The Impact of Public Services on Urban Innovation—A Study Based on Differences and Mechanisms

Abstract

Urban public services can significantly promote the improvement and capacity of urban innovation, yet there are differences. Although some studies have analyzed the impact of public services on technological innovation, few studies have taken Chinese cities at the prefecture level and above as samples to build an urban public service evaluation index system and focus on analyzing the differences and impact mechanisms. Based on panel data of 277 cities at the prefecture level and above from 2005 to 2019, this paper empirically studies the differences and mechanisms of the impact of urban public services on urban innovation. The results show that urban public services can significantly promote the improvement of urban innovation ability. After endogenous treatment and robustness testing, the empirical results remain robust. There are differences in the impact of urban public services on urban innovation: the positive effect of basic public services on urban innovation is greater than that livelihood public services. The innovation effect of public services in small and large cities is significant, but not in medium-sized cities. The effect of urban public services in eastern and central regions on improving innovation capability is higher than that in the western and northeastern regions. In cities with different levels of administration, the technological innovation effect of public services in key cities is not significant, while in generalized cities, it is significant. The study also found that public services can positively affect urban innovation through the talent agglomeration effect, industrial structure effect, and income scale effect.

1. Introduction

1.1. Context

Adhering to the core position of innovation in the overall situation of China’s modernization is a clear requirement of the 14th Five-Year Plan and also outlines the long-term goals for 2035. Innovation has become an important driving force for China’s economy to shift from high-speed growth to high-quality development, with breakthrough key technologies to enter the forefront of all innovative countries. The 2021 Global Innovation Index released by the World Intellectual Property Organization (WIPO) shows that China’s innovation capacity ranks 12th in the world, up two places compared with 2020. It highly evaluated China’s progress in innovation and emphasized the importance of government decision-making and incentive measures for promoting innovation. Although the implementation of China’s innovation-driven development strategy has boosted the overall level of scientific and technological innovation, there is still an innovation dilemma of “considerable quantity and lame quality” [1]. In this context, it is of great theoretical and practical significance to explore additional factors that affect urban innovation.

Schumpeter’s innovation theory holds that innovation is the recombination of production factors. Therefore, in order to improve the innovation ability of a city, it is necessary to create conditions for gathering various and complementary innovation factors. This requires the government to create an environment through the implementation of public policies to generate enough attraction for physical factors, human resources, creativity, and entrepreneurship, and use them together. In the stage of high-quality development, the improvement of people-centered public goods supply can significantly improve people’s livelihoods. Urban public service capacity is an important embodiment of a city’s governance ability and development vitality. The level of urban public service supply will affect the attractiveness of the city to talents and the overall level of income and the speed of industrial upgrading, thus having an important impact on the ability of the city to innovate. China has entered a development stage of new urbanization, and although the quality of urban development is constantly improving and efforts are being made to upgrade the mode of public service supply, the current level of equalization of basic public services in urban and rural areas still needs to be improved, and problems such as regional disparities and unbalanced development still exist. In this context, can the level of urban public services promote the improvement of urban innovation ability? Are there differences in the impacts of different types of public services, different regions, and cities of different sizes on urban innovation? How does public service affect urban innovation? These questions not only help us to understand the functional relationship between public services and urban innovation, but also accurately help to depict the path of public services affecting urban innovation and answers may provide scientific empirical evidence for the improvement of urban innovation ability.

1.2. Purpose and Structure

In this context, the purpose and originality of this paper lie in, firstly, the effect test, which is a test to find whether the supply of urban public services can promote the improvement of urban innovation abilities. The second is difference analysis, which analyzes whether there are differences in the impacts of different types of public services in cities from different regions, of different sizes, and with different administrative levels and what effect these have on urban innovation. The third is the analysis of impact mechanisms, which analyzes how public services affect urban innovation. The fourth is to provide policy suggestions, that is, putting forward useful empirical evidence and suggestions for urban innovation from the perspective of public service supply.

The structure of this paper is as follows: in Section 2, we review the literature from three areas: public services, urban innovation, and the impact of public services on cities. At the same time, we analyze the impact mechanisms of public services on urban innovation from three perspectives—human resources, industrial structure, and income scale—and propose research hypotheses. In Section 3, we elaborate on the research design, construct the research model, analyze the selection and measurement of the variables, and explain the research methods. In Section 4, we conduct a comprehensive empirical test, obtain the results of benchmark regression analysis, and conduct endogenous analysis and robustness testing. In Section 5, we analyze the differences in four aspects: public service type, city size, urban area, and urban administrative level, and discuss the reasons for the differences. At the same time, the impact mechanism is discussed from three perspectives: human resources, industrial structure, and income scale. Finally, in the summary (Section 6), we summarize the results of the empirical analysis, conduct a comparative analysis with the existing literature, and offer policy recommendations according to the conclusions. The steps followed and methods used in this paper are shown in Figure 1.

2. Literature Review, Mechanism Analysis, and Research Hypothesis

2.1. Literature Review

2.1.1. Relevant Research on Public Services

The level of public services is an important manifestation of economic development and social progress. Promoting public service innovation requires the promotion of innovation-driven development and economic and social development [2]. The impact of public services on different fields of the economy and society, and the evaluation of the comprehensive development level, are the focus of academic circles. Existing studies have shown that public service expenditures on education, healthcare, infrastructure, science, and technology can not only promote economic growth [3] but also have a significant positive impact on population mobility and settlement [4] and industrial structure upgrading [5]. At the same time, the supply efficiency and quality of public services can affect income distribution, improve the income level, and narrow the income gap [6]. Public service is a comprehensive indicator; although much literature is concerned with the construction of its indicator systems and the measurement of its comprehensive level, a unified public service indicator system has not yet been formed. Current scholarship mainly focuses on education, culture, healthcare, infrastructure, and social security [7].

2.1.2. Relevant Research on Urban Innovation

Innovation-driven development has become a national strategy, and the research on urban innovation is very rich. Firstly, regarding the measurement of urban innovation capacity, the existing literature mainly includes four types of indicators: the urban innovation capability index from China’s urban and industrial innovation report of 2017, released by the first Institute of Finance and Economics of Fudan University [8]; patent application authorization [9,10]; the number of patent applications [11]; and the number of patent authorizations [12]. Secondly, regarding influencing factors on urban innovation, existing studies have found that many factors can affect urban innovation, such as education investment and higher education [13], urban infrastructure [14], and the rationalization of industrial structures [15]. Transportation infrastructure can promote knowledge spillover and improve the innovation level [16,17]. In addition, the authors of [18] determined that cultural development has a positive impact on technological innovation. Researchers also found that income level is an important factor affecting technological innovation [19,20].

2.1.3. Research on the Impact of Public Services on Innovation

Although both public services and urban innovation are current research hotspots, it is rare to put them within the same framework. As for the research objectives, the authors of [21] studied the innovation performance of small and medium-sized enterprises and determined that public services can help these enterprises obtain various resources and promote the improvement of innovation performance. Reference [22] examined innovation elements and determined that public services had a significant impact on the spatial structure of regional innovation elements. As for the selection of core variables, the authors of [23] studied the impact of eight categories of public goods on innovation ability by taking provincial data as samples and the supply expenditure levels of eight categories of public goods, such as education, healthcare, and social security, as explanatory variables. Researchers [24] used education as a substitute variable for public services and found that public services significantly promoted the growth of innovation by affecting the redistribution of human resources. In terms of research content, the authors of [25] took the supply efficiency of public services as an intermediary variable that affects urban innovation because, in terms of research content, there was no literature that analyzed the differences and mechanisms of public services affecting urban innovation. In terms of impact mechanism, researchers [26] found that public services can affect urban innovation through smart city construction and believed that public services can affect urban innovation through human capital development [27].

In summary, we found that public services have a wide range of impacts, and urban innovation is also affected by many factors. However, there is scarce literature on the impact of public services on urban innovation, with much room for further research on the research objective, variable selection, and content. For this reason, in view of the lack of existing research, this paper took public services as the explanatory variable and urban innovation ability as the explanatory variable and conducted a new analysis of the following three aspects. The first was to build an index system for urban public services, comprehensively investigating the level of urban public services and testing its impact on urban innovation. The second was to analyze the impact and differences in public services on urban technological innovation based on: the types of public services, city size, urban area, and urban administrative levels. Here, “difference” refers to the difference between types of public services, cities of different sizes, cities in different regions, and between different administrative levels. Thirdly, the intermediary effect model was used to identify and measure the mechanism by which public services affect urban innovation through human resources, industrial structure, and income scale. This mechanism refers to the way in which public services affect urban technological innovation.

2.2. Mechanism Analysis and Research Hypothesis

The existing literature fully establishes that there is a direct relationship between public services and urban innovation. Most of the literature has affirmed the positive role of the “public service level” in promoting urban innovation ability. By combing and summarizing the existing literature, we found that urban public services may promote urban innovation by gathering human resources, optimizing industrial structures, and improving income levels, or that urban public services can act on urban innovation through the human resources effect, industrial structure effect, and income level effect.

Urban public services promote the improvement of urban innovation abilities by gathering human resources. Human resources are the first resource for technological progress and an important support for innovation-driven development and high-quality development, with public services being an important factor for attracting human resources. Public service exerts the agglomeration effect of human resources from two aspects: on the one hand, public services can enhance the accumulation of human capital. There are two ways to gather human capital: one is the investment of human capital formed by the increase in the urban population; the second is human capital gathered from underdeveloped areas to developed areas. Public services can improve the educational, professional, and technical levels, travel convenience, good living environments for residents, and improve their quality of life and well-being and have an impact on the formation and flow of human capital. On the other hand, public services can promote the orderly flow and aggregation of labor. In the theoretical, neoclassical economic growth model, the law of diminishing marginal returns of capital is the key to the convergence mechanism of regional economic growth. Similarly, labor will flow from regions with low marginal output to regions with high marginal output. Public services can improve the living environment of migrant workers, increase income, reduce the tangible and intangible costs of mobility, and accelerate the social integration of migrant workers. The level of public service in the inflow area has become an important factor in the choice of labor mobility.

Urban public services affect the improvement of urban innovation ability by optimizing the industrial structure. The optimization of industrial structure is essentially a process of continuous technological progress or innovation. In the evolutionary path of industrial structure, the change in industrial structure in a region is closely related to the policy guidance, division of labor, consumption demand, and human capital of the region, and public services will have an impact on these factors. Firstly, public service policies guide the evolution of industrial structure. Public services include education, medical treatment, infrastructure, environmental protection, and other aspects. The increase in supply and the change in structure reflects the direction of economic development guided by the government to a certain extent, which will inevitably lead to the adjustment of industrial structure and changes in technological innovation. Secondly, public services promote the deepening of the industrial division of labor. The division of labor is limited by the market scope, which depends on the population size and geographical scope. The improvement of public infrastructure, such as the transportation and information network, has shortened the space, time, and distance between cities and enterprises and expanded the market scope. The expansion of the market, the refinement of departments, and the deepening of the division of labor have promoted the evolution of industrial structures from low value added to high value added. Thirdly, public services expand consumer demand. Changes in the total consumption demand and consumption structure will lead to changes in the industrial structure. The government’s investment in public services has indirectly increased the disposable income of residents and has not only expanded consumption demand but has promoted the diversification and upgrading of residents’ consumption structure, thus promoting product upgrading, industrial upgrading, and technological progress. Fourthly, public services accumulate human capital to promote the upgrading of industrial structures. Public services help to improve the quality of labor and promote the upgrading of industrial structures. The improvement of the overall quality of the labor force and the optimization of the endowment structure can promote the evolution of the industrial structure from labor-intensive industries to capital-intensive and knowledge-intensive industries.

Urban public services promote urban innovation through the income scale effect. Public service is an effective driving force for economic development. On the one hand, public service expenditure and government expenditure on the development of science and technology mainly comes from taxes. Economic development drives the increase in government taxes. The government will have more funds to invest in public services and science and technology development projects. On the other hand, with the development of the urban economy, the overall income and profits of enterprises will be increased, which can provide more support for them to carry out product technology innovation and product upgrading. At the same time, the improvement of public services can reduce the operating costs of enterprises and improve production efficiency. It will also have an income scale growth effect on the technological progress of the enterprises. Thirdly, with the development of the urban economy and enterprise, personal income is bound to increase. The increase in income will lead to consumption upgrading and industrial upgrading, leading consumer goods manufacturers to pursue product innovation and technological innovation, adapt to market requirements, meet consumer demand, and achieve enterprise development.

The above theoretical analysis demonstrates that urban public services can promote urban innovation through mechanisms such as gathering human capital, optimizing industrial structures, and improving income levels. The above three mechanisms suggest that the continuous improvement of the urban public service level is likely to be an important force in promoting the improvement of urban innovation capability. At the same time, there may be differences in innovation capacity among different public service types, regions, sizes, and administrative levels of cities. In order to verify the above analysis, three hypotheses are proposed here:

Hypothesis 1 (H1).

Public services can improve urban innovation ability.

Hypothesis 2 (H2).

The impact of public services on urban innovation differs; that is, there are differences in four aspects: public service type, urban area, urban scale, and urban administrative level.

Hypothesis 3 (H3).

The promoting effect of public services on the improvement of urban innovation capability can be realized through the ways and mechanisms of gathering human resources, optimizing industrial structures, and improving income levels.

3. Models and Methods

3.1. Model Setting

Using the method presented by [28], this paper constructed the following regression model to analyze the impact of public service level on urban innovation capacity:

$$P{A}_{it}={\lambda }_1+{\lambda }_{1}P{S}_{it}+{\lambda }_{2}FD{I}_{it}+{\lambda }_{3}F{D}_{it}+{\lambda }_{4}ST{E}_{it}+{\lambda }_{5}PO{P}_{it}+{\epsilon }_{it}$$

(1)

where i refers to 277 city section units at the prefecture level and above and t refers to the year. The dependent variable PA represents the urban innovation capability, and PS is the core explanatory variable of public service level. FDI, FD, STE, and POP refer to foreign direct investment, financial development, science and technology investment, and population size, respectively. λ is the parameter to be estimated, and ε is a random disturbance term.

3.2. Variable Selection

The sample for this paper was the panel data of 277 cities at the prefecture level and above from 2005 to 2019. Relevant original data were mainly from the China Urban Statistical Yearbook, China Urban Construction Statistical Yearbook, and various urban statistical yearbooks over the years, and patent data were taken from the China research data service platform (CNDRS). All monetary value data were calculated at constant prices in 2005. Index data, such as the patent authorization number, were entered into the model after taking the logarithm. The missing data in some cities were supplemented by the median method. All variables were data from municipal districts, and the specific measures were as follows.

3.2.1. Explained Variable

The explained variable is urban innovation capability (PA). Innovation capability can be measured by innovation input and innovation output. The former includes R&D capital investment and R&D personnel investment, while the latter mainly refers to the number of patent applications, authorizations, or citations. Since the R&D expenditure data of cities at the prefecture level and above could not be obtained, this paper used city patent authorization to measure its innovation capacity. The number of urban authorized patents reflects the output benefit of input resources and can better reflect technological innovation ability [29]. According to the detailed rules for the implementation of the patent law of the People’s Republic of China, patents are divided into three categories: invention patents, utility model patents, and design patents. The invention patent is a new technical scheme for products and methods with the highest technical content, reflecting the core competitiveness of innovation. The utility model patent is a new technical scheme for product shape and structure, which is suitable for use. The technical content is lower than that of an invention patent, and it is called a “small patent”. The design patent focuses on the design appearance of the product, does not change the technical performance of the product itself, and has the lowest technical content. Therefore, in order to investigate the impact of public service level on different types of patents, this paper used the natural logarithm of invention patents to measure the innovation of invention patents (PA₁) in cities and used the natural logarithm of the sum of utility model patents and design patents to measure the non-invention patent innovation (PA₂) in cities.

3.2.2. Core Explanatory Variables

The core explanatory variable is public service (PS). Domestic and foreign literature has defined the contents of public services as mainly involving education, healthcare, culture, transportation, and environment. This paper used the research of [30] for reference and selected indicators from five aspects: basic education, healthcare, transportation facilities, public culture, and public environment, to build an urban public service indicator system. We used the entropy weight method to calculate the weight of each indicator (as shown in

Table 1. Index system of urban public service supply level.

Public Service Category	Specific Indicators	Computing Method	Indicator Attribute	Weight
Elementary education	Per capita education expenditure (Yuan/person)	Fiscal expenditure on education/total population	+	0.0961
	Primary education teacher–student ratio (person/person)	Number of primary school teachers/number of students in school	+	0.0703
	Teacher–student ratio of general secondary education (person/person)	Number of teachers/students in ordinary middle schools	+	0.0336
Medical and health work	Number of medical institutions per 10,000 people (per 10,000 people)	Number of medical institutions/total population	+	0.1987
	Number of beds per 10,000 people (piece/10,000 people)	Number of beds/total population	+	0.0601
	Number of doctors per 10,000 people (person/10,000 people)	Number of doctors/total population	+	0.0732
Transportation facilities	Per capita road area (m2/person)	Road area/total population	+	0.0671
	Road network density (km/km2)	Road mileage/urban area	+	0.0841
Public culture	Library collection per 10,000 people (volume/10,000 people)	Library collection/total population	+	0.2238
Public environment	Sewage treatment rate (%)	Sewage treatment capacity/total sewage discharge	+	0.0234
	Per capita public green space area (m2/person)	Green area/total population	+	0.0567
	Greening coverage rate of built-up area (%)	Green planting area/urban area	+	0.0129

Note: + indicates that the indicator is positive.

) and finally obtain the public service level of each city.

3.2.3. Control Variables

Control variables include foreign direct investment (FDI), financial development level (FD), science and technology investment (STE), and population size (POP). Foreign direct investment is expressed as the amount of foreign capital actually used in the current year. The financial development level is measured by the proportion of the balance of various loans from financial institutions in the GDP at the end of the year. Science and technology input is measured by the science and technology expenditure in the local general public budget expenditure every year. The population size is measured by the total population at the end of the year. In order to obtain stable data, data such as patents, foreign direct investment, science and technology expenditure, and population size were processed by logarithm. In summary, the descriptive statistical results of the main variables are shown in

Table 2. Statistical description of main variables and the VIF.

Variable	Variable Name	Mean Value	Unit of Measurement	Standard Deviation	Minimum Value	Maximum Value	Sample Size	VIF
PA	Innovation ability	6.5143	Item	1.8124	0	12.0204	4155
PS	Public service level	0.1920	Index	0.0644	0.0551	0.7411	4155	1.12
FDI	Foreign direct investment	9.4999	Dollar	4.0618	0	16.5403	4155	1.39
FD	Financial development level	1.2052	%	0.6754	0.0428	8.8943	4155	1.13
STE	Scientific and technological input	0.2193	%	0.2893	0.0003	6.0629	4155	1.10
POP	Population size	4.6090	Ten thousand people	0.7705	2.6824	7.8156	4155	1.36

. In addition, to avoid the multicollinearity problem of explanatory variables, the expansion factor (VIF) of explanatory variables was calculated before regression analysis. The results indicated that the VIF was not higher than 2 (as shown in Table 2), indicating that there was no multicollinearity problem.

3.3. Method

This paper used a variety of research methods for the research process. Firstly, the entropy weight method is used to measure the level of urban public services. The entropy weight method is an objective weighting method that can avoid the deviation caused by human factors. In the specific use process, according to the dispersion of the data of each index, the entropy weight of each index was calculated using information entropy, and the entropy weight was then modified according to each index to obtain a more objective index weight. The entropy weight method has high adaptability and is widely used in existing research.

Secondly, in the empirical analysis, the fixed effect model is used, and the instrumental variable method is used to analyze the endogenous problem. The fixed effect model is a panel data analysis method. It refers to the experimental design in which the experimental results only compare the differences between specific categories or categories of each self-variable and the interaction effects with specific categories or categories of other self-variables and does not infer that the same self-variable has not been included in other categories. Fixed effect models can be divided into three categories: individual fixed effect models, time-fixed effect models, and time-individual-fixed effect models. This paper adopted the time-individual-fixed effect model. In social sciences research, endogenous problems have puzzled researchers. The instrumental variable method is a common method of solving endogenous problems. If a variable is highly correlated with the random explanatory variable in the model, but not with the random error term, then a consistent estimator can be obtained by using this variable and the corresponding regression coefficient in the model. This variable is called the instrumental variable, and this estimation method is called the instrumental variable method.

Finally, in the mechanism analysis, the intermediary effect method and Sobel and Bootstrap test were used. The mediation effect was first applied to chemical research by C. K. Ingold, who proposed it in the 1920s to explain the chemical behavior of some molecules that could not be satisfactorily described by classical structural formulas. He believed that electron transfer was occurring in molecules with an unsaturated system under normal conditions, and the effect produced by this electron transfer is called the intermediary effect. At present, intermediary effect analysis is widely used in social science research. This paper used the coefficient product method to test the intermediary effect. The coefficient product method is divided into two categories: the Sobel test method, based on the normal distribution of the sampling distribution based on the intermediary effect, and the bootstrap sampling method, based on the non-normal distribution of the sampling distribution based on the intermediary effect.

4. Empirical Results

4.1. Benchmark Regression Results

Columns (1)–(3) in

Table 3. Benchmark regression results and instrumental variable regression results.

Variable	Benchmark Regression (FE)			Instrumental Variable Regression (2SLS)
	(1) Total Patent Output (PA)	(2) Invention Patent (PA1)	(3) Non-Invention Patent (PA2)	(4) Total Patent Output (PA)	(5) Invention Patent (PA1)	(6) Non-Invention Patent (PA2)
PS	0.6828 *** (0.2250)	0.7945 *** (0.2610)	0.7099 *** (0.2367)	8.3868 *** (1.8406)	2.2789 (2.1626)	9.5456 *** (1.9214)
FDI	0.0177 *** (0.0030)	0.0253 *** (0.0037)	0.0168 *** (0.0031)	0.1070 *** (0.0073)	0.1169 *** (0.0086)	0.1046 *** (0.0075)
FD	−0.0403 ** (0.0177)	−0.0635 *** (0.0234)	−0.0423 ** (0.0188)	0.1675 *** (0.0451)	0.4813 *** (0.0498)	0.1141 ** (0.0473)
STE	0.2206 *** (0.0600)	0.4392 *** (0.0969)	0.1946 *** (0.0576)	0.6245 *** (0.1346)	0.9322 *** (0.1826)	0.5638 *** (0.1294)
POP	0.1501 *** (0401)	0.2033 *** (0.0495)	0.1408 *** (0.0418)	1.0000 *** (0.0235)	1.1933 *** (0.0258)	0.9747 *** (0.0247)
constant	5.1895 *** (0.2596)	2.9076 *** (0.3206)	5.0867 *** (0.2712)	−2.6808 *** (0.3779)	−5.0599 *** (0.4491)	−2.8604 *** (0.3920)
sample size	4155	4155	4155	4155	4155	4155
R2	0.9590	0.9440	0.9537	0.7687	0.7821	0.7446

Note: ***, ** are significant at the levels of 1%, 5%, respectively.

report the regression results of the public service level on the total output of urban innovation capacity, invention innovation, and non-invention innovation. The Hausman test was significant at the 1% level, indicating that the fixed effect model was more desirable and controlled the time and individual effects; this method was used in subsequent analyses. The results indicated that the PS coefficient was significantly positive in the three regressions, indicating that the public service index constructed in this paper was significantly and positively correlated with urban innovation output. In the economic sense, taking column (1) as an example, the level of public services increased by 10% and the total output of innovation increased by 6.828%. The possible reasons are that, on the one hand, the improvement of public services can optimize the production and operation environment of enterprises, improving their production efficiency and offering them more energy and resources to invest in production technology and process upgrading to enhance their innovation ability. On the other hand, public services such as education, healthcare, culture, and environment can improve people’s living standards, giving better play to the talent and knowledge agglomeration effect and improving the level of innovation.

The relationship between the control variables in the regression results and urban innovation ability also basically reached the theoretical expectations. The coefficient of foreign direct investment (FDI) was positive and significant at the level of 1%, indicating that FDI can promote urban innovation. This result was similar to the conclusion of [31]. The coefficients of science and technology investment (STE) and population size (POP) were significantly positive at the level of 1%, indicating that capital investment and human resource accumulation are conducive to improving innovation ability. The coefficient of financial development (FD) was significantly negative, which to some extent reflected the shortcomings of China’s financial development. On the one hand, in the development structure, the banking industry still dominates the financing channels, and the proportion of direct financing is low. On the other hand, as the credit system and risk prevention and control systems are in the process of continuous improvement, bank credit funds tend to invest in large-scale, powerful, and low-risk state-owned enterprises and large-scale private enterprises, while small and medium-sized enterprises with innovation potential tend to set a high threshold and find it difficult to obtain financial support.

4.2. Endogenous Analysis

The public service level is a comprehensive indicator affected by many factors. There may be endogenous problems from two-way causality. On the one hand, urban economic development, public service supply, population expansion, and other factors will affect urban innovation through scale, technology, and other effects; on the other hand, urban innovation will also negatively affect the scale and type of government public service supply, as well as the technical level and service quality. To solve this problem, this paper used the tool variable (2SLS-IV) method to select tool variables based on the geographical environment for endogenous processing. Existing research has shown that physical and geographical conditions have an important impact on the construction of transportation, environment, and other infrastructure [32], in which slope is one of the important factors. With the increase in slope, the difficulty and cost of building public facilities will increase, and the possibility of providing such public services will decrease. In addition, urban innovation ability is directly related to economic and educational activities but not to geographical factors. Therefore, selecting slope as a tool variable can better control endogenous problems. Based on the practice of the authors from [33], the urban slope index (SLOPE) was constructed as a tool variable of public service level.

In order to test the potential endogenous problems, this paper conducted the Davidson MacKinnon test and Hausman test on public services and urban innovation, and the results were significant at the level of 1%, indicating that there may be endogenous problems in the supply of public services. In order to control these problems, this paper used the urban slope index as a tool variable and the 2SLS method for estimation. Columns (4) and (5) in Table 3 display the estimation results after controlling the endogenous problems. The LM test and weak identification test results indicated that there were no insufficient identification and weak identification problems in the tool variables, meaning that the tool variables selected in this paper were reasonable and effective. After controlling the endogeneity of the core variables within the instrumental variables, the direction and significance of the core indicators did not change significantly, and there was still a significant positive relationship between public service level and urban innovation capability, indicating that the model results are robust. It is worth noting that the absolute value of the public service coefficient in column (4) was significantly higher than that in column (1), indicating that the innovation effect of public services may be underestimated without considering the endogenous problem. The above analysis supports Hypothesis 1. This conclusion provides a factual basis for local governments to improve the public service system and the new concept and mechanism of “promoting development with public services”; that is, improving public services will help to improve the innovation ability of cities and promote high-quality development.

4.3. Robustness Test

In order to verify the robustness of the above results, this paper conducted robustness testing through the following methods: (1) changing the core explanatory variables. Based on the evaluation index system of the urban public service level, the principal component analysis method was used to extract the first primer as an alternative variable of the urban public service level. (2) Adjusting the sample. In order to exclude the impact of potential extreme values on the model’s results, this paper adopted two methods to adjust the samples: one to estimate the samples after a 5% tailing treatment and the other to exclude the impact of potential extreme values; that is, to estimate after excluding the sample data of four municipalities directly under the central government, including Beijing, Shanghai, Tianjin, and Chongqing. (3) Override tool variables. Regression (2SLS) was carried out on the whole sample by using the public service lag term as a tool variable.

Table 4. Robustness test results.

Variable	Change Core Variables	Adjust Sample		Override Tool Variables
	(1) FE	(2) FE	(3) FE	(4) 2SLS
PS	0.0307 *** (0.0111)	0.6646 ** (0.2473)	0.6598 *** (0.2264)	1.6938 *** (0.4512)
FDI	0.0177 *** (0.0030)	0.0142 *** (0.0026)	0.0177 *** (0.0030)	0.0168 *** (0.0027)
FD	−0.0375 (0.0176)	−0.0125 (0.0246)	−0.0432 ** (0.0177)	−0.0410 ** (0.0180)
STE	0.2138 *** (0.0595)	0.6887 *** (0.0662)	0.2264 *** (0.0620)	0.1915 *** (0.0282)
POP	0.1580 *** (0.0416)	0.2467 *** (0.0428)	0.1450 *** (0.0402)	0.1883 *** (0.0436)
constant	5.3471 *** (0.0700)	4.7844 *** (0.2813)	5.2234 *** (0.2605)	3.7804 *** (0.2474)
sample size	4155	4155	4095	3878
R2	0.9589	0.9516	0.9565	0.8611

Note: ***, ** are significant at the levels of 1%, 5%, respectively.

reports the robustness test results of the fixed effect panel model. Column (1) shows the public service index calculated by the principal component analysis method; columns (2) and (3) are the estimated results of the 5% tailing treatment and the elimination of samples from municipalities directly under the central government respectively. Column (4) shows the 2SLS regression results with the lag phase I public service level as the instrumental variable. The robustness test results indicated that the coefficients of public services passed the 5% significance level test, indicating that the level of urban public services has a significant positive impact on the improvement of urban innovation ability, which was basically consistent with the estimated results in Table 3, again indicating that the basic regression results had strong robustness.

5. Discussion

5.1. Difference Discussion

5.1.1. Discussion Based on the Differences of Public Service Types

In order to investigate the differences in the impacts of different types of public services on urban innovation, this paper referred to the practices of [34], classifying basic education, healthcare, and public culture as people’s livelihood public services, and infrastructure and public environment as basic public services, measuring the levels of the two types of public services through the entropy weight method and estimating the model using Formula (1). The specific results are shown in columns (1) and (2) of

Table 5. Test results of different types of public services and different city sizes.

Variable	(1)	(2)	(3)	(4)	(5)
	Benchmark Public Services	Public Services for People’s Livelihood	Small Cities	Medium- Sized Cities	Large Cities
PS	0.8150 *** (0.1249)	0.2843 (0.1876)	0.7912 ** (0.4161)	0.4615 (0.4560)	0.5797 ** (0.2941)
FDI	0.0177 *** (0.0029)	0.0177 *** (0.0030)	0.0215 *** (0.0074)	0.0122 ** (0.0050)	0.0228 *** (0.0039)
FD	−0.0386 ** (0.0177)	−0.0392 ** (0.0177)	−0.0679 (0.0607)	−0.0914 *** (0.0338)	0.0053 (0.0228)
STE	0.2313 *** (0.0611)	0.2201 *** (0.0630)	−0.0712 (0.0460)	0.3872 ** (0.1821)	0.2606 *** (0.0427)
POP	0.1355 *** (0.0381)	0.1335 *** (0.0402)	−0.0267 (0.1302)	0.1342 (0.0607)	0.2178 *** (0.0608)
constant	5.1491 *** (0.2379)	−12.1865 *** (0.2481)	3.6320 *** (0.5264)	4.5685 *** (0.0862)	4.6460 *** (0.3790)
sample size	4155	4155	615	1575	1965
R2	0.9594	0.9589	0.9041	0.9265	0.9704

Note: ***, ** are significant at the levels of 1%, 5%, respectively.

. The estimation results indicated that the basic public service coefficient was significantly positive at the level of 1%, while the people’s livelihood public services coefficient failed to pass the significance test. The results proved that basic public services can significantly promote the improvement of urban innovation ability, yet the role of peoples’ livelihood public services was not obvious. The reasons for this difference may include two aspects: first, basic public services can have a more direct impact on economic activities. For example, improving transportation infrastructure can directly reduce transportation costs, improve regional accessibility, lead to factor agglomeration, and enhance regional competitiveness, improving overall production capacity and efficiency and technical level and innovation ability. However, public services as peoples’ livelihoods, such as education, healthcare, and culture, mainly affect urban economic activities through the accumulation effect of human capital. This process involves many links, such as talent training and absorption, which take a relatively long time. Its effect may not be significant, especially when it is below a certain threshold, which was consistent with the research results of [23]. Second, compared with basic public services, the supply of livelihood public services is relatively insufficient, and there are threshold requirements such as registered residence, which make it difficult to play a role in the accumulation of high-quality human capital. At present, the shortage and imbalance of education and medical resources in China are still prominent. The coverage and radiation of high-quality education and medical resources are relatively limited, and there is a large gap between supply and demand. From the measurement of the sample, the livelihood public service index of each city in the sample period was 0.15, which was significantly lower than the basic public service index (0.32), also confirming this inference.

5.1.2. Discussion Based on the Difference of City Size

In order to test the heterogeneous impact of the public service level of cities of different sizes on the innovation ability, this paper averaged the total population of each city at the end of the sample period, defined the “city size” according to the notice on adjusting the classification of standard city size, issued by the State Council. We considered the rationality of using the data of municipal districts and samples, classified under “megacity” and “mega city” into large cities. Therefore, the overall sample is divided into small cities, medium-sized cities and large cities, and estimated respectively. The estimated results are reported in columns (3)–(5) of Table 5. The results indicated that the relationship between the public service level and urban innovation ability in medium-sized cities was positive but not significant. The public service coefficient of both small and large cities was significantly positive at the level of 5%. The possible reasons for this difference are that large cities have a strong factor flow, a stronger ability to absorb capital, more talent and other factors, better resource allocation, higher innovation awareness and efficiency, and they are more conducive to the accumulation of public service factors, knowledge spillovers, and other effects; the authors of [24] reached similar conclusions. Although the population size of small cities is small and the level of industrial agglomeration is not high, the effect of public services becomes more prominent when other factors have no obvious impact on the innovation ability of the region. While medium-sized cities have advantages over small cities in undertaking industrial transfer and human capital agglomeration, they are not as strong as large cities in terms of factor flow and capital supply, so their public service factors fail to play a role in urban innovation.

5.1.3. Discussion Based on Urban Regional Differences

Considering that economic and natural conditions, such as public service supply, income level, and technological innovation, showed certain regional differences, this paper divided the sample region into four regions—the east, the middle, the west and the northeast—and discussed the regional differences on the impact of the public service level on urban innovation ability. The estimated results are reported in columns (1)–(4) of

Table 6. Test results for cities in different regions and cities at different levels.

Variable	(1)	(2)	(3)	(4)	(5)	(6)
	Eastern Region	Central Region	Western Region	Northeast China	Key Cities	Non-Key Cities
PS	0.8182 ** (0.3760)	0.8350 ** (0.3795)	0.4980 (0.3515)	−1.4815 *** (0.5216)	0.0402 (0.2624)	0.7271 *** (0.2539)
FDI	0.0177 *** (0.0056)	0.0044 (0.0051)	0.0149 *** (0.0040)	−0.0087 (0.0053)	0.0126 ** (0.0054)	0.0181 *** (0.0034)
FD	0.0032 (0.0303)	0.0595 (0.0370)	0.0202 (0.0301)	0.0432 (0.0336)	−0.0086 (0.0270)	−0.0424 * (0.0219)
STE	0.2672 *** (0.0551)	0.5281 *** (0.0763)	−0.0058 (0.0512)	0.0558 (0.1201)	0.2059 *** (0.0692)	0.2352 *** (0.0694)
POP	0.1566 *** (0.0538)	0.2843 *** (0.0774)	−0.0111 (0.0722)	−0.2605 ** (0.1285)	−0.1107 (0.0884)	0.1699 *** (0.0420)
constant	4.9836 *** (0.3632)	4.4357 *** (0.2668)	4.8643 *** (0.3787)	9.7393 *** (0.8825)	8.9123 *** (0.6055)	4.4357 *** (0.2668)
sample size	1245	1200	1215	495	495	3660
R2	0.9676	0.9490	0.9519	0.9576	0.9798	0.9469

Note: ***, ** and * are significant at the levels of 1%, 5% and 10%, respectively.

. The results indicated that the estimated coefficient of public services in the eastern and central regions was significant at the level of 5%, which means that the level of public services in these two regions can enhance the innovation ability of cities in the region. The estimated coefficient in the western region was not significant, while that in the northeast region was significantly negative. The possible reasons are that the industrial structure and agglomeration level of the western region need to be improved, with the population size of some cities being relatively small and the supply efficiency of public services is low, which will objectively weaken the effect of improving the innovation ability of the public services. The old industrial cities in northeast China, as a whole, are facing severe challenges of industrial structure transformation and upgrading. There are great pressures on economic development, public service supply, and technological innovation, resulting in the failure of public services to play a positive role in urban innovation.

5.1.4. Discussion Based on the Differences of Urban Administrative Levels

In order to verify the differences in the impact of the public service level of cities at different administrative levels on urban innovation ability, this paper referred to municipalities directly under the central government, sub-provincial cities, and provincial capital cities as key cities. Prefecture-level cities, other than municipalities directly under the central government, sub-provincial cities, and provincial capital cities, are called general cities. The sample data were divided into key city samples, and general city samples, and Formula (1) was estimated from this, respectively. The regression results are reported in columns (5) and (6) of Table 6. The results showed that the effect of the public service level of key cities on urban innovation capability was not significant, while the estimation coefficient of non-key cities was significantly positive at the 1% level. The reason may be that key cities are often the centers and pioneers of national or regional economic and social development. Compared with ordinary cities, they may have better development advantages. There are more policies and resources to support their development. There will be more factors that will affect the role of the public service level on innovation ability, which is not conducive to the innovation effect of public services. The above analysis supports Hypothesis 2.

5.2. Discussion on Impact Mechanism

In order to test the action mechanism of urban public services on urban innovation, this paper used the [35] intermediary effect model for reference and constructed the intermediary effect model as shown in Formulas (2)–(4):

$$P{A}_{it}={\alpha }_0+{\alpha }_{1}P{S}_{it}+{\alpha }_2{X}_{it}+{\upsilon }_{it}$$

(2)

$$M_{it}={\beta }_0+{\beta }_{1}P{S}_{it}+{\beta }_2{X}_{it}+{\epsilon }_{it}$$

(3)

$$P{A}_{it}={\varphi }_0+{\varphi }_{1}P{S}_{it}+{\varphi }_2{M}_{it}+{\varphi }_3{X}_{it}+{\nu }_{it}$$

(4)

where M represents the intermediary variable; X is a group of control variables; υ, ν, and ε are error terms; and other variable symbols are the same as in Formula (1). This paper analyzed them from three aspects: talent resource effect, industrial structure effect, and income scale effect. Other variables are defined in Formula (1). Talent resource effect is measured by the proportion of the non-agricultural employment population in the total urban population. Industrial structure effect is reflected by the proportion of the added value of secondary industry in the GDP and income scale effect is measured by per capita GDP.

Regression was conducted for the mediating effect model using Formulas (2)–(4), and the significance of the mediating variable action mechanism was tested based on the bootstrap method. In column (1) of

Table 7. Intermediary effect test.

Variable	(1)	(2)	(3)	(4)	(5)	(6)	(7)
	PA	talent	PA	indu	PA	pgdp	PA
PS	0.6828 *** (0.1920)	0.0834 *** (0.0184)	0.5912 *** (0.1915)	0.0888 *** (0.0293)	0.6116 *** (0.1909)	0.2070 * (0.1073)	0.3621 *** (0.0282)
FDI	0.0177 *** (0.0027)	−0.0001 (0.0003)	0.0178 *** (0.0027)	0.0020 *** (0.0004)	0.0160 *** (0.0027)	0.0098 *** (0.0015)	0.0141 *** (0.0026)
FD	−0.0403 ** (0.0177)	−0.0041 ** (0.0017)	−0.0358 ** (0.0177)	−0.0303 *** (0.0027)	−0.0160 (0.0179)	−0.1453 *** (0.0099)	0.0124 (0.0179)
STE	0.2206 *** (0.0282)	0.0170 *** (0.0027)	0.2019 *** (0.0281)	0.0072 * (0.0043)	0.2147 *** (0.0280)	0.0272 * (0.0157)	0.2107 *** (0.076)
POP	0.1501 *** (0.0336)	−0.0761 *** (0.0037)	0.2337 *** (0.0407)	−0.0088 (0.0059)	0.1572 *** (0.0385)	−0.3180 *** (0.0217)	0.2652 *** (0.0391)
constant	5.1895 *** (0.2600)	0.5943 *** (0.0249)	4.5364 *** (0.2771)	0.3936 *** (0.0396)	4.8738 *** (0.2614)	11.8984 *** (0.1453)	0.8809 ** (0.4214)
Sobel test		0.0916 (z = 3.734, p = 0.000)		0.0712 (z = 2.821, p = 0.005)		0.0750 (z = 1.908, p = 0.056)
Bootstrap test (indirect effect)		2.6633 (z = 12.71, p = 0.000)		0.2368 (z = 4.60, p = 0.000)		5.0781 (z = 16.71, p = 0.000)
Bootstrap test (direct effect)		1.6676 (z = 5.33, p = 0.000)		4.0941 (z = 12.82, p = 0.000)		−0.7472 (z = −2.43, p = 0.015)
Proportion of indirect effect (%)		13.42		10.43		10.98
sample size	4155	4155	4155	4155	4155	4155	4155
R2	0.9590	0.9040	0.9594	0.8033	0.9596	0.9059	0.9606

Note: ***, ** and * are significant at the levels of 1%, 5% and 10%, respectively.

, the total effect of the urban public service level on urban innovation ability is 0.6828, which was significant at the level of 1%. It can be seen that the urban public service level significantly improved urban innovation ability, which was consistent with the above conclusions. This may be because the city indirectly promoted the improvement of the city’s innovation ability by gathering human capital, optimizing the industrial structure, and expanding the income scale.

Columns (2) and (3), respectively, reflect the regression results of urban public services on human capital and human capital on urban innovation. Column (2) shows that the regression coefficient of urban public services to urban human capital was significantly positive at the level of 1%, indicating that urban public services are conducive to the urban agglomeration of human capital. In column (3), the regression coefficient of human capital on urban innovation was significantly positive at the level of 1%, indicating that human capital plays a positive role in improving innovation ability. Both columns (2) and (3) show that urban public services can effectively promote the agglomeration of human capital, provide a good talent base for urban innovation, and promote the improvement of urban innovation ability. It is consistent with the research conclusions of [27]. The intermediary effect of human capital was 0.0916, accounting for 13.42% of the total effect. The results of the Sobel test and bootstrap test were significant at the level of 1%, which confirmed the existence of the intermediary effect of human capital.

Columns (4) and (5), respectively, give the regression results of urban public services on industrial structure and of industrial structure on urban innovation. Column (4) shows that the regression coefficient of urban public services on the industrial structure was significantly positive at the level of 1%, indicating that urban public services can drive the upgrading of industrial structures. In column (5), the regression coefficient of industrial structure to urban innovation was also significantly positive at the level of 1%, indicating that change in industrial structure contributes to the improvement of urban innovation abilities. Combined with the results in columns (4) and (5), this suggested that urban public services can promote the adjustment of industrial structures and play a significant positive role in improving urban innovation ability. The intermediary effect of the industrial structure was 0.0712, accounting for 10.43% of the total effect. The results of the Sobel test and bootstrap test both supported the existence of the intermediary effect of industrial structure.

Column (6) displays the regression results of urban public services on the income scale, and column (7) displays the regression results of income scale on urban innovation. Column (6) shows that the regression coefficient of public services to income scale was significantly positive at the level of 10%, indicating that public services help to improve the income level. This is consistent with the research conclusions of [6]. As seen in column (7), the regression coefficient of income scale improvement on urban innovation was significantly positive at the level of 1%, indicating that income growth has played a significant role in promoting urban innovation. Both columns (6) and (7) show that public services can increase revenue and have a positive impact on the improvement of innovation abilities. The intermediary effect of the income scale was 0.0750, accounting for 10.98% of the total effect. The Sobel test and bootstrap test both passed the significance test and confirmed the existence of the intermediary effect of the income scale.

The above results were in line with the judgment criteria for the intermediary variables, so it was determined that human resources, industrial structure, and income scale were the intermediary variables for public services to affecting urban innovation, with Hypothesis 3 being supported by this finding. Public services not only have a direct effect on urban innovation, but also have an indirect impact on urban innovation through human resources, industrial structure and income scale. On the whole, the improvement of the current supply level of urban public services in China will promote the accumulation of human resources, the adjustment of industrial structure, and the expansion of the income scale, while the accumulation of human resources, the adjustment of industrial structure, and the expansion of the income scale will further promote the improvement of urban innovation ability.

6. Conclusions

Based on panel data from 277 cities at the prefecture level and above in China from 2005 to 2019, this paper empirically tested the impact of urban public services on urban innovation, discussed the heterogeneous impact of urban public services of different types, sizes, regions, and levels on urban innovation, and analyzed the intermediary mechanism of talent agglomeration, industrial structure, and income scale. The research conclusively proves that: firstly, urban public services can significantly improve urban innovation abilities. After endogenous treatment and robustness testing, our empirical results were still robust. Secondly, basic public services play a greater role in promoting urban innovation than livelihood public services. Basic public services such as transportation infrastructure can directly affect economic activities and have a faster and more obvious impact on technological innovation. However, public services as people’s livelihood, such as education, healthcare, and culture, can have an impact on innovation through the accumulation of human capital. The impact effect is relatively lagging, with its effects not being obvious, which was consistent with the research conclusions of [36]. Thirdly, public services have certain differences in urban scale, region, and administrative level on urban innovation. Because of these differences, at the levels of economic development and the impact of public services, public services in small and large cities play a significant role in promoting urban innovation, while in medium-sized cities, they do not play a significant role, with the authors of [37] reaching this same conclusion. Similarly, public services in the eastern and central regions can improve the innovation ability of cities in those regions, while the western and northeastern regions have no significant positive effect. The difference in urban administrative levels is a major feature of China’s urban economic development. The higher the administrative level, the more support is obtained from the higher-level government. Because key cities have received much support from all areas, the role of public services in promoting their urban innovation has been weakened. On the contrary, when the support for general cities is relatively small, the role of public services in urban innovation is more significant. Fourthly, public services have a positive impact on urban innovation through the human capital effect, industrial structure effect, and income scale effect. Public services can enhance the accumulation of human capital, promote the orderly flow of labor, and provide human support for urban innovation. Public services promote the evolution of industrial structures and trigger technological innovation through policy guidance, promoting the industrial division of labor and expanding consumer demand. Public services promote economic development and enable governments and enterprises to provide more support for technological innovation.

The conclusion of this paper offers the following policy implications. Firstly, the technological innovation effect of public services should be grasped. Public services can significantly enhance urban innovation capacity, which can also be used as an effective means to enhance the ability for urban innovation. In the process of promoting urban development, we should constantly improve the level of public services, improve the public service supply system, and reasonably plan and lay out all kinds of urban public services. We must also make full use of basic public services, such as public transport and environmental governance, optimize urban hardware conditions, reduce transaction costs and innovation costs, and improve enterprise profitability and innovation ability. Secondly, we must establish the concept of “talent is the first resource”. We must enrich basic education, medical, and health resources, improve the quality of education, medical treatment, culture, and other local public services and the convenience of consumption, and optimize the working and living environment. This would gradually solve the problem of resource imbalance by expanding the scope and radiation of services and improving the role of public services as people’s livelihood in labor agglomeration and human capital accumulation, cultivating and absorbing high-quality talents that can serve the innovative development of cities. Thirdly, promote the balanced development of public service areas. It is necessary to improve the matching and effectiveness of public financial expenditure and economic and social development and to increase the support for urban public services in the western and northeastern regions, according to regional differences. Public service supply should dynamically adapt to the changing situation of economic and social development, promote the optimization of the public service supply layout, regionally balance and optimize the benefits, provide strong support for local technological innovation, and realize the balanced and full development of regional innovation. Fourthly, we should enrich basic education, medical, and health resources to gradually solve the problem of resource imbalance by expanding the coverage and scope of services, improving the role of education, healthcare, and other public services for people’s livelihood in labor agglomeration and human capital accumulation, and cultivate and absorb more high-quality talents to serve the innovative development of the city.

There are limitations to this paper: firstly, because of the availability of data, the calculation of the public service level was not comprehensive; we could only use limited data to build the evaluation index system. Secondly, as far as the research objective was concerned, this paper only studied 277 cities in China without considering small-scale areas, so the research results are not universal.

Problems to be studied in the future: firstly, follow-up research will build a more comprehensive evaluation index system of the urban public service level to more specifically reflect the reality. Secondly, follow-up research will select the data from small-scale regions for discussion. For example, the data from the county-level regions in China will be selected for analysis, and the results will therefore be more universal. Finally, because of the acceleration of the development of urban agglomerations, follow-up research will build an urban spatial coordination mechanism.