The Influencing Mechanism of High-Speed Rail on Innovation: Firm-Level Evidence from China

Abstract

There is an urgent need to change the economic development mode from “resources driven” to “innovation driven” with the stagnation of the economy in China. Most existing research on the effect of high-speed rail (HSR) on firm innovation has lacked theoretical support and empirical evidence of firm innovation through knowledge spillover. This study introduces HSR as a cost coefficient to the classical heterogeneous firm model to construct a theoretical framework to determine the impact of HSR on firms’ innovation output. By matching the data of listed firms with the data of prefecture-level cities, the general difference-in-differences (DID) method is used to explore the impact of HSR on firm innovation and its mechanism. The research shows that the construction of HSR has a significant effect on the number of applied patent and authorized patents of firms and that there is a marginal increasing trend relating to the density and timing of HSR. The study found that in peripheral cities, firms in industries with rapid technological advances and highly innovative behaviors benefit more from HSR. HSR is associated with knowledge spillover within and between central and peripheral cities. It also has a heterogeneous sorting effect bounded by city size that promotes highly educated talent and the innovative output of firms that becomes significant only after the population size of a city reaches a certain threshold. HSR stimulates firm innovation mainly by improving the effect of firm resource allocation, promoting the spillover effect of innovation due to the flow and aggregation of resources, and increasing the scale effect of market expansion. Therefore, when designing innovation policies, the role of improving the construction of transportation to increase the frequency of face-to-face communication should be included, thus promoting the flow of knowledge and research collaboration.

1. Introduction

With the stagnation of the global economy and the gradual decline of resources and the demographic dividend in China, there is an urgent need to change the economic development mode from “resources driven” to “innovation driven”. Perhaps one of the most important aspects in that regard is to improve competitiveness at the national level, something that requires developing the innovative abilities of firms [1]. However, the independent innovation ability of Chinese firms has lagged in relation to actual need in terms of economic development for a long time. In December 2020, the 2020 European Union (EU) Industrial R&D Investment Scoreboard (which comprises the 2500 companies investing the most in R&D worldwide) showed that the US ranked first with 775 firms, followed by China with 536 firms. In 2019, the total R&D investment of those 755 US firms was EUR 347.7 billion, accounting for 38.45%. The R&D investment of Chinese firms was EUR 118.8 billion, accounting for 13.14% (https://iri.jrc.ec.europa.eu/scoreboard/2020-eu-industrial-rd-investment-scoreboard (accessed on 1 December 2022)). It can be seen that in terms of real technological standing and innovation capacity, China is not a real “patent power”, and the short duration and low conversion rate of patents has always been a source of criticism.

According to endogenous growth theory, innovation is mainly the result of R&D investment, knowledge spillover, and human capital. Knowledge spillover can be categorized into spatial knowledge spillover within a region and spatial knowledge spillover from nearby regions [2]. Given that knowledge is rooted in personal ability and that labor mobility is the main route of knowledge spillover between regions, particularly tacit knowledge spillover, the concentration of labor within regions further promotes knowledge spillover [3]. As Arrow (1971) states, economists recognize that innovation tends to occur and aggregate in the same space, similar to economic growth [4]. For example, large cities (e.g., New York, Beijing) are the main places where innovation takes place, and the spatial aggregation of innovation corresponds to the hierarchical structure of cities and the regional pattern of the economy. Many economists have proposed various theories and models to reveal the relationships between innovation, agglomeration (including urban and regional agglomeration), and economic growth. Endogenous growth theory states that the flow of resources promotes knowledge spillover between regions. Urban economists combine endogenous growth theory with the urban structure model to explain the relationship between urban structure, innovation, and growth, while national economists combine endogenous growth theory with the new economic geography (NEG) theory to explain the relationship between regional aggregation, innovation, and growth.

Knowledge and technology are rooted in scientists, research institutions, private sectors, and government [5], while new innovations and ideas build on past achievements and collaborations between participants. Collaboration between different holders of knowledge can facilitate knowledge creation, diffusion, and new innovations. Face-to-face access is closely associated with increased communication and intellectual interaction [2,6], eliminating flow barriers is the key to technological progress and innovation ability, and individual mobility has proven to be an important mechanism of knowledge diffusion [7]. Reducing transport costs can increase the flow of people and promote the flow, diffusion, and spillover of knowledge, thereby increasing the possibility of innovation; this is a common phenomenon, particularly in industries with rapid technological development [8]. Although there is literature on reducing transportation and trade costs, there remains a gap in terms of the theory and mechanisms explaining the impact of HSR on firm innovation, it still does not know the role of transportation on the promoting effect of firm innovation, and literature does not systematically explanate how transportation promote the population mobility and knowledge spillover to improve firm innovation in theoretical perspective.

According to NEG, transportation infrastructure helps promote labor mobility between regions, which has an important impact on city size and innovation level. The flow of resources brings firms intelligence resources; this results in firm innovation, as human resources are the key resources in innovation. Along with the rapid development of China’s HSR construction, decreased boundary barriers shorten communication time and the speed of labor mobility, capital flow, and information between cities, thus increasing traditional market efficiency. Davis and Dingel (2019) state that the exchange of ideas with the external market promotes knowledge creation and spatial agglomeration because the benefits of this exchange are greater in locations with a greater number of dialogue partners [9]. Exploring the impact and mechanism of the opening of HSR on firm innovation allows analyzing the influencing factors from the perspective of objective environmental changes, such as infrastructure construction, and provides innovation-based empirical evidence on resource allocative efficiency. It also helps in providing a theoretical reference for the government to reasonably plan the construction of HSR and coordinate regional economic development and for firms to seize the opportunity presented by the opening of HSR to improve their innovation level and achieve sustainable development.

Although many studies have investigated the determinants of innovation, such as investment [10], international trade [11,12,13], industrial agglomeration [14,15], cultural diversity [16], and public policy and entrepreneurship [17], empirical tests on the impact of transport infrastructure improvements on innovation are still quite limited. Overall, the existing literature contains a rich discussion of the effect of the construction of HSR on innovation; however, a theoretical framework focusing on firm innovation from the perspective of transportation improvement is still lacking. The literature discusses mechanisms promoting knowledge spillover effects on firm innovation, but there is a theoretical and empirical gap in terms of how to identify these spillover effects. “New” new economic geography (NNEG) states that an agglomeration economy can improve firm productivity, but the high cost and competitive environment of big cities also has selection effects on heterogeneous firms and the labor force. The larger the city size, the lower the average critical cut-off marginal cost of cities will be due to the competitive effect [18,19]. At the same time, based on their maximum utility, firms and labor carry out endogenous location selection according to the expected returns under different market conditions. How does the transport aspect of HSR play a role in the heterogeneity sorting of different city sizes? Does the aggregation effect of HSR no longer play a role for heterogeneous workers under the critical cut-off marginal cost of cities? In addition, both HSR and knowledge spillover have spatial attributes, and knowledge spillover must have a spatial attenuation effect. What then is the optimal radius of the impact of HSR on firm innovation? For cities with different human capital, there are differences in the innovation and knowledge spillover effects of HSR on firms. This paper looks at the opening of HSR in prefecture-level cities as a quasi-natural experiment and adopts the DID method to empirically investigate the impact of the opening of HSR on firm innovation and its mechanism.

The contributions of this paper are as follows. First, based on the technology selection model proposed by Bustos (2011), this present paper proposes a theoretical framework based on the resource aggregation and diffusion attributes of HSR and the effects on firm innovation behavior [20]. This theoretical framework also highlights our hypothesis that how HSR affect firm innovation by promoting the aggregation and diffusion of knowledge. Second, from the perspective of knowledge spillover and distance attenuation, the paper verifies the role HSR plays in firm innovation activities and its mechanism and explores the differences in the sorting effect of city size. The aim is to provide new empirical evidence concerning the construction of transportation infrastructure from a micro-level perspective. Finally, the paper adopts time-varying DID and staggered DID to conduct empirical research and discusses the endogeneity of HSR construction through the estimation of different instrumental variables (IV) to improve the credibility of the estimation results.

2. Conceptual Framework

This paper adopts the classical heterogeneous firm model [21] and refers to Bustos’s technology selection model [20]. The latter assumes that firms’ selection of different technologies directly affects their actual productivity level without explaining the sources of production technology differences. In our model, a firm indirectly changes its actual productivity level via its innovation behavior rather than directly via its choice of technology, thus revealing the mechanism of firm innovation. We introduce resource allocation, the knowledge spillover effect, and the market scale effect into the cost function of firm innovation; these effects reduce the cost of information searching and matching, reduce the marginal cost of innovation, and improve the efficiency of firm innovation.

2.1. Consumers

It is assumed that the utility function of typical consumers of heterogeneous products satisfies the form of the constant elasticity of substitution (CES) utility function:

$$U={[{{\displaystyle \int }}_{i\in \mathsf{\Omega }}q{\left(i\right)}^{\rho }di]}^{1/\rho }, \rho =\frac{\sigma -1}{\sigma },$$

(1)

where $q\left(i\right)$ represents the consumption quantity of products, $\sigma$ is the substitution elasticity of products $i$, and $\rho$ is the substitution parameter. The price index and consumer total income are set as:

$$P\equiv {[{{\displaystyle \int }}_{i\in \mathsf{\Omega }}q{\left(i\right)}^{1-\sigma }di]}^{1/1-\sigma }, R\equiv {{\displaystyle \int }}_{i\in \mathsf{\Omega }}r{\left(i\right)}^{1-\sigma }di, Q=\frac{R}{P}.$$

(2)

where $P$ is the price index, $R$ is total income and $Q$ represent the quantity of goods.

2.2. Firm

Referring to Bustos (2011), it is assumed that total firm costs consist of the marginal cost $\frac{1}{\phi }$ and the fixed cost $f$ [20]. For cities without HSR, the total cost function can be expressed as follows:

$$T{C}_l=f+\frac{q}{\phi }.$$

(3)

For cities with HSR, the opportunity cost of time between employees and customers is lower. Therefore, a fixed cost influence factor $\eta <1$ is introduced, so the total cost function can be expressed as:

$$T{C}_h=f\eta +\frac{q}{\phi },$$

(4)

where $f$ represents fixed cost, $\phi$ represents firm productivity, $q$ represents product output, $h$ represents cities with HSR, and $l$ represents cities without HSR. Further, the product pricing under a monopoly is:

$$p\left(\phi \right)=\frac{\omega }{\rho \phi }=\frac{\sigma -1}{\sigma \phi },$$

(5)

where $\omega$ is the wage. For firms without HSR in the city, the firm profit function can be expressed as:

$${\pi }_l\left(\phi \right)=r\left(\phi \right)-TC\left(\phi \right)=\frac{r\left(\phi \right)}{\sigma }-f=\frac{R{\left(P\rho \phi \right)}^{\sigma -1}}{\sigma }-f.$$

(6)

For firms with HSR in city, the firm profit function can be expressed as:

$${\pi }_h\left(\phi \right)=r\left(\phi \right)-TC\left(\eta ,\phi \right)=\frac{r\left(\phi \right)}{\sigma }-f\eta =\frac{R{\left(P\rho \phi \right)}^{\sigma -1}}{\sigma }-f\eta .$$

(7)

2.3. Firm Innovation Choice

Referring to Guadalupe et al. (2012) [22], it is assumed that the innovation input of a firm is $\gamma$ and that successful innovation can improve productivity by $\gamma \phi$. At this point, the firm profit function is expressed as:

$$\pi \left(\phi \right)=R{\left(P\rho \gamma \phi \right)}^{\sigma -1}-f.$$

(8)

The hypothesis $\lambda ={\gamma }^{\sigma -1}$ indicates the level of innovation output by the firm. Part of the innovation activities of firms come from the improved efficiency of resource allocation, such as R&D investment and R&D personnel allocation. Other parts come from the knowledge spillover from the external market. The R&D investment of firms is also affected by the market scale, which depends on transportation costs. The opening of HSR improves the market scale. The larger external market scale is synonymous with more fierce competition and higher revenue, as the larger external market can share the fixed cost of investing in innovation, thus improving earning power after successful innovation. Therefore, firms are more motivated to invest [23]. Moreover, firm entry into the external market also means obtaining advanced technologies and knowledge, which means benefiting from the larger scale of the external market [24,25]. Specifically, for cities with HSR, innovators can improve innovation efficiency by improving the effect of firm resource allocation, promoting the spillover effect of innovation due to the flow and aggregation of resources, and increasing the scale effect of market expansion. In

$$g=\left(m_r+m_c+m_s\right)\theta ,$$

(9)

$g$ represents the contribution of innovation to productivity growth, $m_r$, represents the efficiency of firm resource allocation, $m_c$ represents the spillover effect of innovation due to the flow of resources, and $m_s$ represents the scale effect of market expansion. $\theta$ captures the ability to innovate and continuously generate ideas, which can be regarded as the marginal input cost of innovation.

This paper assumes that the innovation output of unit input (that is, promoting the effect of successful innovation on productivity) is exogenous, that is, $g=\lambda$. Therefore, in the model of this paper, this difference of firm innovation output is reflected as the difference of firm cost input coefficient $c$, that is:

$$\theta =\frac{\lambda }{m_r+m_c+m_s}=c\lambda , c=\frac{1}{m_r+m_c+m_s}.$$

(10)

A city with HSR can prompt the efficiency of firm resource allocation $m_r$ by reducing the firm cost of information searching and matching and improving the efficiency of firm communication and learning $m_c$ by promoting the flow and aggregation of innovation resources due to the reduced information exchange cost of internal and external communication. In addition, the opening of HSR in a city improves the spatial accessibility between regions, resulting in lower transportation costs and a larger product market [25] and thus a higher output effect $m_s$ through market scale expansion. Therefore, it can be stated that:

$$\mathsf{\Delta }{m}_r^h>\mathsf{\Delta }{m}_r^l, \mathsf{\Delta }{m}_c^h>\mathsf{\Delta }{m}_c^l, \mathsf{\Delta }{m}_s^h>\mathsf{\Delta }{m}_s^l.$$

(11)

The marginal cost of the firm is further obtained by:

$$M{C}_h=\mathsf{\Delta }{c}_h\lambda =\frac{\lambda }{\mathsf{\Delta }{m}_r^h+\mathsf{\Delta }{m}_c^h+\mathsf{\Delta }{m}_s^h}, M{C}_l=\mathsf{\Delta }{c}_l\lambda =\frac{\lambda }{\mathsf{\Delta }{m}_r^l+\mathsf{\Delta }{m}_c^l+\mathsf{\Delta }{m}_s^l}.$$

(12)

Furthermore, it can be obtained from Equation (11) that:

$$M{C}_h<M{C}_l,$$

(13)

where $M{C}_h$ means the marginal cost when the city has HSR, and $M{C}_l$ means the marginal cost when the city does not have HSR.

As can be seen from Equation (13), compared with firms without HSR in the city, firms with HSR in the city have improved allocative efficiency and knowledge spillover and an increased scale effect of external economic activities. This makes the firm marginal cost of innovation input lower, that is, $M{C}_h<M{C}_l$. In addition, the firm innovation cost functions meet the following requirements:

$$C_h=\frac{1}{2}{c}_h{\lambda }^2, C_l=\frac{1}{2}{c}_l{\lambda }^2.$$

(14)

2.4. Profit Maximization

Combined with the production function of the firm, it can be obtained that:

$${\pi }_l^d\left(\phi \right)=\frac{R{\left(P\rho \phi \right)}^{\sigma -1}\lambda }{\sigma }-f-\frac{1}{2}{c}_l{\lambda }^2,$$

(15)

$${\pi }_l^x\left(\phi \right)=\frac{\left(1+n{\tau }^{1-\sigma }\right)R{\left(P\rho \phi \right)}^{\sigma -1}\lambda }{\sigma }-f-\frac{1}{2}{c}_l{\lambda }^2-f_e,$$

(16)

$${\pi }_h^d\left(\phi \right)=\frac{R{\left(P\rho \phi \right)}^{\sigma -1}\lambda }{\sigma }-f\eta -\frac{1}{2}{c}_h{\lambda }^2,$$

(17)

$${\pi }_h^x\left(\phi \right)=\frac{\left(1+n{\tau }^{1-\sigma }\right)R{\left(P\rho \phi \right)}^{\sigma -1}\lambda }{\sigma }-f\eta -\frac{1}{2}{c}_h{\lambda }^2-f_e,$$

(18)

where $f_e>0$ represents the fixed cost of an export product, and $\tau >1$ represents the iceberg transportation cost of trade. $d$ representative goods are sold locally, and $x$ representative goods are sold in the external market. It is assumed that there are $n$ symmetrical export regions in the world, which means $P_H=P_L=P, R_H=R_L=R$.

2.5. Optimal Innovation Input

For firms without HSR in the city, the first-order conditions on the innovation investment level meet the following requirements:

$${\lambda }_l^d=\frac{R{\left(P\rho \phi \right)}^{\sigma -1}\lambda }{\sigma c_l}; {\lambda }_l^x=\frac{\left(1+n{\tau }^{1-\sigma }\right)R{\left(P\rho \phi \right)}^{\sigma -1}\lambda }{\sigma c_l}, {\lambda }_l^x>{\lambda }_l^d>0.$$

(19)

For firms with HSR in the city, the first-order conditions on the innovation investment level meet the following requirements:

$${\lambda }_h^d=\frac{R{\left(P\rho \phi \right)}^{\sigma -1}\lambda }{\sigma c_h}; {\lambda }_h^x=\frac{\left(1+n{\tau }^{1-\sigma }\right)R{\left(P\rho \phi \right)}^{\sigma -1}\lambda }{\sigma c_h}, {\lambda }_h^x>{\lambda }_h^d>0.$$

(20)

Let us divide Equation (19) by Equation (20) to obtain two equations:

$$\frac{{\lambda }_h^d}{{\lambda }_l^d}=\frac{{\lambda }_h^x}{{\lambda }_l^x}=\frac{c_l}{c_h}>1.$$

(21)

Thus, we get:

$${\lambda }_h^d>{\lambda }_x^d, \mathrm{and} {\lambda }_h^x>{\lambda }_l^x$$

(22)

In this way, under the same circumstances firms (whether local sales firms or export firms) in cities with HSR will have a greater level of innovation output. This leads to hypothesis 1, as follows.

Hypothesis 1. 

The existence of HSR is conducive to promoting the innovation of local firms (whether local or export firms).

Hypothesis 2. 

HSR promotes firm innovation by improving the effect of firm resource allocation, promoting the spillover effect of innovation due to the flow and aggregation of resources, and increasing the scale effect of market expansion.

3. Data and Methods

3.1. Estimation Specification

When evaluating the treatment effect of HSR construction on promoting the innovation and development of firms, the time effect caused by natural growth or a change in the economic situation with time should be separated. In the existing research literature, the research method to evaluate the treatment effect is typically the DID method. This method allows unobservable factors to influence the explained variables by relaxing the limitation of policy evaluation. However, the assumption with DID is that the unobservable factors do not change over time, which requires that the change paths of the explained variables over time in the treatment and control groups are parallel when the policy is not implemented. This limitation increases the matching difficulty of the treatment and control groups. Therefore, the propensity score matching (PSM) method was used to deal with the problem of sample matching between the treatment group and the control group. If the common trend hypothesis is satisfied, the PSM + DID method can be used as an effective tool for causal inference. Considering that China’s HSR has been built year by year since 2008, the time-varying DID method is more useful for our parameter estimation. According to Equation (22), we plan to capture the promoting effect of firm innovation driven by city which have covered by HSR, the estimated model of HSR in relation to firm innovation is as follows to verify hypothesis 1:

$$P_{iut}=\alpha +{\beta }_{1}HS{R}_{ut}+{\theta }_1{X}_{it}+{\theta }_2{X}_{ut}+{\delta }_t+{\mu }_u+{\epsilon }_{iut}$$

(23)

where $i$ represents firm, $u$ represents city, $t$ represents year, and $P_{iut}$ is the innovation output level of firm $i$ located in prefecture city $u$ in period $t$ and is measured by the number of patents applied for by and the number of parents authorized for firm $i$. The dummy variable $HS{R}_{ut}$ indicates whether a city has HSR in that year. $X_{it}$ are a series of firm-level control variables, including the size of total assets (Size), firm age (Age), asset–liability ratio (Lev), Tobin’s Q, ratio of the largest shareholder (LAROWN), net profit margin of total assets (ROA), growth rate of operating income (GOR), an affiliation relationship with a state-owned firm (Property), and government subsidies (Subsidy). $X_{ut}$ are a series of city-level control variables, including the distance to the nearest port (This study does not directly use GDP to represent a city economy level but uses the distance to the coastal port cities. This is because the closer to a coastal port a city is, the better its economy. Using the distance to coastal port cities as a proxy variable of economic level can solve the endogenous problems between economic development and firm innovation.) (Distance), growth rate of gross domestic product (GGDP), and the average number of employees in the city (Employment). ${\mu }_u$ and ${\delta }_t$ are two-way fixed effects at city and time, respectively, and ${\epsilon }_{iut}$ is the random disturbances. The PSM–DID method uses the control variables in this paper as the features of HSR opening to conduct PSM so the matched samples meet the common trend hypothesis. This will reduce the sample selection bias in the model. The matched samples are then used for DID estimation. The data of all control variables are lagged one period to avoid simultaneity bias.

The outcome variable (p) is the number of patents granted to firms. Although the innovation activities of firms include two dimensions of innovation input and innovation output, many innovation inputs do not have practical significance for firms due to the risks of innovation activities, and only some of the patents firms apply for will be authorized, which cannot truly reflect the level of innovation output of firms. Firms’ authorized patents indicate the real number of patents. However, authorized patents are unstable because they require testing and the payment of annual fees and are susceptible to political interference. Applied patent by firms have been used during the application process, which can reflect the real innovation capacity of firms, meanwhile, innovation persistence is thus an important source of dynamics in the later innovation context. Therefore, this paper chooses the number patents applied for and the number of authorized patents as the proxy variables of firm innovation. Due to the time lag of HSR in relation to the production and innovation process of firms and to avoid the reverse causal effect, we included the lag of patent variable in the econometric model.

The core explanatory variable of this paper is whether a city has HSR this year. Time-varying DID estimation is adopted in this paper, so there is no clear treatment group and control group. Therefore, if the city where the firm is located has HSR in year $t$, the value $HS{R}_{ut}$ is set to 1; otherwise, the value is set to 0.

3.2. Data Description

The data for empirical analysis in this paper relate to listed firms in Shanghai and Shenzhen in China, which were obtained from the China Stock Market & Accounting Research Database (CSMAR). The HSR data for prefecture-level cities were manually sorted according to the National Railway Passenger Train Schedule from 2008 to 2019. To ensure the reliability of the research conclusions, firms with missing important indicators and firms that were delisted during the research period were excluded. Considering HSR was only opened in 2008, we obtained 12-year unbalanced panel data for 3201 listed firms from 2008 to 2019 and a total of 23,881 observations. Corrections were made to accurately match the urban development data based on the matching between the firm office address and the city in which it is located. In the case of outliers for some indicators, 1% cut-off was carried out for all continuous variables. The descriptive statistics of the main variables used in this paper are shown in

Table 1. Statistics of main variables.

Variables	Obs.	Mean	Std. Dev.	Min	Max
Applied Patent	23,881	38.754	97.918	0	725
Authorized Paten	23,881	26.169	64.936	0	477
HSR	286	0.711	0.453	0	1
Age	23,881	15.83	5.663	2	29
Size	23,879	22.04	1.449	19.08	26.85
Lev	23,879	0.443	0.227	0.052	1.143
ROA	23,880	0.042	0.064	−0.260	0.221
GOR	22,395	0.213	0.582	−0.680	4.330
Tobin Q	23,881	2.015	0.917	0	3.219
Property	23,881	0.398	0.490	0	1
LAROWN	23,881	34.90	15.07	8.760	74.82
Subsidy	22,782	0.338	0.853	0	6.111
Employment	286	487.2	433.0	24.61	1570
GGDP	286	9.540	4.107	−9.38	26.97
Distance	286	369.7	443.7	0	2526

. Among year between 2008 and 2019, firms get 38.754 applied patents and 26.169 authorized patents on average per year, but part of firms still do not get more than one applied patent and authorized patent in some years.

Figure 1 shows the comparison results regarding to the applied patent and authorized patents of firms with and without HSR in their cities. Obviously, both the applied patent and authorized patents of firms are greater in number in cities with HSR than in those without. Moreover, over time, the growth rate of patents for firms in cities with HSR is higher than that for firms in cities without HSR. This indicates that the innovation effect of HSR may have a cumulative effect over time. Of course, the statistical results based on the mean cannot eliminate the effect of the time trend and other factors; therefore, further regression analysis is needed to reveal the causal relationship between the opening of HSR and the innovation level of firms.

4. Results

4.1. Impact of HSR on Firm Innovation

Before the DID analysis, we conducted a parallel trend test between firm innovation and HSR, the results of which are shown in Figure 2. The figure shows that all pre-processing coefficients of HSR regarding in firm innovation do not have significant differences before the opening of HSR but shows significant differences in the period after the opening of HSR with one-year lag (There are 11 periods before and after the opening of HSR, but we combined the data after the 5th period into the 5th period so that the parallel trend chart could be more concise). This proves that the impact of HSR on firm innovation meets the hypothesis of parallel trend, so we further take the empirical analysis in the next section.

Table 2. Influence of HSR on firms’ output of patent.

Variables	Applied Patent		Authorized Patent
HSR	22.86 ***	5.883 ***	15.00 ***	4.557 ***
	(1.960)	(1.830)	(1.439)	(1.215)
Age		−0.930 **		−0.697 **
		(0.388)		(0.279)
Size		15.21 ***		9.630 ***
		(2.334)		(1.538)
Lev		−10.10		−4.665
		(7.903)		(4.773)
ROA		41.01		14.95
		(27.46)		(20.77)
GOR		−1.266		−1.897 ***
		(1.171)		(0.635)
Tobin Q		2.403		1.804
		(2.608)		(1.787)
Property		−3.308		−2.416
		(4.456)		(2.798)
LAROWN		−0.047		0.029
		(0.153)		(0.102)
Subsidy		41.62 ***		27.67 ***
		(4.081)		(2.918)
Employment		0.031 ***		0.021 ***
		(0.007)		(0.007)
GGDP		8.106 ***		6.218 ***
		(1.376)		(1.216)
Distance		−4.065 **		−2.524 **
		(1.569)		(0.998)
Year FE	√	√	√	√
City FE	√	√	√	√
Obs	23,853	21,167	23,853	21,167
Adjust R2	0.191	0.394	0.194	0.393

Note: *** p < 0.01, ** p < 0.05. Standard errors are reported in the parentheses and clustered at the prefecture-city. All results were estimated by OLS.

shows the estimated results of HSR in relation to firms’ applied patent and authorized patents. Columns (1) and (3) show the influence of HSR on firms’ applied patent and authorized patents without any controlling variables, estimated coefficient of the HSR variable on firm innovation is significantly positive, indicating that the opening of HSR at prefecture-level cities significantly improves the innovation output of local firms. Columns (2) and (4) further control a series variable at both firm- and city-level, the regression coefficient of HSR on firm innovation is still significantly positive. These results show that firms in cities with HSR get more applied patent and authorized patents than firms in cities without HSR, further indicating that the opening of HSR stimulates the innovation level of firms in cities along HSR lines. Thus, hypothesis 1 is verified.

4.2. Endogeneity of HSR Opening

Identifying the causal relationship between the opening of HSR and the level of firm innovation has some potential endogeneity problems. As a major strategic plan at the national level, HSR links the regional central cities that account for about half of the GDP in China. However, government preferences and economic development potential may be key factors in determining whether these cities can become nodes for the HSR network. Another problem relates to omitted variables. Cities with HSR are generally relatively well developed in terms of their economies and levels of innovation. Some unobserved variables may be omitted in the model, which may affect the opening of and innovation level associated with HSR. Therefore, this paper uses IV regression to solve this problem. An effective IV should be a very good predictor of HSR construction and should be orthogonal to the error of the estimation model. Based on Agrawal et al. (2017) [26] and Wang and Cai (2020) [27], historical railway lines in 1961 were used as IVs in relation to HSR lines in the sample period of this paper. On one hand, historical railway lines are related to current railway line construction; on the other hand, historical railway lines can hardly affect current firm innovation activities through channels other than HSR connection. Therefore, the historic railway of 1961 is unlikely to be relevant to the innovation activities of firms in the 21st century through other channels but only through the construction of HSR to influence the innovation behavior of firms. In addition, to further ensure the robustness of the results, we construct another IV using the geographical gradient to increase the robustness of handling endogeneity problems [28]. On one hand, the greater the average gradient of the city, the more difficult it is to build HSR lines, which means the geographical gradient is negatively correlated with the probability of opening HSR. On the other hand, the geographical gradient is an exogenous geographical variable that does not directly affect the innovation ability of firms.

Specifically, $HS{R}_{Iu}$ indicates whether there was a railway station in city $u$ in 1961 (or $HS{R}_{Iu}$ indicates the geographical gradient of this location). If the city had a railway station in 1961, we assign a gradient value of 1; otherwise, it is 0. Because the IV does not change with time, this study takes its interaction with time as the IV using panel data, so that it has time-varying characteristics [29]. Therefore, the first stage of panel IV estimation is:

$$HS{R}_{ut}={\alpha }^{\prime }+{\beta }_1^{\prime }HS{R}_{Iu}\ast {\mathsf{\Phi }}_t+{\theta }_1^{\prime }{X}_{it}+{\theta }_2^{\prime }{X}_{ut}+{\delta }_t^{\prime }+{\mu }_u^{\prime }+{\epsilon }_{iut}^{\prime }$$

(24)

where $HS{R}_{Iu}$ is whether city $u$ had a railway station in 1961. The potential endogeneity shows that ${\epsilon }_{iut}$ may be related to $HS{R}_{ut}$ in Equation (23); adding Equation (24) into the estimation equation can solve the endogeneity problem. In short, the unobservable factors $HS{R}_{Iu}$ and are independent under controlled $X_{it}$ and $X_{ut}$, which meets the hypothesis of IV externality when $E\left[HS{R}_{Iu}\ast {\epsilon }_{iut}\right]=0$.

In

Table 3. The impact of HSR on firm innovation estimated by IV.

Variables	Applied Patent	Authorized Patent	Applied Patent	Authorized Patent
HSR	87.94 ***	54.34 ***	67.90 ***	46.99 ***
	(7.533)	(4.991)	(10.45)	(6.973)
First stage
Rail1961	0.024 ***	0.024 ***
	(0.000)	(0.000)
Gradient			0.005 ***	0.005 ***
			(0.0001)	(0.0001)
F-statistic	1755.45	1755.45	848.87	848.87
	(0.000)	(0.000)	(0.000)	(0.000)
KP test statistic	1636.79	1636.79	824.42	824.42
	(0.000)	(0.000)	(0.000)	(0.000)
Obs	21,167	21,167	21,167	21,167
Adjust R2	0.188	0.194	0.213	0.207

Note: *** p < 0.01. Standard errors are reported in the parentheses and clustered at the prefecture-city. Table 3 controls all control variables as shown in Table 2, and adopts both time and city fixed effects.

, the Hausmann test shows that the ordinary least squares (OLS) and IV estimates differ greatly. In addition, the F-test statistic is higher than the standard of 10, and the KP statistical test shows that the estimates derived from historical railway construction (or geographical gradient) are not affected by weak IVs. Table 3 shows that the result of IV estimation is positive and significant, but it is larger than the OLS estimate, which is similar to the conclusions of some previous studies. This may be due to the non-random distribution of transportation infrastructure investment. Cities with good economic development usually have more resources, which leads to further investment bias in their preference, resulting in an underestimate of the estimation coefficient. However, the distribution of HSR is determined by the allocation principle of HSR investment under the guidance of historical railway construction routes (or geographical gradient), so the estimation coefficient can more accurately identify the promotion effect of HSR on firm innovation. Therefore, the firm promotion effect of HSR investment based on certain criteria is greater than that of transport infrastructure investment with non-random distribution [30].

4.3. Spillover Effect of HSR on Firm Innovation

Lower transportation costs and higher spatial accessibility speed up the flow of labor and the diffusion of knowledge. Firms and their R&D personnel have to integrate knowledge and innovative ideas to further stimulate innovation [31]. In general, large cities have larger external markets and more resources, and fierce competition makes the marginal production cost of big cities lower, which means that big cities have stronger innovation ability [18]. On one hand, the opening of HSR has both a siphon effect and a radiation effect on peripheral cities, and the comprehensive combination of these two forces influence the direction of the final force. On the other hand, HSR will connect central cities with peripheral cities, so the spatial spillover effect of knowledge and innovation will overflow from central cities to peripheral cities through personnel mobility and communication, thus promoting firm innovation in peripheral cities. Therefore, this paper examines whether the HSR connection between cities promotes the spillover of firm innovation from central cities to peripheral cities. In the present study, provincial capital cities, sub-provincial cities, and municipalities are deleted from the original sample because these cities are the main central cities in China. Then, the number of connections between peripheral cities and the nearest central city is calculated based on the classified boundaries of 0–100 km, 100–200 km, 200–300 km, 300–500 km, and 500 km. If the connections between cities is higher, these peripheral cities are more closely connected with the central cities, and the spillover effect of knowledge and innovation is more likely to affect them. The specific identification model is as follows:

$$P_{iut}=\alpha +{\beta }_{1}HS{R}_{ut}+{\beta }_{2}Di{s}_{u{u}^{\prime }}+{\beta }_{3}HS{R}_{ut}\ast Di{s}_{u{u}^{\prime }}+{\theta }_1{X}_{it}+{\theta }_2{X}_{ut}+{\delta }_t+{\mu }_u+{\epsilon }_{iut}$$

(25)

where $Di{s}_{u{u}^{\prime }}$ is a dummy variable of number that peripheral city $u$ is connected to any nearest central city differentiated by the distance (0–100 km, 100–200 km, 200–300 km, 300–500 km, and 500 km away). For example, within the distance of 0–100 km, $Di{s}_{u{u}^{\prime }}$ is assigned a value of 1 if city $u$ is connected to one central city and a value of 2 if city $u$ is connected to two central cities, and so on. If city $u$ is not connected to any central city, a value of 0 is assigned. The estimation coefficient ${\beta }_3$ indicates whether the opening of HSR promotes the innovation of firms under this distance type, that is, to identify the spillover effect of firm innovation under different HSR distances.

The estimation results in

Table 4. Knowledge spillover effect across cities.

Panel A	Applied Patent
HSR	23.46 ***	20.39 ***	14.15 **	24.49 ***	29.11
	(3.160)	(4.275)	(5.620)	(6.497)	(12.60)
100 km	−8156 ***
	(1058)
100 km × HSR	−17.59 ***
	(3.827)
200 km		5078 ***
		(1032)
200 km × HSR		11.06 ***
		(3.207)
300 km			3592 ***
			(684.6)
300 km × HSR			4.702
			(4.416)
400 km				−3667
				(2096)
400 km × HSR				14.92 **
				(4.895)
500 km					−2046
					(1016)
500 km × HSR					−7.029
					(4.275)
Obs	9233	5385	1611	403	92
Adjust R2	0.251	0.261	0.278	0.415	0.472
Panel B	Authorized patent
HSR	16.66 ***	14.51 ***	9.208 *	18.95 **	24.88
	(2.456)	(3.149)	(4.437)	(6.098)	(10.47)
100 km	−5300 ***
	(682.1)
100 km × HSR	−14.14 ***
	(2.526)
200 km		2795 ***
		(750.0)
200 km × HSR		5.578 **
		(2.445)
300 km			2269 ***
			(394.0)
300 km × HSR			2.536 **
			(1.249)
400 km				2408
				(1573)
400 km × HSR				10.27 **
				(3.190)
500 km					−2447 *
					(715.8)
500 km × HSR					−8.778
					(3.305)
Obs	9233	5385	1611	403	92
Adjust R2	0.262	0.271	0.297	0.445	0.469

Note: *** p < 0.01, ** p < 0.05, * p < 0.1. Standard errors are reported in the parentheses and clustered at the prefecture-city. Table 4 controls all control variables as shown in Table 2, and adopts both time and city fixed effects.

show that the regression coefficients of both patents applied for and authorized patents within 100 km are negative, while the regression coefficients of cities beyond 100 km away from central cities are positive and significant. This may be because the opening of HSR has a siphon effect on adjacent peripheral cities, which makes the firm innovation effect of these cities negative. The regression coefficient decreases gradually with increasing distance from the central city, showing the distance attenuation effect. Furthermore, it is no longer significant in cities that are 500 km away. These results indicate that the opening of HSR accelerates communication within medium distance by promoting the spillover effect of the central city on firm innovation in the peripheral cities.

Table 4 shows that the opening of HSR has both a siphon effect and a radiation effect on peripheral cities, and the two forces may counteract each other. The geographical distance from peripheral cities to central cities determines the size and direction of the siphon and radiation effects. Specifically, the opening of HSR has a positive innovation promotion effect on firms within a medium distance from central cities but has a negative impact on firms within the closest distance from central cities and does not show any significant impact on firms that are the farthest distance from central cities. This may be because medium-distance cities experience less siphoning and more radiation than close-distance cities. This shows that HSR widens the technological gap between central cities and peripheral cities by differentiating the innovation activities of firms between central cities and peripheral cities. When the technological level of central cities improves rapidly, the improvement of transportation infrastructure accelerates the marginalization of peripheral cities in terms of technological innovation, especially those near and far from the central cities, thus promoting the redistribution of technological innovation at the urban level.

A well-known feature of innovation is that its output distribution is highly skewed across inventors in the right tail. Agrawal et al. (2014) found that “star” firms in innovation have a greater knowledge spillover effect. Our paper explores whether the opening of HSR will accelerate the spillover effects of knowledge and innovation within cities. Agrawal define an innovation “star” as a firm whose patent output is above the 99th percentile in the current year [32]. If a city has at least one innovation “star” in the current year, we give it a score of 1 in this year; otherwise, it is 0. Furthermore, “star” firms are removed from the next analysis. Based on Agrawal et al. (2014), we divided firms into two groups according to the city score defined above; one group consists of cities with an innovation “star”, and the other consists of cities without an innovation “star”. We then conducted separate regression analyses for the two sub-samples. These results are shown in

Table 5. Knowledge spillover effect within city.

Variables	Applied Patent		Authorized Patent
	No Star Nearby	Star Nearby	No Star Nearby	Star Nearby
HSR	21.49 ***	22.02 ***	14.17 ***	15.05 ***
	(1.646)	(3.725)	(0.998)	(2.746)
Obs	15,214	8403	15,214	8403
Adjust R2	0.233	0.195	0.250	0.197

Note: *** p < 0.01. Standard errors are reported in the parentheses and clustered at the prefecture-city. Table 5 controls all control variables as shown in Table 2, and adopts both time and city fixed effects.

. Cities with an innovation “star” benefit more from the opening of HSR than cities without an innovation “star”, no matter firms’ number of patents applied for or authorized. This finding suggests that the opening of HSR promotes knowledge and innovation spillover within innovation “star” cities and enables other firms in the same city to produce more innovation output.

Knowledge spillover is significant between cities, illustrating that firms can choose a more efficient and convenient means of transportation for trans-regional information and technology exchanges and cooperation when the city has HSR. HSR benefits the firm in terms of cross-regional face-to-face communication to acquire more useful knowledge; thus, the firms began to influence each other due to the cross-regional communication. This proves the role of HSR in promoting knowledge spillover across and within regions and thus that HSR significantly strengthens innovation externalities among firms.

4.4. Sorting Effect of HSR in Promoting Firm Innovation

Melitz (2003) states that firms do not have the same marginal cost in new trade theory. By introducing the efficiency parameter and its distribution function of firms, the heterogeneity model states that firms pay a certain sunk entry cost to obtain productivity from the labor market. It has been proven that there is a critical cut-off marginal cost in the city, and firms that exceed the cut-off marginal cost of city cannot survive in the city [21]. Syverson (2007) points out that the higher the density of suppliers for one product in the market, the easier it is for consumers to find alternative firms; therefore, the market competition is more intense and inefficient firms will withdraw from the market because of nonprofit [33]. However, the distribution of firms’ productivity depends on the distribution of initial productivity, which makes endogenous sorting effect for heterogeneity firms and labor in the location selection based on market size of cut-off marginal cost. The different productivity levels of firms determine the investment level of their entry costs, which in turn determines their choice of location. The distribution of firms’ productivity puts strict requirements on the distribution of labor productivity; high firm productivity will require highly skilled labor so as to realize the matching of firms’ skill demand and labor skill level [6]. This also puts strict requirements on the distribution of the labor market, which in turn determines the location of labor. Therefore, the opening of HSR will influence firm and labor market distribution, and labor mobility based on skill level will cause a heterogeneity sorting effect according to the cut-off effect on cities. Finally, dynamic changes in heterogeneous firm innovation and development will occur when HSR promotes heterogeneity innovation resources mobility based on the city sorting effect. Therefore, this paper tests the sorting effect of heterogeneous firms and labor in cities of different sizes from the perspective of the opening HSR, whether high productivity firm and labor will flow into the large city in the promoting agglomeration effect of HSR. In short, there is a cut-off effect of city size, and firms below the cut-off point will have a more obvious inflow effect of high-skilled talent and a more obvious innovation effect.

To avoid the deviation of grouping caused by artificially dividing the population size, this study uses the panel threshold regression model proposed by Hansen (1999) [34] according to which data can be divided into classes based on their characteristics. It aims to study the impact of HSR on the innovation activities of heterogeneous firms and the educational distribution of firm personnel under different population sizes. The specific identification model using the nonlinear threshold model is as follows:

$$P_{iut}=\alpha +{\beta }_{1}HS{R}_{ut}I\left(PO{P}_{ut}\le {\gamma }_1\right)+{\beta }_{2}HS{R}_{ut}I\left(PO{P}_{ut}>{\gamma }_2\right)+{\theta }_1{X}_{it}+{\theta }_2{X}_{ut}+{\delta }_t+{\mu }_u+{\epsilon }_{iut}$$

(26)

$PO{P}_{ut}$ is the threshold variable for city size based on the number of people employed [35].${\gamma }_1$ and ${\gamma }_2$ are the threshold values, and $I(·)$ is the indicating function (if the assumption is true, the value is 1; otherwise, the value is 0).

Considering that the panel threshold regression model requires complete balanced panel data, this paper uses three years of data from 2016–2018 to explore the impact of the heterogeneous innovation effect, with population size as the threshold variable. First, we tested the panel threshold effect in

Table 6. Testing of different threshold values.

Items	Threshold	F Value	p Value	Crit 10%	Crit 5%	Crit 1%
Applied patent	730	19.87	0.021	27.551	32.742	62.759
Authorized patent	757	30.10	0.080	27.814	33.792	50.987
Junior college	641	14.74	0.470	46.432	73.765	170.086
Undergraduate	381	14.23	0.027	40.086	52.953	133.186
Postgraduate	287	13.97	0.017	31.179	41.974	74.200

Note: The estimated parameters are repeated sampling 500 times by Boostrap self-help method.

. Only the number of applied patent and authorized patents and the number of undergraduates and postgraduates employed by firms passed the significance level test of 10% at the first threshold; however, they failed the second and third threshold tests. The results show that the number of applied patent and authorized patents and the number of undergraduates and postgraduates have a heterogeneity sorting effect based on the size of a city’s population.

The further threshold regression model in

Table 7. The threshold effect of HSR on firm innovation.

Variables	Applied Patent	Authorized Patent	Junior College	Undergraduate	Postgraduate
Regime 1	2.000	1.168	25.60	−5.529	−5.032
	(1.436)	(0.898)	(24.59)	(17.76)	(3.719)
Regime 2	3.466 **	1.885 **	0.698	12.93 *	4.290 ***
	(1.443)	(0.899)	(24.86)	(7.61)	(1.465)
Obs	6645	6645	6645	6645	6645
Adjust R2	0.069	0.087	0.108	0.108	0.088

Note: *** p < 0.01, ** p < 0.05, * p < 0.1. Standard errors are reported in the parentheses and clustered at the prefecture-city. Table 7 controls all control variables as shown in Table 2, and adopts both time and city fixed effects.

shows the impact of HSR on firm innovation under the threshold value of population size. Columns (1) and (2) of Table 7 show that when the population size critical value is 7.3 million, HSR can significantly promote firm innovation activities, while for cities with a population size less than 7.3 million, HSR has no significant impact on firm innovation activities. Column (3) of Table 7 shows that HSR has no threshold effect on the flow of personnel with a junior college education. Columns (4) and (5) show that when the critical value of population size is about 3 million, HSR promotes the mobility of undergraduates and postgraduates into firms in big cities, while for small cities with a population of less than 3 million the opening of HSR does not promote the aggregation of population into firms. HSR has a different threshold effect than the promoting effect of firm innovation in the two aspects of innovation output and human capital accumulation. A possible explanation is that the main purpose of a firm is to be profitable, and therefore the market reaction tends to be more rational. However, the mobility of laborers will not only be affected by things in the external environment, such as transport infrastructure, but also by laborers’ mobility preferences and the cost of living in cities. Therefore, there is an obvious difference in the population threshold between innovation output and human capital accumulation. Table 7 shows that in the process of HSR promoting firm innovation, there is indeed an obvious heterogenous sorting effect of the aggregation of innovation resources. The transport aspect of HSR accelerates the aggregation of more highly skilled talent in big cities, thus stimulating firms in big cities to produce more innovative output.

The opening of HSR strengthens the geographical contact between professional and technical personnel in central and non-central cities, thus promoting the knowledge spillover effect [36]. With the shortening of space–time distance and the increase in commuting frequency, the marginal benefit of acquiring knowledge through communication will also increase, although information technology cannot perfectly replace face-to-face communication. However, knowledge spillover emphasizes the face-to-face communication between professionals in central and non-central cities brought by HSR. In this process, information is symmetrical, which means there is a knowledge sharing effect. This has a definite and positive impact on firm innovation in non-central cities. Due to uncertainty in terms of the direction of resources flow, the results of influencing firm innovation in non-central cities through resources flow can be uncertain; there may be a game between the siphon effect and the diffusion effect bounded by the threshold effect relating to city size. Therefore, innovation resources may converge in central cities at the same time, and peripheral cities can also benefit from the spillover effect of central cities through HSR.

4.5. Robustness Test

4.5.1. Staggered DID Estimation

Cities with HSR have different rail schedules. Most studies mainly use the time-varying DID method to study the impact of HSR on the market economic activities of firms and calculate an average treatment effect. This ignores the heterogeneity of the average treatment effect at different treatment times. The traditional time-varying DID model estimates the average processing effect, including the overall linear projection of the policy processing effect and omitted variables on the existing regression variables (processing state, individual and time indicator variables), ignoring the heterogeneous effect of the processing queue and the length of the processing time on the average processing effect. However, staggered DID makes up for the deficiency of time-varying DID in estimating the actual effect of policy processing by separating various policy processing queues and setting the duration of receiving policy processing [37,38,39]. Therefore, this study uses staggered DID as the robust regression to estimate the heterogeneous treatment effect of HSR. The specific staggered DID model according to the different opening time of HSR in each city is as follows:

$$P_{iut}={{\displaystyle \sum }}_{c=0}^C{{\displaystyle \sum }}_{p=0}^{P_c}{\beta }_{cp}{D}_{cput}+{\theta }_1{X}_{it}+{\theta }_2{X}_{ut}+{\delta }_t+{\mu }_u+{\epsilon }_{iut}$$

(27)

where $C$ is the policy processing queue divided based on the opening time of HSR in city $u$. The policy processing queue is divided into 12 queues because the span of time for the opening of HSR in this study is from 2008–2018; that is $c=0,1, \dots , 11$. Specifically, cities that do not have HSR are classified as $c=0$, cities that opened HSR in 2008 are classified as $c=1$, …, and cities that opened HSR in 2018 are classified as $c=11$. $p$ is the duration of receiving policy processing for the queue $c$, and $D_{cput}$ is an indicator variable indicating whether city $u$ belongs to both queue $c$ and duration $p$.

Table 8. Impact of HSR on firm innovation estimated based on staggered DID.

Variables	Applied Patent	Authorized Patent
Average treated effect	13.068 *** (3.587)	8.199 *** (2.404)
P = 1	2.108 (1.108)	0.963 (0.851)
P = 2	3.527 * (1.829)	3.339 *** (1.165)
P = 3	4.664 ** (2.333)	3.627 ** (1.733)
P = 4	6.937 ** (2.800)	4.357 ** (1.864)
P = 5	9.181 ** (3.937)	6.322 *** (2.442)
P = 6	12.328 ** (5.197)	8.163 *** (2.997)
P = 7	18.574 *** (5.323)	10.704 *** (3.531)
P = 8	21.146 *** (6.799)	12.792 *** (4.675)
P = 9	39.033 *** (7.939)	23.793 *** (5.624)
P = 10	59.279 *** (11.440)	34.959 *** (7.763)
P = 11	36.837 *** (9.032)	17.365 (11.726)
Obs	23,425	23,425
Adjust R2	0.121	0.119

Note: *** p < 0.01, ** p < 0.05, * p < 0.1. In parentheses are robust standard errors of clustering to prefecture-level cities. Table 8 controls all the control variables as shown in Table 2, and simultaneously adopts the time-fixed effect.

shows the average treatment effect of HSR on firm innovation and the dynamic effect of opening time of HSR based on staggered DID estimation. Compared with firms in cities without HSR, firms in cities with HSR have a significant increase in applied patent and authorized patents, respectively; the estimated coefficients were higher than those of time-varying DID estimation, respectively. This indicates that the impact of HSR based on staggered DID estimation of firm innovation output is greater than the estimated coefficient based on time-varying DID. This may be because the estimated result of staggered DID is the average treatment effect weighted by different processing time, while the estimated result of time-varying DID is the average treatment effect directly calculated by comparing cities with and without HSR. This ignores the dynamic cumulative effect of the duration of time from when the HSR opened. Considering the promoting effect of firm innovation from different cities covered by HSR at different times, the number of applied patent and authorized patents of firms is higher the longer city $u$ has been covered by HSR. HSR showed a trend of increasing marginal output vis-à-vis firm innovation, which inspires firms to speed up absorption of the knowledge spillover effect to produce innovation after the city in which they are located is covered by HSR.

4.5.2. Replacing Core Variables

This study estimates the impact of HSR on firm innovation by using the number of applied patent and authorized patents as proxy variables. However, patent holders need to pay an annual fee to update the duration of validation. Generally, the older a patent is, the greater its actual value. Therefore, the total patents do not reflect the impact of HSR on firm innovation behavior by year. It is possible that a persistence effect of firms’ previous patents may exist and that firms will further improve their innovation behavior based on previous output. In addition, although the analysis of total patents can help explain current firm innovation behavior, it does not explain the change of innovation behavior in relation to different types of patents. Generally, invention patents, utility patents, and design patents are the main types of patents held by firms. Firms have different responses to different types of patents after the opening of HSR in the cities in which they are located that indicate the importance of those different patent types in knowledge exchange and spillover. Therefore, this paper uses robustness tests in relation to firms’ invention, utility, and design applied patent and authorized invention, utility, and design patents.

Table 9. Influence of HSR on annual applied and authorized patent.

Variables	Applied Patent			Authorized Patent
	Invention	Utility	Design	Invention	Utility	Design
HSR	0.968 ***	0.626 ***	0.022 **	0.400 ***	0.556 ***	0.018 ***
	(0.073)	(0.065)	(0.008)	(0.045)	(0.049)	(0.006)
Obs	23,853	23,853	23,857	23,853	23,853	23,853
Adjust R2	0.147	0.137	0.058	0.137	0.136	0.061

Note: *** p < 0.01, ** p < 0.05. Standard errors are reported in the parentheses and clustered at the prefecture-city. Table 9 controls all control variables as shown in Table 2, and adopts both time and city fixed effects.

shows that HSR has a significant effect on the annual number of invention, utility, and design patents applied for and authorized for firms, but its average promotion effect is relatively small compared with the total effect estimated in Table 2. This further indicates that the opening of HSR has a cumulative effect on firm innovation over time, and the annual innovation effect is lower than the total average effect of innovation.

Due to the constraints of economic development and social demand, different cities have different operating density in terms of HSR. For example, some cities are covered by just one HSR station and some are covered by several HSR stations. In addition, the number of operating HSR lines in each city is closely related to the economy and population size. These differences in HSR operating quality must have an important impact on firm innovation and spillover effect. Therefore, this study introduces the number of HSR stations and the number of HSR lines to replace the binary variable of HSR measured by whether city $u$ is covered by HSR, thus testing the impact of HSR operating quality on firm innovation.

Table 10. Influence of number of HSR stations and operational lines on firm innovation.

Variables	Applied Patent		Authorized Patent
Number of stations for HSR	1.409 **	0.788 **
	(0.657)	(0.378)
Number of lines for HSR			5.678 ***	3.483 ***
			(1.180)	(0.779)
Obs	21,167	21,167	21,167	21,167
Adjust R2	0.395	0.394	0.396	0.395

Note: *** p < 0.01, ** p < 0.05. Standard errors are reported in the parentheses and clustered at the prefecture-city. Table 10 controls all control variables as shown in Table 2, and adopts both time and city fixed effects.

shows that the number of HSR stations and HSR lines has a significant positive impact on firm innovation. The higher the HSR operating quality, the greater the promotion effect of HSR on improving the level of innovation. Every time a city adds another HSR station or line, the innovation output of firms will significantly increase. Therefore, to maximize the promoting effect of HSR on firm innovation, a city with HSR should strengthen the supporting facilities related to HSR and improve the HSR service quality, thus promoting improvements in the innovation level of firms.

4.5.3. Placebo Test

To exclude the influence of other random factors and non-observable factors on the estimated results of this study, a placebo test was conducted by randomly changing the HSP opening time to generate different “pseudo” treatment groups. The specific method is to randomly select the opening year of HSR in any city from all the cities as the policy time. The randomly selected treatment time ensures that the proxy variable of HSR has no impact on firm innovation. If the estimated coefficient is significantly different from the baseline regression coefficient, it indicates that the improvement in firm innovation level is indeed caused by the opening of HSR. Otherwise, it indicates that the above research results are not robust. The estimated coefficients of applied patent and authorized patents obtained from 500 random samples are distributed with 0 as the center, and the corresponding $p$ value is approximately greater than 0.1, which is similar to the expectations of the placebo test. These results indicate that the effect of HSR on firm innovation is unlikely to be affected by the omitted variables, making the estimated results in this study robust.

4.6. Heterogeneity Analysis

In the above analysis, we study the impact of HSR on firm innovation and demonstrate the robustness of this impact. In this section, we will study the heterogeneity effect of HSR on firm innovation based on the specific characteristics of cities and firms, focusing on the heterogeneity effect of city size, firms, and industries. This is conducive to further analysis of the heterogeneity effect of HSR on firm behavior in terms of innovation.

4.6.1. City Size

The core resources of firm innovation is highly skilled labor, and their cross-regional and cross-departmental mobility is conducive to knowledge transfer and knowledge spillover, thus promoting the dynamic development of innovation systems (Michael et al., 2011) [40]. At the present stage, there are significant differences in the stock of innovative talent in different cities. In large cities, the larger the stock of innovation talent, the more capital and technology are required for innovation. This makes a better foundation for innovation. On the contrary, small cities have a weaker foundation of innovation but are more eager for external innovation resources. There is often a big difference in structure between the knowledge spread and the new knowledge generated in the communication between cities of different size. Related studies also focus on the bidirectionality of resources mobility caused by the shortening of space–time and the transportation cost between cities as a result of HSR. On one hand, the opening of HSR improves the availability of innovation resources for small cities, which means that big cities have a “diffusion effect” on small cities along the line. On the other hand, HSR also accelerates the transfer of innovation resources from small cities to big cities, resulting in a “siphon effect”. Therefore, despite the frequent personnel communication and knowledge dissemination between cities after the opening of HSR, different cities may still have different impacts on the innovation output of firms due to the degree of aggregation of innovation resources.

This study first analyzes the innovation behavior of firms in relation to the opening of HSR lines between large cities and small cities to explore the difference in the diffusion and siphon effects of innovation resources. Large cities are defined as provincial capitals, sub-provincial cities, and municipalities. Other types of cities are defined as small cities. The results in

Table 11. Influence of HSR on firm innovation between different city size.

Variables	Applied Patent		Authorized Patent
	Small City	Large City	Small City	Large City
HSR	10.09 ***	0.852	7.142 ***	1.259
	(3.042)	(2.513)	(1.688)	(1.508)
Obs	8365	12,802	8365	12,802
Adjust R2	0.433	0.382	0.430	0.383

Note: *** p < 0.01. Standard errors are reported in the parentheses and clustered at the prefecture-city. Table 11 controls all control variables as shown in Table 2, and adopts both time and city fixed effects.

show that the opening of HSR has a significant promoting effect on firm innovation in small cities, while the promoting effect on firm innovation in big cities is not significant. This may be because the opening of HSR strengthens the diffusion of resources. The opening of HSR can widen firm diversified selection of human resource, thus promoting firm innovation. This is especially so when the marketization degree of the city is low or the original transportation conditions are poor; thus, the effect of HSR will be more important [41]. Broekel and Brachert (2015) [42] cite data from Germany to show that cities with low innovation capacity benefit the most from firm cooperation. In fact, after the opening of HSR, due to the substantial increase in congestion cost, firms will be driven by the benefits of reducing the cost of land rent, procurement, employment, and public services to accelerate the outward diffusion of innovation resources from central cities to peripheral cities. However, inter-city resources flow will also cause industrial reconstruction so that the original advantages of central cities will spread along the HSR line, thus promoting firm innovation. This is consistent with the conclusions regarding knowledge spillover in Table 4 and Table 5 of this study. Big cities have a spatial spillover effect in terms of spreading knowledge to surrounding cities, which has a marginal decreasing effect with the increase in distance. However, the dependence on innovation resources brought by HSR becomes less important in big cities. Big cities may be more dependent on the intra-city spillover effect, such as that produced by “star” firms in terms of innovation.

4.6.2. Difference in the Update Speed of Technology

Table 2 shows that HSR promotes the innovative output of local firms. Further indirect evidence in this study suggests that HSR increases local knowledge exchange by reducing the cost of communication between innovators. The reduced travel time that HSR brings may be more valuable in relation to fast-updating technology, which means that patenting activity is heterogeneous among sectors. In this context, direct acquisition of the source of new knowledge is particularly beneficial. Therefore, we expect HSR to have a greater effect on innovation in terms of the rapid turnover of technology. Agrawal et al. (2017) use the citation age profile of patents to measure the rate of technology obsolescence. These studies show that in all industries, old knowledge is eventually rendered obsolete by the emergence of newer knowledge. However, there are two industries in which technological turnover is much faster, namely the communications and computer industry and the electrical and electronics industry. This paper defines these industries as having “high velocity technologies” and contrasts them with the other “low velocity technologies” subsamples.

Table 12. Industry innovation effect of different technological updating speed.

Variables	Applied patent		Authorized patent
	LVT	HVT	LVT	HVT
HSR	21.93 ***	24.58 ***	14.37 ***	16.47 ***
	(1.783)	(4.726)	(1.243)	(3.454)
Obs	18,291	5556	18,291	5556
Adjust R2	0.178	0.323	0.183	0.328

Note: *** p < 0.01. Standard errors are reported in the parentheses and clustered at the prefecture-city. Table 12 controls all control variables as shown in Table 2, and adopts both time and city fixed effects.

shows that the influence of HSR is mainly concentrated in industries with high velocity technologies, the increasing number of firms’ applied patent and authorized patents is larger than industries with low velocity technologies. This shows that the opening of HSR has a bigger effect on industries with high velocity technologies. This conclusion is consistent with the research of Agrawal and Galasso (2017). Compared to low velocity technologies, high velocity technologies are more sensitive to time saving and efficiency improvements and are therefore more affected by the opening of HSR [26].

4.6.3. Firm Innovation Capability

Generally, the innovation activities of firm are inconsistent in terms of dependence on external innovation resources. The stronger the innovation ability of firms, the greater the need to communicate and exchange with the external market so as to integrate the innovative knowledge and transform it into innovation output. However, firms with weak innovation ability may not pay attention to innovation and are less affected by external innovation resources. To observe the difference in the contribution of HSR to the innovation of heterogeneous firms, the firms are divided into large and small innovative firms by the 50% quantile point in terms of patents. The results in

Table 13. Innovation effects of different firm sizes in patent.

Variables	Applied Patent		Authorized Patent
	Small Firm	Large Firm	Small Firm	Large Firm
HSR	0.394 ***	24.18 ***	0.920 ***	15.65 ***
	(0.041)	(3.627)	(0.125)	(3.111)
Obs	11,936	11,904	11,936	11,904
Adjust R2	0.394	0.316	0.235	0.311

Note: *** p < 0.01. Standard errors are reported in the parentheses and clustered at the prefecture-city. Table 13 controls all control variables as shown in Table 2, and adopts both time and city fixed effects.

show that the promoting innovation of HSR regarding in applied patent and authorized patents in large innovative firms is higher than small innovative firms. There is a large gap in the promoting effect of HSR on the different innovation capabilities of firms, which indicates that the output effect of HSR on promoting firm innovation does have a heterogeneity difference among firms. A possible explanation is that the demand of large innovation firms in terms of cross-city information and technology communication is stronger than that of small innovation firms. In addition, large innovation firms can better bear the cost of cross-city exchanges and cooperation, so the utilization efficiency of HSR is higher in large innovation firms than in small innovation firms. This makes the output effect of HSR on promoting firm innovation more obvious in the subsample of large innovation firms.

5. Mechanism Analysis

The role of HSR is similar to that of other means of transportation, but HSR provides faster, more comfortable and more punctual transportation. As Hanan and Bart (2009) [25] and Wang et al. (2018) [31] argue, the improvement of transportation brings a larger external market, promotes communication, and stimulates the diffusion and spillover of ideas, technologies, and knowledge, thus creating opportunities for innovation. HSR plays a similar role in facilitating innovation by accessing external markets, thereby creating new demand for existing products and new suppliers for cheap inputs and attracting external competitors. In addition, entrepreneurs may better realize the importance of innovation when their firms face fierce market competition. For firms in peripheral regions, access to external markets also means acquiring advanced ideas, technologies, and knowledge. This enables firms to carry out various innovation activities through cooperation or acquisition [30]. Therefore, this study holds that there are three channels for HSR connection to promote firm innovation—by optimizing resource allocation of firms; obtaining the spillover effect of the mobility and aggregation of innovation resources; and increasing the scale effect of the larger external market. To test these mechanisms, we adopted the following DID estimation methods based on hypothesis 2:

$$Channe{l}_{ict}={\alpha }^c+{\beta }_1^{c}HS{R}_{ut}+{\theta }_1^c{X}_{it}+{\theta }_2^c{X}_{ut}+{\delta }_t^c+{\mu }_u^c+{\epsilon }_{iut}^c$$

(28)

where $Channe{l}_{ict}$ are proxy variables of different channel variables.

5.1. Resource Allocation Effect

The space–time compression effect of HSR can accelerate the accessibility between cities by reducing transportation costs, optimizing the allocation of resources across cities, and reshaping the spatial structure of resources and economic distribution patterns [43]. In the era of knowledge economy, human resources are the main resource and the most active and positive factor in innovation activities. Undoubtedly, the aggregation of high-quality talent will directly affect the innovation output of firms. The opening of HSR is conducive to reducing the space–time distance between cities, thus reducing the cost of the mobility of high-skilled talent to cities along the HSR line. In particular, the “same-city effect” brought by HSR is conducive to the flexible employment of highly skilled talent in adjacent areas. Firms will be able to hire more high-skilled talent to carry out technology research, which in turn will increase their innovation output. In addition, the opening of HSR reduces the information asymmetry between investors and firms along the HSR line, so firms can get more investment, invest more in R&D, and pay more for labor. These aggregating effects further improve the innovation output of firm.

To accurately reflect the impact of the opening of HSR on the resource allocation efficiency of local firms, this study extracted the changes in R&D investment and in terms of talent based on the degree of education (junior college, bachelor’s degree, master’s degree, and PhD degree) of those employed by the listed firms during the sample period. This was done by manually retrieving the annual reports of listed firms over years. Due to the small number of employees with PhDs, this degree is merged with master’s degrees. This paper not only observed the changes in firm R&D investment but also divided R&D investment by total assets to observe the impact of HSR on firm R&D intensity. The estimation results in

Table 14. The impact of HSR on the employed of capital and talents in firm.

Variables	R&D	R&D Intensity	R&D Personnel	Junior	Undergraduate	Postgraduate
HSR	0.947 ***	1.602 ***	155.6 ***	327.8 ***	309.3 ***	45.62 ***
	(0.190)	(0.192)	(19.91)	(73.68)	(40.47)	(6.547)
Obs	16,864	16,864	19,444	19,444	19,444	19,444
Adjust R2	0.056	0.427	0.239	0.197	0.175	0.168

Note: *** p < 0.01. Standard errors are reported in the parentheses and clustered at the prefecture-city. Table 14 controls all control variables as shown in Table 2, and adopts both time and city fixed effects.

show that the opening of HSR significantly promotes R&D investment and the investing intensity of firms along the HSR line. Compared to firms in cities without HSR, the R&D investment of firms in cities with HSR has increased by 0.947 million yuan, and R&D intensity has increased by 1.602%. In addition, HSR has contributed to a significant increase in the number of employees with undergraduate and graduate degrees in firms in cities along the HSR line. This shows that the opening of HSR has promoted capital and highly educated talent to aggregate in cities along the HSR line, thus prompting more resources from firm allocated to innovation activities.

5.2. Knowledge Spillover Effect

The opening of HSR has accelerated the mobility of various resources of production between cities, including human resources, materials, and capital. HSR accelerates the dissemination of knowledge among firms in cities along the HSR line based on personnel mobility, thus creating a knowledge diffusion effect. The improvement of a region’s technological level depends not only on its own input of innovation resources but also on the aggregation effect of the inflow of innovation resources from other cities. As an important means of transporting passengers, HSR has greatly promoted the transfer of talent in a larger economic area. In particular, HSR has the advantages of fast speed, a high punctuality rate, and a lower weather effect compared with traditional means of transportation, thus better meeting the need for the mobility of high-quality talent in a time-sensitive way. The opening of HSR reduces the transportation and time costs in relation to benefitting from talent in the external market. The increased mobility of various innovation resources between cities improves the scale of those resources. All these changes generate the flow of knowledge, technology, and experience. This further promotes the dissemination and exchange of knowledge and technology in cities along the HSR line, thus forming communication and aggregation effects between innovation subjects and improving the innovation output of firms.

From the opening of HSR in 2008 to 2018, the Chinese Statistical Yearbook shows that the passenger volume of HSR increased from 7.34 million to 2.562 billion, meaning that the passenger capacity of HSR is gradually improving. The important carrier of knowledge dissemination is the mobility of innovation resources, which includes not only human capital but also material capital. This study uses the volume of passengers and freights transported by HSR at the prefecture city level to analyze the effect of mobility and aggregation, as the Urban Statistical Yearbook did not report this information. The estimated results in Columns (1) and (2) of

Table 15. The impact of HSR on mobility and aggregation of innovation elements.

Variables	Passengers	Freighting Volume	Teachers in College
HSR	1.259 *	1.687 ***	0.0451 **
	(622.2)	(522.6)	(0.0196)
Obs	2167	1466	2135
Adjust R2	0.720	0.866	0.986

Note: *** p < 0.01, ** p < 0.05, * p < 0.1. Standard errors are reported in the parentheses and clustered at the prefecture-city. Table 15 controls all control variables as shown in Table 2, and adopts both time and city fixed effects.

show that the opening of HSR has significantly increased the volume of passengers and freight, indicating HSR has promoted the increased mobility and aggregation of innovation resources to and in cities along the HSR line, thus benefiting local firms.

The innovation output of firms is not entirely dependent on their internal innovative activities. External innovative activities (such as those at universities and other scientific institutions) also have a positive impact on firm innovation (Laura and Helen, 2011) [44]. It is noted that universities are usually the main sources of innovation. Therefore, firm innovation may be increased through cooperation with universities, and HSR can further promote the mobility and aggregation of knowledge and technology to and at universities (Yi et al., 2021) [45]. Therefore, this study investigates the number of college teachers in cities along the HSR line. The estimated results in Column (3) of Table 15 show that the opening of HSR has increased the number of college teachers in cities along the HSR line. The continuous aggregation of college teachers is conducive to the further spillover of knowledge, thus benefiting firm innovation by getting more knowledge spillover effects.

5.3. Market Size Effect

The reduction of cross-city transportation costs and the improvement of market accessibility will stimulate firms to enter larger external markets, thus increasing the product market size of firms. According to a study on the productivity of firms [20,46], firms will invest more to improve productivity when they face an expansion of market. This is because a larger market can share the fixed input costs of innovation and improve the ability to earn profits after successful innovation. In addition, entering the external market also means acquiring the benefits of advanced knowledge and technologies. Therefore, we take the operating revenue, total profit, gross profit, and total assets of a firm to represent the changing size of assets and profits of firm. If the opening of HSR increases the external market size for a firm’s products, the size of the firm will increase to meet market demand [30].

Table 16. The impact of HSR on firm asset and profit.

Variables	Revenue	Total Profit	Gross	Total Capital
HSR	21.40 ***	3.621 ***	2.712 ***	169.9 ***
	(2.444)	(0.721)	(0.515)	(41.24)
Obs	23,421	23,881	23,881	23,881
Adjust R2	0.147	0.043	0.043	0.030

Note: *** p < 0.01. Standard errors are reported in the parentheses and clustered at the prefecture-city. Table 16 controls all control variables as shown in Table 2, and adopts both time and city fixed effects.

shows that the opening of HSR has increased firms’ operating revenue by 2.14 billion yuan (Chinese money), total profit by 362 million yuan, net profit by 271.2 million yuan, and total assets by 16.99 billion yuan, respectively. These results show that the opening of HSR promotes firm expansion, thus further promoting firm innovation through size effect, because larger firm size can decrease the marginal cost for innovation output, thus promoting firm innovation.

6. Conclusions and Policy Implications

Developing an “innovation-driven” strategy is urgent in China, and the key way to drive innovation development is to give full play to the knowledge spillover effect of firm innovation. HSR can reduce the space–time distance between cities and promote the mobility of resources between cities, which is greatly beneficial for the innovation of firms that need to exchange talent and integrate innovative ideas. We introduced HSR as a cost coefficient into the classical heterogeneous firm model and constructed a theoretical framework of the impact of HSR on firm innovation output. Taking China’s HSR construction as a natural experiment, this study used the time-varying DID method to identify the impact of HSR construction on firm innovation and its mechanism by matching firm data with HSR construction and relevant prefecture–city data. The results show that the construction of HSR has made a significant contribution in terms of the patents applied for by and authorized for firms, and the innovation effect of HSR has increased as the operating quality of HSR has improved. We found that firms located in peripheral cities, industries with rapidly developing technologies, and high innovators benefit more from HSR construction. In addition, the opening of HSR has a dynamic cumulative effect on time based on staggered DID estimation, with a marginally increasing trend in terms of firm innovation. The study found that the construction of HSR improves knowledge spillover within and between cities, and there is a marginally decreasing trend in terms of distance from central cities to peripheral cities. However, the study also found that in terms of the effect of HSR promoting firm innovation there is a heterogeneity sorting effect bounded by city size and that the impact of HSR on a firm’s highly educated talent and innovation output is significant only when the population size reaches a certain threshold. HSR mainly promotes the innovative development of firms by improving the effect of firm resource allocation, promoting the spillover effect of innovation due to resources flow and aggregation, and increasing the scale effect of market expansion.

As Agrawal et al. (2014) [32] have argued, the set of tools available to stimulate firm innovation is much broader than targeted R&D subsidies and tax. The study found that firms’ patent output increased significantly when cities opened HSR. Therefore, the role of providing transport infrastructure to facilitate knowledge mobility and spillover should also be included when designing innovation policies.

Further improving the construction of transportation to increase the frequency of face-to-face communication, thus promoting the flow of knowledge and research collaboration. Generally, each city should build a comprehensive and reasonable knowledge spillover mechanism, where the knowledge recipient should enhance the absorption capacity, so that the chain effect, imitation effect and communication effect of knowledge spillover can play a smoother role. In the context of the rapid development of high-speed lines for passenger, the knowledge spillover effect of HSR can be fully brought into play by optimizing the station layout of HSR network. It is need to consider the establishment of a “HSR city circle” centered on the nodes of HSR network, thus giving full play to the driving role of central cities in the innovation to non-central cities, effectively integrating the talent resources and innovation factors of different places, continually promoting the introduction of high-end talents and cross-regional technological cooperation, and promoting the collaborative innovation and linkage development of firm within the urban circle.

There are some limitations to our study. The lack of firm patent citations prevents us from studying the impact of HSR construction on the cross-regional link network of innovation quality analyzed based on patent citations. It is known that knowledge dissemination is gradually attenuated with increasing geographic distance and that reducing the space–time distance has a great impact on firm innovation via transportation infrastructure. In addition, our research results show that the expansion of product market size due to HSR construction is conducive to firm innovation. However, the theoretical model in this study does not focus on the mechanism of iceberg cost from the perspective of HSR vis-à-vis the change in market size for a firm. This may be because the focus of this study is on firm innovation; therefore, the relationship between HSR, market size, and firm innovation requires further research.