How Does Public Capital Affect Enterprise Technological Innovation Based on Empirical Evidence from Chinese Listed Companies

Abstract

Public capital is an important force for promoting industrial agglomeration and enterprise technological innovation, and enterprise technological innovation is the core element in promoting green economic growth. To further reveal the influence mechanism of public capital on enterprise technological innovation, based on the data of A-share listed companies in China from 2007 to 2020, this paper uses the nonlinear moderating effect model and the intermediating effect model to verify the nonlinear influence and transmission mechanism of public capital on enterprise technological innovation. This paper discusses the influence and mechanism of public capital on enterprise innovation from the perspective of industrial agglomeration. The study finds that public capital has a significant role in promoting enterprise technological innovation. Moreover, economic public capital plays a greater role in promoting enterprise technological innovation than social public capital. Further analysis shows that the innovation effect of public capital is nonlinearly regulated by industrial agglomeration. In the initial stage of industrial agglomeration, the higher the degree of industrial agglomeration, the weaker the innovation effect of public capital; however, in the advanced stage of industrial agglomeration, the higher the degree of industrial agglomeration, the stronger the innovation effect of public capital. The nonlinear effect is realized by affecting the profits of enterprises. From enterprise heterogeneity, public capital has a significant role in promoting the technological innovation of non-state-owned enterprises but has no significant impact on the technological innovation of state-owned enterprises; public capital has a significant positive effect on the technological innovation of mid- and high-end technology enterprises, while its impact on the technological innovation of low-end technology enterprises is not significant. From the type of innovation output, public capital has a significant role in promoting enterprise green technology innovation, and the role of public capital in promoting enterprise green invention patents is greater than that of green utility model patents. This study provides a theoretical basis for government public capital investment decisions and empirical evidence for the sustainable development of enterprise technological innovation.

1. Introduction

Public capital is the government investment in infrastructure or public sector fixed assets such as transportation, water conservancy, electricity, education, culture and sports, health care, etc. [1]. The economic growth mechanism of public capital has always been a hot topic in the field of economics, such as the economic growth mechanism of public material capital [2,3], the public human capital [4,5,6,7], and both of them [8,9]. As an important basis for economic and social development, public capital has long played a role in stimulating China’s economic growth and the counter-cyclical adjustment in China. For example, the Chinese government launched the “Four Trillion Yuan Plan” to ease the impact of the financial crisis in 2008. Funds accounting for 37.5% of the total were mainly used for the construction of major infrastructure and the renovation of urban power grids, such as railways, roads, airports, and water conservancy. Since the spread of the COVID-19 epidemic in 2020, China’s government further expanded the general public budget expenditure and implemented a proactive fiscal policy to ensure a smooth economic transition. In July 2022, China’s government once again emphasized that infrastructure investment remained the focus of national macro-control policies and made up for the lack of social demand in consumption, real estate, and export.

However, public capital has been criticized for the misallocation of resources due to the chronic problems of blindness, repeatability, and inefficiency in investment [10]. China will continue to implement the innovation-driven development strategy, unleash the driving force for innovation in the whole society, and constantly create new advantages for development. It is not only necessary to give full play to the role of the private sector as the main body of innovation, but the support and guidance of public capital is also needed to achieve sustainable economic development. The key to maintaining the appropriate scale of public capital investment to promote enterprise technological innovation is to clarify the mechanism of public capital’s impact on enterprise technological innovation. The excessive investment of public capital not only causes a waste of resources but also may squeeze out the private capital investment and hinder technological innovation; however, insufficient investment of public capital will lead to a shortage of public goods and the increasing costs of production and transaction and then restrain enterprise innovation.

Endogenous growth theory holds that both public capital and technological innovation are the key forces to promote economic growth. However, whether public capital can promote technological innovation is still controversial in academia. Some researchers believe that public capital can promote technological innovation [11,12,13,14]. However, other studies claim that public capital has no significant influence on technological innovation [15,16]. The reasons for the different results are as follows: First, there are differences between the flow and stock of public capital in the research data; second, the heterogeneity of public capital is not considered; third, public capital may have a nonlinear influence on enterprise technological innovation.

Because of this, according to the functions and characteristics of public capital, this paper investigates the impact of the economic and social public capital on enterprise technological innovation based on the stock and flow data of the public capital of A-share listed companies from 2007 to 2020. At the same time, we also consider the important role played by industrial agglomeration. When enterprise competition intensifies in the industrial agglomeration area, the input and output of enterprise technological innovation will change, resulting in the non-linear effect of public capital on enterprise technological innovation [17]. Therefore, industrial agglomeration is an important factor that cannot be ignored when studying the relationship between public capital and enterprise technological innovation.

The main contributions of this paper are as follows: (1) It enriches the research on the influence mechanism of public capital and enterprise technological innovation. From the perspective of the heterogeneity of public capital and industrial agglomeration, this paper empirically tests the dynamic evolution process of the influence of public capital on enterprise technological innovation when the degree of industrial agglomeration changes continuously. This not only deepens the understanding of the impact of public capital on enterprise technological innovation but also provides a theoretical basis and empirical evidence for optimizing the investment structure of public capital and improving investment efficiency. (2) This paper further examines the transmission mechanism of the innovation effect of public capital in different stages of industrial agglomeration, which more accurately identifies the causal relationship between public capital and enterprise technological innovation. (3) From the perspective of enterprise heterogeneity, this paper examines the impact of public capital on the technological innovation of non-state-owned enterprises and mid- and high-end technological enterprises. (4) This paper examines the heterogeneous influence of public capital on enterprise green technology innovation and non-green technology innovation and finds that the influence of public capital on non-enterprise green technology innovation is greater than that of enterprise green technology innovation. The conclusion provides a practical basis for the Chinese government to optimize the structure of public capital investment. The Chinese government needs to further increase green public capital investment, promote green technology innovation of enterprises, and then change the kinetic energy of economic development to promote green and sustainable economic development.

2. Theory and Hypothesis

2.1. The Influence of Public Capital on Enterprise Technological Innovation

According to the different functions of public capital, it can be divided into economic public capital and social public capital. The economic public capital, such as water and electricity, transportation and storage, environmental facilities, information software, and other fields, can improve enterprise profits and stimulate technological innovation motivation to directly promote enterprise technological innovation by reducing transportation costs, production costs, and market transaction costs. At the same time, economic public capital indirectly promotes enterprise technological innovation through its positive externalities to form industrial agglomeration. Economic public capital can provide basic conditions and investment opportunities for enterprise production and operation, guide enterprises to transfer to public capital-intensive areas, and form industrial agglomeration to affect enterprise technological innovation [18,19]. The social public capital includes education, science and technology, health and social security, culture and sports, public management, and other fields. Among them, public education capital can promote enterprise technological innovation by improving the quantity and quality of human capital [20]. Public R&D capital promotes enterprise technological innovation mainly in the following three aspects: increasing R&D investment through pre-funding and post-subsidy, forming an R&D resource-sharing mechanism through the establishment of R&D public service platform, solving the problems of resource sharing and information asymmetry, and improving innovation efficiency through industry–university–research cooperation model [21,22]. The increase of public capital investment by the government in medical care, culture and sports, public management, and social organizations can ensure the physical and mental health of enterprise employees and reduce the transaction costs between enterprises by forming a culture of mutual trust and promoting organizational communication and contact. Therefore, social public capital can directly or indirectly promote enterprise technological innovation [23].

Hypothesis 1 (H1).

Public capital promotes enterprise technological innovation directly or indirectly.

2.2. The Nonlinear Regulating Effect of Industrial Agglomeration on the Innovation Effect of Public Capital

According to the external economic theory [24], economic agglomeration refers to the interaction between enterprises, institutions, and infrastructure in a certain spatial region in the production process, forming economies of scale and scope, promoting the development of the labor market, and concentrating on specialized skills, thus increasing the interaction between regional suppliers and consumers and sharing infrastructure and other regional externalities. In theory, public capital can promote the formation of industrial agglomeration in the area of public capital investment by creating a public resource endowment, reducing production costs, and accelerating talent agglomeration [25]. First of all, from the perspective of creating a public resource endowment, the public capital is the public infrastructure formed by the government relying on national rights to concentrate financial resources in a certain area. Enterprises in the investment area can obtain government public goods and services at a lower cost, form the cost advantage of public services, and induce industrial agglomeration. Secondly, from the perspective of reducing production costs, the public capital is conducive to reducing the comprehensive transportation costs, search costs, transaction costs, and energy consumption costs; reducing the resistance to industrial agglomeration; improving the matching rate and success rate of the market transactions; increasing the marginal income of enterprise technological innovation; forming an innovation network; and promoting industrial agglomeration [26,27]. Finally, from the perspective of accelerating the concentration of human capital, the public capital investment in education, medical care, social security, and other infrastructure forms the “siphon effect” of human capital, accelerates the development of human capital, and makes the value of the human capital increase in the movement, thus promoting industrial agglomeration [28].

However, the influence of public capital on enterprise technological innovation may change in different stages of industrial agglomeration [29].

From the objective conditions and laws of forming industrial agglomeration, asset-light, low-cost, and small-scale enterprises can take the lead in forming industrial agglomeration in the primary stage in the public capital investment area due to their short decision-making time and fast transfer speed. Most of these enterprises are at the low end of the value chain, with weak independent innovation ability; insufficient technology absorption ability; low requirements for production technology, capital scale, and human capital; and insufficient reserves of technical talents and innovation talents, which can hardly meet the needs of enterprise technological innovation and development. At the same time, in the stage of primary industrial agglomeration, the scientific and technological chain and industrial chain between enterprises are not effectively connected. The transformation of scientific and technological achievements is insufficient. A specialized division of labor and cooperation is not yet formed. The degree of trust among enterprises is very low, and there is little cooperation. Therefore, in the initial stage of industrial agglomeration, enterprises also intensify the degree of market competition among them while sharing public resources. The competition further reduces the profit level of enterprises, leads to the outflow of innovative talents, reduces the R&D input of enterprises, and weakens the promoting effect of public capital investment on enterprise technological innovation. In short, in the initial stage of industrial agglomeration, the higher the degree of industrial agglomeration, the weaker the impact of public capital investment on enterprise technological innovation.

The process of accelerating the formation of industrial agglomeration by the public capital is also the process of transforming industrial agglomeration from the primary stage to the advanced stage [30]. On the one hand, through the competition mechanism of the survival of the fittest in the market, excellent enterprises with abundant funds and strong innovation ability survive in the industrial agglomeration area, merge some enterprises, and form industrial giants. On the other hand, with time, large enterprises with heavy assets, high costs, and strong innovation capabilities are gradually gathered in the areas of public capital and finally realize the transformation of industrial agglomeration from the primary stage to the advanced stage [31]. In the advanced stage of industrial agglomeration, the cooperative relationship among enterprises is greater than the competition, and the talent agglomeration effect of public capital begins to appear [32]. At this time, enterprises in the region have strong innovation consciousness and technology absorption ability and are good at integrating market resources. The collaborative innovation mechanism among enterprises is thus formed [33]. Leading enterprises and small- and medium-sized enterprises jointly builds a collaborative innovation network [34], jointly integrates scientific and technological resources, shares innovation achievements, carries out technical cooperation, and jointly overcomes technical problems. Scientific and technological links, industrial chains, and capital chains are thus gradually formed, which greatly improves the conversion rate of scientific and technological achievements, further raises the profit level of enterprises, and improves the ability to coordinate and innovate among enterprises. In short, in the advanced stage of industrial agglomeration, the higher the degree of industrial agglomeration, the stronger the influence of public capital investment on enterprise technological innovation. Accordingly, this paper puts forward hypothesis 2.

Hypothesis 2 (H2).

In the initial stage of industrial agglomeration, the higher the degree of industrial agglomeration, the weaker the innovation effect of public capital; in the advanced stage of industrial agglomeration, the higher the degree of industrial agglomeration, the stronger the innovation effect of public capital.

3. Study Design

3.1. Models Setting

To verify whether public capital affects enterprise technological innovation, the following regression model is established [35]:

$$Innovatio{n}_{pft}={\alpha }_0+{\alpha }_{1}Inves{t}_{pt}+\sum Controls+Firm+Year+Industry+Province+{\xi }_{pft}$$

(1)

In Equation (1), f represents the enterprise, t represents the year, and p represents the province to which the enterprise belongs; Innovation_pft is the number of R&D investments or invention patent applications of enterprise f in province p in t years; Invest_it refers to the public capital of province p in t years; Controls represent a series of control variables at the level of enterprises, industries, cities, and provinces. Firm, Year, Industry, and Province represent the fixed effects of enterprise, year, industry, and province, respectively; α₀ represents the constant term, α₁ is the regression coefficient, and ε_pft represents the error term.

To investigate the nonlinear regulation mechanism of industrial agglomeration, the following regression model is established in this paper [36]:

$$\begin{array}{ll}\hfill Innovatio{n}_{pft}& ={\lambda }_0+{\lambda }_{1}Ag{g}_{pit}\times Inves{t}_{pt}+{\lambda }_2{Ag{g}_{pit}}^2\times Inves{t}_{pt}+{\lambda }_{3}Ag{g}_{pit}+{\lambda }_4{Ag{g}_{pit}}^2+{\lambda }_{5}Inves{t}_{pt}\\ \hfill +\sum Controls& +Firm+Year+Industry+Province+{\chi }_{pit}\end{array}$$

(2)

In Equation (2), i represents the industry to which the enterprise belongs, Agg_pit represents the industrial agglomeration of industry i in province p in year t, λ₀ represents the constant term, λ₁–λ₅ is the regression coefficient, and χ_pit represents the residual item.

To examine the transmission mechanism of the nonlinear regulation mechanism of industrial agglomeration, this paper uses the average total profit of enterprises as the intermediary variable to construct the following model to test [37].

$$\begin{array}{cc}Profi{t}_{pt}={\beta }_0+& {\beta }_{1}Ag{g}_{pit}\times Inves{t}_{pt}+{\beta }_2{Ag{g}_{pit}}^2\times Inves{t}_{pt}+{\beta }_{3}Ag{g}_{pit}+{\beta }_4{Ag{g}_{pit}}^2+{\beta }_{5}Inves{t}_{pt}\\ & +\sum Controls+Firm+Year+Industry+Province+{\theta }_{pit}\hfill \end{array}$$

(3)

$$\begin{array}{cc}Innovatio{n}_{pt}& ={\mu }_0+{\mu }_{1}Ag{g}_{pit}\times Inves{t}_{pt}+{\mu }_2{Ag{g}_{pit}}^2\times Inves{t}_{pt}+{\mu }_{3}Ag{g}_{pit}+{\mu }_4{Ag{g}_{pit}}^2+{\mu }_{5}Inves{t}_{pt}\\ +{\mu }_{6}Profi{t}_{pt}& +\sum Controls+Firm+Year+Industry+Province+{\eta }_{pit}\hfill \end{array}$$

(4)

In Equations (3) and (4), Profit_pt represents the total average profit of the enterprise in p province t year, β₀ and μ₀ represent constant term, β₁–β₅ and μ₁–μ₆ represent regression coefficient, and θ_pit and η_pit represent the residual term.

3.2. Variables

3.2.1. Setting of Enterprise Technological Innovation Variables

In this paper, R&D investment and patent applications are used as indicators to measure enterprise technological innovation [38], and patent citations and R&D probability are used to test robustness.

3.2.2. Setting of Public Capital Variables

The public capital is the sum of economic public capital stock and social public capital stock. Economic public capital includes the capital formed by investment in the fields of electricity, gas and water production and supply, transportation, storage and postal services, information transmission, computer services and software, water conservancy, environmental and public facilities management, etc. Social public capital includes the capital formed by investment in scientific research, technical services and geological exploration, education, health, social security, social welfare, culture, sports and entertainment, public management, and social organizations.

3.2.3. Mediating Variables

This paper uses the ratio of the employment density of each industry in each region to the total employment of the industry to measure industrial agglomeration [39].

$$Ag{g}_{Pit}=\frac{L_{pit}/S_p}{L_{it}}$$

(5)

In Equation (5), L_pit represents the number of employees in the industry i during period t in province p, S_p represents the land area in province p, and L_it represents the number of employment in i industry throughout the country during period t.

3.2.4. Control Variables

This paper controls the variables that may affect innovation technological activities at the enterprise, industry, city, and provincial levels. These control variables include company size, company age, company liquidity ratio, the proportion of company currency funds to total assets, the company retained earnings, company cash flow ratio, industry market competition, city per capita GDP, city savings scale, deposit–loan ratio, and provincial population size. In addition, it also has a fixed effect on enterprises, the year of inspection, the industry to which enterprises belong, and the province where enterprises are located. The descriptive statistical results of each variable are shown in

Table 1. Descriptive Statistics of Variables.

Variable	Definition	N	Mean	Sd
R&D	The logarithm of the company’s R&D investment in that year	7413	17.250	3.157
Patent	The logarithm of the company’s patent applications in the current year lags by one period	7421	4.399	1.361
Public capital	The logarithm of public capital stock	7421	10.040	0.753
Economic public capital	The logarithm of economic public capital stock	7421	9.785	0.760
Social public capital	The logarithm of social public capital stock	7421	8.494	0.774
Agg	Degree of industrial concentration	7421	1.476	0.754
Size	The logarithm of total assets plus 1	7421	21.710	1.178
Age	The logarithm of the number of years since the establishment of the company	7421	2.760	0.361
Hi	Using the total assets of a single company to calculate its market share in the industry	7421	0.069	0.091
Current	Current assets/current liabilities	7421	3.532	4.764
Funds	Monetary funds/total assets	7421	0.216	0.161
Income	The logarithm of retained earnings plus 1	7056	20.010	1.183
Cash	Cash flow ratio = (Depreciation of fixed assets + Net profit)/(Total assets × 10)	7421	0.007	0.008
Save	Resident savings deposit/the GDP of cities	7366	0.789	0.265
Loan–deposit	The logarithm of total loan/total deposit plus 1	7376	0.567	0.233
GDPPC	The logarithm of urban GDP/urban population plus 1	7420	11.560	0.484
Population	The logarithm of the provincial population plus 1	7421	17.880	0.617

.

3.3. Data Source

This paper takes A-share listed companies in China from 2007 to 2020 as the research object. The data of the public capital and the control variable data from the provincial level and urban level are all from the China Statistical Yearbook and China Urban Statistical Yearbook. Enterprise technological innovation data and enterprise-level control variable data are all from the China Economic and Financial Research Database (CSMAR Database), including enterprise R&D investment, patent citations, etc. The data on enterprise green technology innovation are from the China Research Data Service Platform (CNRDS database). According to the existing research practice, the sample data of ST and *ST in listed companies are deleted, and the tail is truncated by 1% to eliminate extreme interference. Regarding the treatment of missing values, on the one hand, we exclude listed companies with serious missing data; on the other hand, the linear interpolation method is used to supplement some small amounts of data of individual listed companies. The unbalanced panel data of 2229 listed companies from 2007 to 2020 were obtained after the above processing. Among them, 2227 companies have R&D investments, 1177 companies have patent applications, and 2229 companies have the patent citations.

4. Empirical Results and Discussion

4.1. Basic Regression Test

The data structure of this paper consists of unbalanced panel data from 2007 to 2020. The correlation test results between variables show that the maximum correlation coefficient is 0.5, i.e., less than 0.7, which can be used for regression analysis of panel data. The variance inflation factor test shows that VIF is less than 10, and there is no multicollinearity. The Hausmann test results show that the p-value is 0.0000, and the fixed-effect model should be used. Therefore, this empirical study uses the fixed-effect model of unbalanced panel data for least squares estimation.

Table 2. Basic Regression Result.

Variable	m1	m2	m3	m4	m5	m6
	Public Capital		Economic Public Capital		Social Public Capital
	R&D	Patent	R&D	Patent	R&D	Patent
Invest	0.915 ***	0.189 ***	0.888 ***	0.186 ***	0.791 ***	0.168 **
	(0.208)	(0.072)	(0.204)	(0.070)	(0.197)	(0.071)
Constant	−155.00 *	−285.30 ***	−153.60 *	−284.80 ***	−198.30 **	−291.50 ***
	(91.870)	(33.330)	(92.170)	(33.370)	(88.970)	(32.930)
Controls	Yes	Yes	Yes	Yes	Yes	Yes
Firm, Industry fixed	Yes	Yes	Yes	Yes	Yes	Yes
Province, Year fixed	Yes	Yes	Yes	Yes	Yes	Yes
Observations	6995	3308	6995	3308	6995	3308
R-squared	0.156	0.663	0.156	0.663	0.156	0.663

Notes: *** p < 0.01, ** p < 0.05, and * p < 0.10; the values in parentheses are standard errors.

examines the overall impact of public capital on enterprise technological innovation from the perspective of innovation input and innovation generation. Models 1 and 2 add the fixed effect of enterprise, industry, province, and year to eliminate the influence caused by the characteristic differences of enterprise, industry, year, and province. The regression results of model 1 show that the influence coefficient of the public capital passed the significance test of 1%, and the sign is positive. If the public capital increases by 1%, the innovative technological investment of enterprises will increase by 0.915. The regression results of model 2 show that the influence coefficient of the public capital is significantly positive at the level of 1%. When public capital increases by 1%, enterprise technological innovation will increase by 0.189. Theoretical hypothesis 1 is verified.

To further verify the innovation effect of public capital, this paper divides public capital into economic public capital and social public capital to investigate their different effects on enterprise technological innovation. Models 3 and 4 examine the impact of economic public capital on enterprise technological innovation, while models 5 and 6 examine the impact of social public capital on enterprise technological innovation. The regression results of model 3–6 show that, on the one hand, from the significance of economic public capital and social public capital on firm innovation, both economic public capital and social public capital have significant effects on the input and output of enterprise technological innovation. On the other hand, judging from the influence of economic public capital and social public capital on enterprise innovation, the influence of economic public capital on enterprise innovation input and output is greater than that of social public capital on enterprise innovation input and output. It may be because the economic public capital has a higher degree of marketization, more effective allocation of resources, and greater impact on enterprise innovation. On the contrary, social public capital is mainly allocated by the government, with low efficiency and relatively small impact on enterprise technological innovation.

4.2. Robustness Test

To ensure the reliability of the empirical research results, this paper further changes the measurement standards of dependent variables and independent variables, the model estimation methods, the regression samples, and other ways to conduct robustness tests.

(1) The investment flow is used to represent the public capital. The public capital can be expressed by investment flow and stock. The stock represents the infrastructure stock formed by public capital investment. The flow measures the investment scale of the public capital in a region in the current year. Model 1 in

Table 3. Robustness Results.

Variable	m1	m2	m3	m4	m5	m6
	Flow Invest	Patent Citation	R&D Probability	Robust Standard Error	Excluding Municipalities	Excluding 2020
Invest	0.311 **	1.677 ***	0.058 ***	0.915 **	1.038 ***	0.796 ***
	(0.146)	(0.153)	(0.012)	(0.372)	(0.258)	(0.265)
Constant	−282.30 ***	1.60 ***	−2.30	−155.00	−198.60 *	−378.70 ***
	(86.050)	(70.390)	(5.310)	(178.400)	(109.600)	(118.600)
Controls	Yes	Yes	Yes	Yes	Yes	Yes
Firm, Industry fixed	Yes	Yes	Yes	Yes	Yes	Yes
Province, Year fixed	Yes	Yes	Yes	Yes	Yes	Yes
Observations	6995	4220	7001	6995	5771	5852
R-squared	0.154	0.372	0.063	0.156	0.153	0.151

Notes: *** p < 0.01, ** p < 0.05, and * p < 0.10; the values in parentheses are standard errors.

uses public capital flow for the robustness test. The results show that the impact coefficient of public capital flow is 0.311, which passes the 1% significance test and is smaller than the stock estimation parameter. This shows that the benchmark regression model is still valid by changing the measurement method of independent variables.

(2) This paper changes the measurement standard of enterprise technological innovation. The patent citation and R&D probability of the enterprise in that year are used for the robust tests. The regression results of Model 2 in Table 3 show that public capital can significantly promote the patent citation of enterprises. The regression results of Model 3 in Table 3 show that public capital investment also has a significant role in promoting the R&D probability of enterprises. The regression results of Models 2 and 3 show that the regression results are still robust after the change of enterprise technological innovation metrics.

(3) This paper uses robust standard error to test. The regression results of model 4 in Table 3 show that the results are consistent with the basic regression after adding robust standard error.

(4) Sample data of municipalities directly under the central government are excluded. There is a logic of resource allocation among Chinese cities according to the administrative level; that is, the higher the administrative level, the more public capital investment a city may receive. The municipalities directly under the central government have a wide urban area and a large population density, which plays an important role in politics, economy, science, culture, transportation, and so on. Public capital investment and enterprise technological innovation activities are more concentrated than in ordinary cities, which may affect the estimated results in the full sample regression. Therefore, data from municipalities directly under the central government are excluded for the robustness tests in this paper. The regression results of model 5 in Table 3 show that public capital investment still has a significant promoting effect on enterprise technological innovation after changing regression samples.

(5) The influence of the special year is eliminated. The epidemic of COVID-19 broke out completely in January 2020. To eliminate the impact of public capital on enterprise technological innovation in abnormal years, this paper shortens the sample period, deletes the relevant data in 2020, and retests the model of the relationship between them. The regression results of model 6 in Table 3 show that the role of public capital in promoting enterprise technological innovation still exists.

4.3. Instrumental Variables (IV) Test

In this paper, the influencing factors and time-fixed effect of enterprises, industries, cities, and provinces are considered, which can eliminate the estimation bias of missing important variables. However, there may be endogenous problems caused by reverse causality between public capital and enterprise technological innovation. At present, local governments at all levels in China have fully recognized that innovation is an important factor in promoting high-quality economic development. When the technological innovation of enterprises in a region increases, enterprises or government leaders may lobby the superior authorities to increase public capital investment in the region. To avoid the endogenous problem of reverse causality, this paper uses China’s infrastructure investment in 1997 and the number of middle schools as instrumental variables to perform two-stage least square regression, respectively.

(1) This paper uses China’s infrastructure investment in 1997 as an instrumental variable of public capital. The existing public capital stock is formed based on infrastructure investment in 1997, but the infrastructure investment in 1997 has little influence on the current enterprise’s technological innovation behavior, which meets the requirements of instrumental variables. The statistic of IV-F is 73.69 > 10, indicating that there is no problem with weak instrumental variables. Models 1 and 2 in

Table 4. Instrumental Variables (IV) Results.

Variable	m1	m2	m3	m4
	First Stage	Second Stage	First Stage	Second Stage
	Public Capital	Innovation	Public Capital	Innovation
Infrastructure_97	−0.074 ***
	(0.009)
Middle schools			−0.169 ***
			(0.013)
Invest		2.256 ***		2.274 ***
		(0.121)		(0.121)
Constant	−239.40 ***	0.00	−246.90 ***	0.00
	(2.448)	(0.000)	(2.416)	(0.000)
Controls	Yes	Yes	Yes	Yes
Firm, Industry fixed	Yes	Yes	Yes	Yes
Province, Year fixed	Yes	Yes	Yes	Yes
IV-F stat		73.69		169.1
Observations	6995	6995	6995	6995
R-squared	0.895	0.093	0.896	0.092

Notes: *** p < 0.01, ** p < 0.05, and * p < 0.10; the values in parentheses are standard errors.

use infrastructure investment in 1997 as instrumental variables. The results show that infrastructure investment in 1997 in the first stage has a significant impact on public capital, while public capital in the second stage still has a significant promotion effect on enterprise technological innovation after eliminating endogeneity.

(2) This paper uses the number of middle schools in China as an instrumental variable of the public capital. Secondary education investment is an important part of public capital investment, and the more secondary schools, the greater the public capital investment. Although secondary education is an important foundation for the formation of human capital, limited by the educational system and the requirements of employing people in enterprises and institutions, the number of secondary schools cannot directly measure the local human capital, and it is even more difficult for it to affect enterprise technological innovation. Moreover, the number of colleges and universities or the number of college students is usually used to express the level of human capital in existing studies. Therefore, the number of secondary schools meets the assumptions of exogeneity and meets the requirements of instrumental variables. The statistic of IV-F is 169.1 > 10, indicating that there is no problem with weak instrumental variables. The regression results of model 3 and 4 in Table 4 using the number of secondary schools as instrumental variables show that the number of secondary schools in the first stage has a significant impact on public capital investment, and the public capital after the elimination of endogenous in the second stage still has a significant role in promoting enterprise technological innovation.

4.4. Enterprise Heterogeneity Test

4.4.1. Differences in the Nature of Enterprise Property Rights

Compared with non-state-owned enterprises, state-owned enterprises have special resource advantages, relatively stable capital sources, and less financing pressure [40]. At the same time, the technological innovation behavior of state-owned enterprises is interfered with by the government [41], and the technological innovation behavior of enterprises usually does not change significantly because of public capital investment. Non-state-owned enterprises usually face more fierce market competition and serious financing constraints and usually make use of the advantages of public capital as much as possible to make up for the shortcomings of funds and improve market competitiveness. Therefore, public capital plays a significant role in promoting the technological innovation behavior of non-state-owned enterprises. To verify the above analysis, the samples were divided into state-owned enterprises and non-state-owned enterprises, and the grouped estimation results are shown in models 1 and 2 in

Table 5. Enterprise Heterogeneity Results.

Variable	m1	m2	m3	m4	m5
	Nature of Property Rights		The Technical Level of Enterprise
	State-Owned Enterprise	Non-State-Owned Enterprise	Low-End Technology Industry	Mid-End Technology Industry	High-End Technology Industry
Invest	0.831	0.746 ***	0.550	1.854 ***	0.989 ***
	(0.747)	(0.199)	(0.451)	(0.708)	(0.246)
Constant	−1.00 ***	12.00	−149.00	−142.60	−169.10
	(332.700)	(88.790)	(191.600)	(357.700)	(116.800)
Controls	Yes	Yes	Yes	Yes	Yes
Firm, Industry fixed	Yes	Yes	Yes	Yes	Yes
Province, Year fixed	Yes	Yes	Yes	Yes	Yes
Observations	1116	5879	1893	1090	4012
R-squared	0.171	0.174	0.202	0.140	0.159

Notes: *** p < 0.01, ** p < 0.05, and * p < 0.10; the values in parentheses are standard errors.

. The regression results show that public capital has no significant effect on the technological innovation behavior of state-owned enterprises but has a significant effect on the technological innovation behavior of non-state-owned enterprises. This indicates that the influence of public capital on the technological innovation of non-state-owned enterprises is greater than that of state-owned enterprises, which may be because the technological innovation activities of state-owned enterprises are affected by government intervention, which reduces the innovation effect of public capital.

4.4.2. Differences in the Technological Level of Enterprises

According to the classification criteria of OECD, the sample is divided into low-end, mid-end, and high-end technology enterprises. Low-end technology enterprises are mostly labor-intensive industries, which mainly maintain low-cost advantages through economies of scale and have low demand for technological innovation. For medium- and high-end technology enterprises, technological innovation is the key to enhancing market competitiveness [42]. Only by taking advantage of all internal and external conditions, increasing R&D investment, actively carrying out technological innovation activities [43], and striving for the heights of technological innovation can they win in the competition. Therefore, there are differences in the innovation effects of public capital on different types of technology enterprises.

The regression results of models 3–5 in Table 5 show that the innovation effect of public capital of low-end technology enterprises is not significant, while the innovation effect of public capital of high-end technology industries is significantly positive at the level of 1%, and the innovation effect of public capital of mid-end technology industries is twice that of high-end technology industries. This is mainly because the technological innovation factors affecting the high-end technology industry are mainly advanced and sophisticated technologies in some core and key fields [33], so the external factor of public capital has a greater impact on the technological innovation of the mid-end technology industry than that of the high-end technology industry.

4.4.3. Different Types of Enterprise Technological Innovation

Enterprise technological innovation is the first driving force to lead social and economic development. Enterprises provide green products and process through green technology innovation, reduce natural resource consumption, reduce ecological environmental damage, improve resource allocation efficiency, and create new impetus and realization paths for sustainable economic development. According to the different types of innovation output, this study obtained the number of green patent applications from the CNRDS database. The number of green patent applications and the number of non-green patent applications represent the level of green technology innovation and non-green technology innovation of enterprises, respectively. Meanwhile, the green patent is divided into green invention patent and green utility model patent. This paper further discusses the difference between the impact of public capital investment on the level of green technology innovation and the level of non-green technology innovation.

The regression results of model 1–model 2 in

Table 6. Heterogeneity of Enterprise Technological Innovation Types.

Variable	m1	m2	m3	m4
	Non-Green Patent	Green Patent	Green Invention	Green Utility
Invest	0.111 ***	0.052 ***	0.051 ***	0.026 **
	(0.021)	(0.016)	(0.013)	(0.013)
Constant	−18.80 ***	−44.60 ***	−32.00***	−27.10 ***
	(6.913)	(5.379)	(4.513)	(4.255)
Controls	Yes	Yes	Yes	Yes
Firm, Industry fixed	Yes	Yes	Yes	Yes
Province, Year fixed	Yes	Yes	Yes	Yes
Observations	25113	27173	27173	27173
R-squared	0.035	0.063	0.062	0.032

Notes: *** p < 0.01, ** p < 0.05, and * p < 0.10; the values in parentheses are standard errors.

show that the green technology innovation effect and non-green technology innovation effect of public capital are significantly positive at the level of 1%, which shows that public capital has a significant role in promoting the green technology innovation of enterprises, and the non-green technology innovation effect of public capital is twice that of green technology innovation. The regression results of model 3 and model 4 show that the impact of public capital on green invention patents and green utility model patents is significantly positive at the 1% level, and the impact of public capital on green invention patents is greater than that of green utility model patents.

5. Further Discussion

5.1. The Nonlinear Moderating Effect of Industrial Agglomeration

Theoretical analysis shows that it is easy to form public resource advantage, cost advantage, talent gathering, and other advantages in public capital investment areas to promote industrial agglomeration and then stimulate enterprise technological innovation. In different stages of industrial agglomeration, the impact of public capital on enterprise technological innovation may be different. In the initial stage of industrial agglomeration, vicious competition leads to the decline of enterprise profits, weakening the promotion of public capital to enterprise technological innovation. In the advanced stage of industrial agglomeration, collaborative innovation among enterprises improves the conversion rate of scientific and technological achievements, enhances the profit rate of enterprises, and strengthens the role of public capital in promoting enterprise technological innovation.

To examine the nonlinear impact of industrial agglomeration on the innovation effect of public capital, this paper takes the R&D investment and patent application number of enterprises as the explained variables, respectively, and adds public capital, industrial agglomeration, the square of industrial agglomeration, the cross item of industrial agglomeration and public capital (Agg × Invest), and the multiplication of the square of industrial agglomeration and public capital (Agg² × Invest) as well as the control variables and then controls the fixed effects of enterprises, industries, years, and time for regression. The regression results of models 1 and 2 in

Table 7. The Nonlinear Moderating Effect of Industrial Agglomeration.

Variable	m1	m2	m3	m4	m5	m6
	Public Capital		Economic Public Capital		Social Public Capital
	R&D	Patent	R&D	Patent	R&D	Patent
Agg × Invest	−2.617 ***	−0.357 **	−2.647 ***	−0.336 **	−2.383 ***	−0.364 ***
	(0.450)	(0.139)	(0.447)	(0.137)	(0.424)	(0.132)
Agg2 × Invest	0.766 ***	0.100 **	0.791 ***	0.096**	0.639 ***	0.092 **
	(0.131)	(0.042)	(0.130)	(0.042)	(0.123)	(0.0 40)
Agg	27.730 ***	3.679 **	27.380***	3.383 **	21.640 ***	3.151 ***
	(4.636)	(1.446)	(4.507)	(1.400)	(3.672)	(1.170)
Agg2	−8.148 ***	−1.018 **	−8.202 ***	−0.969 **	−5.881 ***	−0.789 **
	(1.321)	(0.435)	(1.283)	(0.423)	(1.051)	(0.352)
Invest	2.371 ***	0.125	2.298 ***	0.128	2.419 ***	0.106
	(0.306)	(0.093)	(0.297)	(0.091)	(0.320)	(0.098)
Constant	−259.30 **	−218.70 ***	−261.00 **	−213.60 ***	−273.70 ***	−223.90 ***
	(104.300)	(29.840)	(105.600)	(30.150)	(94.710)	(27.970)
Controls	Yes	Yes	Yes	Yes	Yes	Yes
Firm, Industry fixed	Yes	Yes	Yes	Yes	Yes	Yes
Province, Year fixed	Yes	Yes	Yes	Yes	Yes	Yes
Observations	6995	4013	6995	4013	6995	4013
R-squared	0.166	0.600	0.166	0.599	0.165	0.600

Notes: *** p < 0.01, ** p < 0.05, and * p < 0.10; the values in parentheses are standard errors.

show that the impact coefficient of public capital on enterprise R&D investment is significantly positive at the level of 1%, and the impact coefficient of public capital on enterprise patent application is not significant, which may be on the one hand because public capital is more direct to enterprise R&D investment; on the other hand, there is a lag in the impact of public capital on enterprise technological innovation output. The multiplication term between industrial agglomeration and public capital (Agg × Invest) is significantly negative at 1% level, and the multiplication term between industrial agglomeration square and public capital (Agg² × Invest) is significantly positive at 1% level. This shows that there is a “U” relationship between industrial agglomeration and the innovation effect of public capital. Public capital can promote the formation and development of industrial agglomeration. In different stages of industrial agglomeration, the influence of public capital on enterprise technological innovation is different; that is, in the initial stage of industrial agglomeration, the higher the degree of industrial agglomeration, the weaker the effect of public capital on enterprise technological innovation; in the advanced stage of industrial agglomeration, the higher the degree of industrial agglomeration, the stronger the impact of public capital on enterprise technological innovation. Theoretical hypothesis 2 is verified.

Furthermore, different types of public capital may have different influence mechanisms on firm technological innovation. This paper divides public capital into economic public capital and social public capital to further verify the moderating effect of industrial agglomeration on the innovation effect of public capital. The regression results of models 3–6 show that there is still a “U” relationship between industrial agglomeration and the influence coefficient of different types of public capital on enterprise technological innovation, which shows that the conclusion that industrial agglomeration has a nonlinear regulating effect on public capital innovation is stable and reliable.

5.2. The Transmission Mechanism of Industrial Agglomeration

How does the nonlinear regulation of industrial agglomeration on public capital innovation effect occur? In the initial stage of industrial agglomeration, the enterprises’ independent innovation ability is poor, the transformation rate of innovation achievements is low, and the vicious price competition and other factors reduce the profit level of enterprises, resulting in a higher degree of industrial agglomeration, weakening the innovation effect of public capital. In the advanced stage of industrial agglomeration, enterprises in the agglomeration area have a high sense of innovation, and they improve innovation efficiency through collaborative innovation mechanisms such as technical cooperation and resource sharing. The integration of the science and technology chain, innovation chain, and industrial chain improves the conversion rate of innovation achievements so that the enthusiasm for technological innovation of enterprises and the profit level of enterprises are greatly improved. Therefore, there are differences in the level of corporate profits in different stages of industrial agglomeration, which may lead to the non-linear effect of public capital on enterprise technological innovation. The empirical test is conducted below.

Table 8. The Transmission Mechanism of Industrial Agglomeration.

Variable	m1	m2	m3	m4	m5	m6	m7	m8	m9
	Public Capital			Economic Public Capital			Social Public Capital
	Profit	R&D	Patent	Profit	R&D	Patent	Profit	R&D	Patent
Agg × Invest	−0.195 ***	−2.569 ***	−0.341 **	−0.217 ***	−2.596 ***	−0.315 **	−0.156 ***	−2.342 ***	−0.358 ***
	(0.048)	(0.451)	(0.139)	(0.048)	(0.448)	(0.137)	(0.046)	(0.424)	(0.132)
Agg2 × Invest	0.087 ***	0.744 ***	0.090 **	0.093 ***	0.768 ***	0.086 **	0.068 ***	0.619 ***	0.086 **
	(0.014)	(0.131)	(0.042)	(0.014)	(0.130)	(0.042)	(0.013)	(0.124)	(0.040)
Agg	1.847 ***	27.280 ***	3.532 **	2.016 ***	26.910 ***	3.192 **	1.214 ***	21.320 ***	3.120 ***
	(0.497)	(4.643)	(1.446)	(0.483)	(4.516)	(1.401)	(0.395)	(3.676)	(1.170)
Agg2	−0.821 ***	−7.940 ***	−0.931 **	−0.862 ***	−7.993 ***	−0.874 **	−0.526 ***	−5.734 ***	−0.741 **
	(0.142)	(1.326)	(0.436)	(0.138)	(1.289)	(0.424)	(0.113)	(1.053)	(0.352)
Invest	0.131 ***	2.346 ***	0.124	0.143 ***	2.272 ***	0.123	0.0757 **	2.408 ***	0.116
	(0.033)	(0.306)	(0.093)	(0.032)	(0.298)	(0.091)	(0.035)	(0.321)	(0.098)
Profit		0.285 **	0.093 ***		0.271 **	0.091 ***		0.330 **	0.097 ***
		(0.135)	(0.032)		(0.135)	(0.032)		(0.135)	(0.032)
Constant	47.54 ***	−266.60 **	−221.50 ***	47.09 ***	−267.60 **	−215.90 ***	34.75 ***	−279.20 ***	−226.50 ***
	(11.200)	(104.700)	(30.000)	(11.330)	(105.900)	(30.310)	(10.190)	(94.950)	(28.110)
Controls	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
Firm, Industry fixed	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
Province, Year fixed	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
Observations	6993	6987	4008	6993	6987	4008	6993	6987	4008
R-squared	0.164	0.167	0.601	0.165	0.167	0.601	0.159	0.166	0.602

Notes: *** p < 0.01, ** p < 0.05, and * p < 0.10; the values in parentheses are standard errors.

reports the transmission mechanism of the regulatory effect of industrial agglomeration. Models 1 and 2, respectively, report the regression results with the average profit and technological innovation of enterprises as the explained variables. The symbols and significance of Agg × Invest, Agg² × Invest, and Profit are the focus of this paper. In models 1–3, the coefficient of Agg × Invest is significantly negative at 1% level, the coefficient of Agg² × Invest is significantly positive at 1% level, and the coefficient of Profit in model 3 is significantly positive at 1% level, indicating that the average profit of enterprises plays an intermediary role in the non-linear adjustment of industrial agglomeration. In the initial stage of industrial agglomeration, the lack of technological innovation ability of enterprises, the difficulty in transforming innovation achievements, the disorderly market competition, and other factors reduce the profit level of enterprises. The higher the degree of industrial agglomeration, the lower the profit of enterprises, thus weakening the effect of public capital innovation. In the advanced stage of industrial agglomeration, the coordinated innovation mechanism among enterprises improves the innovation efficiency, the talent agglomeration effect of public capital is formed, and the mutual integration of the science and technology chain, innovation chain, and industrial chain improves the profit level of enterprises. The higher the degree of industrial agglomeration, the higher the profit level of enterprises, thus expanding the effect of public capital innovation effect. Models 4–9 use economic public capital and social public capital instead of public capital for similar tests, and the regression results are consistent with those of models 1–3, which shows that the innovation effects of different types of public capital all have the transmission path of corporate profits.

6. Conclusions and Policy Implications

Stimulating enterprise technological innovation through public capital investment and promoting high-quality economic growth is an important way to alleviate the current downward pressure on China’s economy. The effect and mechanism of different types of public capital investment on enterprise innovation may be heterogeneous. This paper conducts empirical research based on panel data of A-share listed companies from 2007 to 2020. The results show that public capital significantly promotes enterprise technological innovation, and the innovation effect of economic public capital is greater than that of social public capital. The above conclusion is still valid after a series of robustness tests. Further analysis shows that industrial agglomeration has a “U” regulatory effect on the innovation effect of public capital. In the initial stage of industrial agglomeration, industrial agglomeration weakens the impact of public capital on enterprise technological innovation; in the advanced stage of industrial agglomeration, industrial agglomeration strengthens the impact of public capital investment on enterprise technological innovation. The profits of enterprises play an intermediary role in this process. The analysis of enterprise heterogeneity shows that public capital significantly promotes the technological innovation behavior of non-state-owned enterprises but has no significant impact on the technological innovation behavior of state-owned enterprises. Public capital significantly promotes the innovation behavior of middle-end and high-end technology enterprises but has no significant impact on the innovation behavior of low-end technology enterprises. The promotion effect of public capital on green technology innovation of enterprises is less than that of non-green technology innovation, and the promotion effect of public capital on green invention patents of enterprises is greater than that of green utility model patents.

From the perspective of industrial agglomeration, this study clarifies the impact and mechanism of different types of public capital on enterprise technological innovation, which has important implications for optimizing the investment structure of public capital and improving investment efficiency.

(1) The Chinese government should maintain the appropriate proportion of economic public capital and social public capital and optimize the investment structure of public capital. This paper verifies that economic public capital and social public capital can significantly promote enterprise technological innovation. Driven by the interests of the promotion championship of Chinese officials, government leaders tend to ignore the long-term benefits of social public capital and prefer to invest in economic public capital with large, short-term returns and obvious political achievements, resulting in unreasonable investment structure of public capital and weakening its driving force for enterprise technological innovation. Take public education capital as an example: its investment has been insufficient for a long time, especially in Shanxi, Chongqing, and other provinces in China, where public education capital investment has only accounted for about 3% from 2018 to 2020, which is far below the national average of 7%. Therefore, it is suggested that Shanxi, Chongqing, Heilongjiang, Jilin, Inner Mongolia, and other places appropriately increase public education capital investment, enhance the proportion of social public capital, and optimize the structure of public capital investment.

(2) The Chinese government should promote the upgrading of industrial agglomeration. The innovation effect of the public capital can only be given full play in the advanced stage of industrial agglomeration. This paper finds that the adjustment effect of industrial agglomeration on the innovation effect of public capital presents a U-shaped curve, and the inflection point of the industrial agglomeration degree is 1.782. In 2020, the industrial agglomeration in Guangdong, Jiangsu, and Zhejiang exceeded the critical value, and that in Shanghai and Fujian was close to the critical value. However, the industrial agglomeration in other provinces had not yet crossed the inflection point, and the innovation effect of public capital has still not been fully brought into play. Therefore, the provinces with a low degree of industrial agglomeration, especially Hainan, Gansu, Heilongjiang, Yunnan, Guizhou, Qinghai, and other provinces, should realize the advanced industrial agglomeration as soon as possible to avoid the “low-end lock-in” of industrial economic development that weakens the innovative effect of public capital.

(3) The Chinese government should deepen the reform of state-owned enterprises and optimize the layout of public capital investment. On the one hand, the technological innovation activities of state-owned enterprises are often interfered with by the government, resulting in the impact of public capital on the technological innovation of non-state-owned enterprises being greater than that of state-owned enterprises. It is suggested that the Chinese government should further deepen the reform of state-owned enterprises, improve the marketization of state-owned enterprises, enhance the efficiency of the allocation of innovative resources of state-owned enterprises, and increase the technological innovation role of public capital in state-owned enterprises. On the other hand, the innovation effect of public capital of middle-end technology enterprises is greater than that of high-end technology enterprises, while the innovation effect of public capital of high-end technology enterprises is greater than that of low-end technology enterprises. Therefore, it is suggested that the Chinese government should increase the scale of public capital investment, and at the same time, public capital investment should be inclined to the areas where middle- and high-end industries gather, especially to increase the scale of public capital investment in high-tech industrial development zones and upgrade the level of infrastructure, software, and hardware.