient, as they cannot meet their innovation needs, and the innovation ability of SMEs has not been fully tapped. Consciously tilting policies toward SMEs can rapidly improve their innovation performance while preventing excessive subsidies to large enterprises by wasting resources. Second, China should continue to deepen its reform of state-owned enterprises, enhance its innovation capacity through government subsidies, and strengthen the role of state-owned enterprises in China's economy. Simultaneously, they continue to increase subsidies to non-state-owned enterprises, increase their R&D investment, and stimulate their innovation enthusiasm. Finally, we focused on strengthening policy investments in the central and western regions. In recent years, the economic development of the eastern region has entered a bottleneck period; the central and western regions still have room for growth, and the marginal effect of policy supply is relatively large. More government subsidies can enhance the innovation capacity of the central and western regions and the competitiveness of enterprises and bring about new growth points for further improvement in the national economy.

5.2.3. Improve the screening and evaluation mechanism of government subsidies and improve the efficiency of the use of financial funds

On the one hand, it is necessary to build a comprehensive and scientific evaluation system, reduce the differences caused by information asymmetry, promote government subsidies to be fairer and more just, and be more conducive to the improvement of enterprise innovation performance. On the other hand, it is also necessary to continuously improve some deficiencies of the regulatory evaluation mechanism in the use of government subsidies, such as preventing government subsidies from being used to supplement the business performance of enterprises rather than for innovation and R&D, ensuring that government subsidies play their due incentive role, and preventing the crowding out and misallocation of police resources. The competent department may strengthen the special use of government subsidies or post-supervision and immediately take relevant measures to recover funds once the applicant is found to have illegally used or fraudulently obtained funds.

In short, government subsidies should be targeted with overall consideration given to local conditions and a focus on the formulation of subsidy policies. Enterprise managers should innovate strategic planning and focus on future competitiveness, be patient enough to tolerate short-term losses from innovation failures, establish the goal of innovative enterprises to better assume social responsibility while improving future profitability, and continuously enhance sustainable economic development by ensuring continuous innovation.

CRediT authorship contribution statement

Ge Ban: Writing – review & editing, Writing – original draft, Validation, Software, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. Thitinan Chankoson: Supervision, Methodology, Funding acquisition, Formal analysis, Conceptualization. Yun Wang: Writing – review & editing, Resources, Funding acquisition, Data curation.

Data availability statement

These data were derived from the following resources available in the public domain: Government subsidy data were obtained from the CSMAR database, patent data from the CNRDS database, and enterprise R&D investment data from the Chico database (http://www.cnrds.com). More detailed data will be made available on request.

Additional information

No additional information is available for this paper.

Funding statement

No funding

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.