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Public Services, Urban Innovation and Green Total Factor Productivity

  • Pengzhen Liu , Heng Gu , Yueting Shao and Jiayu Chen EMAIL logo
Published/Copyright: February 2, 2026
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Economics
From the journal Economics Volume 20 Issue 1

Abstract

Institutional inertia and development path dependence have increasingly constrained improvements in green total factor productivity (GTFP). This study develops a theoretical framework to examine how public services influence urban innovation and GTFP, and conducts an empirical analysis using panel data from 272 prefecture-level cities in China from 2006 to 2019. The results indicate that higher-quality public services significantly enhance urban innovation, which subsequently promotes GTFP, and this relationship remains robust across multiple sensitivity tests. Further analysis shows that public services foster urban innovation mainly through human capital accumulation and industrial agglomeration, which raise technological efficiency and thereby improve GTFP. These findings provide new evidence on the interplay between social development and economic performance, offering a productivity-based perspective to evaluate the role of public expenditure in supporting sustainable urban growth.

Keywords: public services; urban innovation; green total factor productivity; knowledge production; theoretical derivation

1 Introduction

As China transitions from rapid to high-quality economic growth, its annual GDP growth rate has moderated to around 6–7 %, with per capita GDP reaching approximately USD 10,000 (Heng 2018). Although this level exceeds that of most middle-income economies, it remains only about one-quarter of the average among OECD countries, indicating considerable room for further development. According to neoclassical growth theory and the historical development patterns of Western economies (King and Rebelo 1990), a country’s growth trajectory typically accelerates in the early stages but later slows due to changes in the international environment and domestic structural adjustments. Without timely industrial upgrading and a break from past development path dependencies, economies may stagnate and fall into the “middle-income trap” (Agénor 2017). Therefore, shifting from a factor- and investment-driven model to an innovation-driven growth model has become essential for China’s economic transformation (Ghosh et al. 2022; Song et al. 2023).

GTFP plays a central role in sustaining long-term economic growth and serves as a key indicator of future economic potential. While neoclassical theory highlights innovation as the primary driver of GTFP, endogenous growth theory further emphasizes the role of systemic arrangements, public services, and human capital by incorporating them into the production function alongside capital and labor (Shaw 1992). This perspective broadens the concept of GTFP and underscores how public services and urban innovation reinforce each other through positive feedback and cumulative effects, strengthening economic, social, and institutional dynamics. However, although China recorded substantial numbers of invention, utility model, and design patents in 2020, the share of invention patents was only 14.6 %, compared with 84.9 % in Japan and 70.9 % in France (Hu et al. 2017). This indicates that China’s urban innovation remains more quantitative than qualitative, partly due to inadequate public service provision and the insufficient realization of its potential positive externalities (Guo et al. 2023; Xu et al. 2024).

Experiences from developed economies show that public services not only enhance social welfare and equity but also improve productivity and efficiency. In these contexts, public services have raised the efficiency of urban innovation and consequently boosted GTFP. This raises several questions for China: Does a similar mechanism exist? If so, does it act primarily by improving technical efficiency or by promoting technological progress? Moreover, which has the stronger effect, public infrastructure or services that improve quality of life? Existing research tends to focus more on entrepreneurial indicators such as inward investment, trademark registrations, and new business formation, which reflect the transformation efficiency of urban innovation and represent key pathways through which innovation contributes to GTFP. From the perspective of urban innovation–driven entrepreneurship, this study examines whether public services also play a facilitating role, combining theoretical modeling with empirical analysis.

The contributions of this study are threefold. First, it constructs an integrated analytical framework linking public services, urban innovation, and GTFP, and evaluates both the direct and indirect effects of public services. Second, it develops a model that endogenizes public service accumulation and innovation-driven economic growth by incorporating both the household utility function and the knowledge production function. Third, it distinguishes between livelihood-oriented and infrastructure-oriented public services, identifying their respective mechanisms and comparative impacts on urban innovation and GTFP.

2 Literature Review

Concerning urban public services and innovation, empirical research predominantly affirms the crucial role of public service infrastructure in augmenting knowledge production. Infrastructure-related public services such as transportation and communication are regarded as essential for reducing spatial and temporal barriers and facilitating the dissemination of knowledge (Allen and Arkolakis 2022; Alotaibi et al. 2022; Branco et al. 2022). Livelihood-oriented public services, particularly education, also play a central role in cultivating human capital and fostering knowledge spillovers, which jointly contribute to optimizing industrial structures and strengthening capacities in knowledge production and scientific and technological innovation. Unlike monetary wages, infrastructure and livelihood-oriented public services function as non-monetary welfare that attract skilled professionals and enhance total factor productivity (Gyamfi et al. 2023; Lupu and Nuţă 2023). The theoretical perspective initially proposed by Tiebout (1956) suggests that improvements in public service provision intensify talent and industrial clustering, raising urban human capital levels. This clustering effect expands local markets, deepens the specialized division of labor in industries and technologies, and stimulates aggregate urban demand, thereby reinforcing knowledge production and innovation and contributing to higher GTFP. Recent research further identifies knowledge spillovers, innovation diffusion, and competition avoidance as important channels through which transportation infrastructure supports human capital development and innovation, with technologically advanced firms benefitting the most from these mechanisms (Ahamed et al. 2023; Obschonka et al. 2023). In addition, cross-country comparative studies indicate that the efficiency and governance quality of public service provision critically shape the functioning of urban innovation systems and productivity dynamics, underscoring the importance of institutional design in leveraging public expenditure for innovation-driven growth (Pomázi 2013).

Regarding urban innovation and green total factor productivity, there is growing consensus that knowledge production plays a key role in promoting GTFP growth. This line of research increasingly considers factors such as human capital, foreign direct investment, trade openness, and knowledge spillovers (Ferreira et al. 2024; Madsen 2008; Zhu and Jeon 2007). The underlying mechanism posits that urban innovation enhances production technologies, reduces resource consumption, introduces new production factors, and improves the configuration of existing ones. This process replaces outdated production capacities, strengthens labor specialization, and boosts GTFP. Empirical evidence from prefecture- and provincial-level studies in China shows that both technological innovation and GTFP significantly contribute to overall productivity improvements (Guo et al. 2024; Wen et al. 2024). Meanwhile, global studies on GTFP highlight the increasing significance of environmental regulation, energy system restructuring, and eco-innovation in shaping productivity trajectories, suggesting the need to interpret urban innovation within a broader sustainability-oriented productivity framework (Sharma et al. 2025). In contrast, the literature on the relationship between public services and GTFP remains less consistent, focusing primarily on the link between public expenditure and economic growth. Some scholars argue that increased public spending supports private capital accumulation and strengthens human and health capital, thereby improving economic efficiency; others caution that excessive public expenditure may crowd out private investment and suppress technological progress (Easterly and Rebelo 1993; Roy 2009). Notably, some studies identify an inverted U-shaped relationship between public expenditure and economic growth (Chen 2006).

In summary, existing literature extensively explores the nexus between public services, urban innovation, and green total factor productivity. However, there remains a significant gap in integrating public services within the framework of knowledge production and GTFP analysis, and in dissecting their intricate mechanisms. Moreover, research predominantly focuses on specific types of public services, often neglecting the holistic impact of both infrastructure and livelihood services on economic growth, particularly in quantifying their contributions to GTFP and entrepreneurial activity. Addressing these gaps, this paper aims to broaden the analysis of public services, urban innovation, and GTFP. It develops a theoretical model to elucidate the pathways through which public services influence urban innovation and GTFP, and empirically validates these relationships using data spanning 2006 to 2019 from 272 prefecture-level cities across China.

3 Theoretical Derivation and Econometric Modeling

3.1 Theoretical Derivation

Based on the preceding analysis, public services, knowledge production, and green total factor productivity are closely interrelated. This section develops a unified theoretical framework to clarify their internal linkages. Drawing on Romer (1990) and Heng-fu (1995), we construct an endogenous growth model that incorporates both knowledge production and public service provision. In this model, public services support human capital formation and provide essential welfare, thereby fostering innovation and contributing to long-term economic growth. Accordingly, public services are included in both the knowledge production function and the utility function of representative households. The model emphasizes the productive and efficiency-enhancing roles of public services in promoting knowledge creation, and consists of five key components: final goods production, intermediate goods production, R&D activity, representative households, and government behavior.

  1. Government

The government funds public expenditures through income taxation, denoted by the tax rate τ. The government budget equation is represented as follows:

(1) G = τ y t

It is assumed that the government allocates a fraction θ of tax revenue to public service construction expenditures and the remaining fraction (1 − θ) to administrative expenditures. To simplify the model, we assume there are no depreciation issues concerning urban public services. The expansion of urban public service provision results from ongoing government investments in this sector. The dynamic equation governing urban public services is presented below:

(2) P S ˙ t = θ τ y t

  1. Final goods production sector

(3) Y t = 1 1 − β ∫ 0 A t x v , t 1 − β d v L Y β

(4) max x v , t , L π f v , t = 1 1 − β ∫ 0 A t x v , t 1 − β d v L Y β − ∫ 0 A t p x v , t x v , t d v − w t L Y

(5) w t = β 1 − β ∫ 0 A t x v , t 1 − β d v L Y β − 1

Final goods production function, v represents the type of intermediate goods v ∈ 0 , A t , and L Y denotes the number of workers employed within this sector. The final goods production sector maximizes profit by utilizing labor and intermediate goods, where p x signifies the price of intermediates and w t denotes the wage rate of laborers.

According to the capital market clearing condition, the aggregate supply of capital to households must equate with the aggregate demand for capital in the intermediate goods sector. Therefore, the equilibrium condition for the capital market can be expressed as follows:

(6) K t = ∫ 0 A t x v , t d v

Further, in accordance with the market equilibrium condition, the aggregate market supply of any intermediate good equals its total market demand, expressed as x v , t = x . In this study, we substitute this formula into equation (6) to derive the subsequent equation:

(7) K t = A t x

Substituting equation (7) into equation (3) yields the aggregate output function of the final goods-producing sector:

(8) Y t = 1 1 − β A t β L Y β K t 1 − β

  1. Intermediate goods sector

Suppose the intermediate goods sector holds monopoly market power and rents capital to produce intermediate goods at marginal cost r t , with r representing the interest price per unit of capital, and p x denoting the selling price of intermediate goods. Consequently, the profit maximization problem confronting the intermediate goods sector can be formulated as follows:

(9) max : π m v , t = p x x v , t − r t x v , t

(10) r t = 1 − β L Y x v , t β

  1. R&D sector

Romer (1990) posits that knowledge production depends on both the total number of researchers and the existing body of social knowledge. Building on Romer’s framework, this study integrates urban public service provision into the knowledge production function. It contends that a robust urban public service system can create an optimal research environment, alleviating researchers’ concerns and thereby enhancing the efficiency of knowledge creation. Moreover, well-developed education and infrastructure facilitate the rapid dissemination of knowledge and bolster the spillover effects of urban innovation. Hence, incorporating public services into the knowledge production function is essential to better capture their role in compensating for efficiency in economic growth.

(11) A ˙ t = δ L A A t ϕ P S t 1 − ϕ

In the context where A ˙ t denotes the quantity of new knowledge produced, δ signifies the efficiency coefficient of knowledge production within the R&D sector, L A represents the total number of researchers, A t denotes the current stock of social knowledge, PS t denotes the level of public service supply, and 1 −  ϕ and ϕ represent the elasticity coefficients of the current social knowledge stock and urban public service supply to knowledge production, respectively. The condition of market arbitrage without distortion can be expressed as follows, with P A denoting the unit price of knowledge and Z t representing total R&D costs:

(12) w L A = P A A ˙ t = Z t

(13) P A = ∫ t + ∞ π m T e − ∫ t T r s d s d T

  1. Representative households

The conventional utility function typically posits that utility increases solely with the level of consumption. Heng-fu (1995) extends this framework by introducing capitalist psychological variables such as thrift and wealth into the individual utility function, suggesting that higher wealth leads to greater utility for an individual. This study integrates the level of urban public service provision into the household utility function. Specifically, the utility function for a representative household is assumed as follows:

(14) max ∫ 0 + ∞ C t P S t v 1 − σ 1 − σ e − p t d t

The equation above illustrates that the representative household aims to maximize not only consumption but also the levels of public service provision in both urban infrastructure and urban livelihood categories. Additionally, this paper presents the dynamic capital equation as follows, where I 1(t) and I 2(t) denote investments in infrastructure and livelihood public services in each period, respectively.

(15) K ˙ = 1 − τ Y t + w L A − ∫ 0 A t π v , t d v − C t

  1. Equilibrium solution

To solve the optimization problem, we combine Equations (2), (14) and (15) to formulate the Hamiltonian equation:

(16) H = C t P S t v 1 − σ 1 − σ + μ 1 − τ Y t + w L A − ∫ 0 A t π v , t d v − C t

λ denotes the shadow price of capital:

(17) H C t = C t − σ P S t v − σ v − μ = 0

(18) H K t = μ 1 1 − τ r t = ρ μ 1 − μ ˙ 1

Inada conditions:

(19) lim t → ∞ λ K t e − ρ t = lim t → ∞ λ PS t e − ρ t = 0

Solving this equation yields:

(20) C ˙ C = 1 − τ r t − ρ σ 1 + v − v

From Equations (2), (11) and (15), it is established that the growth rates of C t , K t , A t , PS(t) and Y t are equivalent when economic growth exceeds the Balanced Growth Path (BGP). It is assumed that the growth rate, denoted by γ, and the labor market parameters L A , L Y , P A , x are constant, ensuring the labor market remains balanced, i.e. L A  + L Y  = L.

Building on the analysis provided, the ratio of research personnel to personnel in the final product production sector can be determined as L A /L Y , and the economic growth rate as γ.

(21) L A L Y = 1 − τ 1 − α γ γ σ 1 + v − v + ρ

γ = 1 − α δ α 1 − α ( 1 − ϕ ) γ σ 1 + v − v + ρ 1 − τ ( 1 − α ) γ + γ ( σ 1 + v − v ) + ρ L 2 α − α ϕ 1 − α 1 − ϕ 1 − τ 1 − α γ γ σ 1 + v − v + ρ 1 + α ϕ − ϕ 1 − α 1 − ϕ θ τ γ α 1 − α

In this study, a parametric simulation was conducted using Matlab to address the optimization problem outlined. Drawing from empirical precedents in the literature on parametric simulations, we set the parameters as follows: α = 0.3, τ = 0.2, v = 0.2, ρ = 0.02, L = 1, and δ = 0.8. The research primarily explores the impact of government public service expenditure ratios on economic growth and other pertinent variables. For this analysis, benchmark values of Φ = 0.2 and θ = 0.1 were employed. The results of the simulations are presented in Table 1.

Table 1:

Parameter simulation results.

Φ = 0.2
θ 0.1 0.15 0.2 0.3 0.4 0.5 0.7 0.9
L A/L 0.135236 0.147587 0.155188 0.164536 0.170323 0.177468 0.179855 0.183491
γ 0.014815 0.018996 0.022393 0.027886 0.032353 0.039622 0.042652 0.048081
Φ = 0.3
θ 0.1 0.15 0.2 0.3 0.4 0.5 0.7 0.9
L A/L 0.120551 0.135754 0.144942 0.156094 0.162969 0.167735 0.17412 0.178407
γ 0.011226 0.014978 0.018007 0.022886 0.02684 0.030233 0.035953 0.040727
Φ = 0.4
θ 0.1 0.15 0.2 0.3 0.4 0.5 0.7 0.9
L A/L 0.091465 0.114187 0.126979 0.141821 0.150649 0.156666 0.16476 0.17005
γ 0.00654 0.009978 0.012651 0.016879 0.020277 0.023181 0.02805 0.032124

The analysis reveals that an increase in the proportion of government expenditures on public services correlates with higher rates of economic growth; this relationship remains consistent across various coefficients of public services’ impact on urban innovation. Moreover, green total factor productivity growth, which may more accurately reflect the quality of economic development than economic growth alone (Wang et al. 2022, 2024), is found to equal the rates of economic and knowledge growth along the equilibrium growth path. Consequently, this model suggests that elevated levels of government spending on public services accelerate both the accumulation and provision of these services. This, in turn, boosts the efficiency of knowledge production within the R&D sector and encourages the employment of additional researchers, thereby enhancing green total factor productivity. Based on these findings, the paper advances the following hypothesis.

Hypothesis: Public services enhance green total factor productivity by facilitating the production of knowledge.

3.2 Econometric Model

The identification strategy employed in this study comprises a two-step process. Initially, drawing upon the functional form of the knowledge production function as delineated in Equation (11) of our theoretical model, we construct a series of regression equations. These equations are designed to empirically assess and compare the influence of public services on innovation levels across cities.

(22) I i t = α 1 + β 1 P S i t + β 2 Contro l i t + ε i t

In Equation (22), PS it denotes the level of public services, while Control it consists of the control variables, which include the stock of knowledge, the number of individuals employed in knowledge-producing sectors, population size, the proportion of the secondary industry, and the level of financial development. ε it corresponds to the random disturbance term. Following this, based on the theoretical analysis, public services are incorporated into the total output function, as specified in Equation (8). When merged with Equation (11), this integration leads to the derivation of the subsequent equation:

(23) TF P i t = α 2 + β 3 I i t + β 4 P S i t + β 5 Contro l i t + ε i t

In Equation (23), the control variables encompass the degree of fiscal vertical imbalance, the size of local government, the number of individuals employed in the knowledge production sector, and the level of financial development. This study examines the relationship between urban public service provision and urban innovation levels on green total factor productivity by analyzing the positive and negative coefficients of β 3 and β 4. Furthermore, acknowledging the interdependence between the variables in these equations, and to mitigate the risk of estimation bias inherent in single equation estimations, this paper establishes a system of joint equations models based on Equations (22) and (23):

(24) I i t = α 1 + β 1 P S i t + β 2 Contro l i t + ε i t TF P i t = α 2 + β 3 I i t + β 4 P S i t + β 5 Contro l i t + ε i t

  1. Core Variables

Public services (PS it ): This paper adopts a multidimensional approach to measure the level of public service provision, selecting six key dimensions based on data availability and the scientific validity of indicators: road transportation, energy, communication, basic education, medical care, and environmental protection (refer to Table 2). Additionally, the study employs the global entropy weight method to assign weights to each public service data point, facilitating the evaluation and comparison of data across different years. This method addresses the limitations of the traditional entropy method, which is confined to the weighting of cross-sectional data only.

Table 2:

Evaluation index system of urban public service supply level.

Category Primary indicator Secondary indicator Indicator calculation
Public services Public services for livelihood Education Secondary education Student-teacher ratio in secondary schools (%)
Primary education Student-teacher ratio in primary schools (%)
Medical care Hospitals Number of hospitals per 10,000 people (units)
Hospital beds Number of hospital beds per 10,000 people (units)
Practicing physicians Number of practicing physicians per 10,000 people (persons)
Environmental protection Urban greening Green space ratio in built-up areas (%)
Park green areas Per capita Park green area (M2)
Public toilets Number of public toilets per 10,000 people (units)
Public services for infrastructure Transportation Road area Per capita road area (M2)
Public transport Number of public buses and trams per 10,000 people (Units)
Energy Gas supply Gas penetration rate (%)
Water supply Water usage rate (%)
Drainage system Density of drainage pipes in built-up areas (kilometers)
Communication Mobile phones Number of mobile phones per 10,000 people (units)
Landline phones Number of landline phones per 10,000 people (units)
Internet Internet penetration rate (%)

City Innovation Level (I it ): This study utilizes the City Invention Patent Authorization Index from the Enterprise Big Data Research Center at Peking University to represent new knowledge production in cities. Additionally, the robustness of these findings is tested using the City Utility Model Patent Index.

Green total factor productivity (GTFP it ): This paper employs the GML Index, derived from the super-efficiency relaxation model (Super-SBM), to measure the GTFP of Chinese cities. The input variables include physical capital accumulation, the employment in non-research sectors, and city-wide electricity consumption. The targeted output variable is real GDP, while the undesired outputs encompass emissions of industrial soot, SO2, wastewater, and PM2.5.

  1. Control variable

The measurement of variables in this study is operationalized as follows: The number of persons employed in knowledge-producing sectors is quantified using the logarithm of individuals engaged in research and comprehensive technology services. Population size is captured by the logarithm of the total population at year-end. Knowledge stock is represented by the logarithm of the city’s per capita real GDP. The prominence of the secondary industry within the economy is gauged by its GDP share. The size of local government is measured by the proportion of local general public budget expenditures relative to the city’s GDP. Lastly, the level of financial development is assessed through the logarithm of the year-end balance of all RMB deposits in financial institutions.

This study analyzes a sample of 272 prefecture-level cities in China, spanning from 2006 to 2019. In quantifying the GML index, physical capital accumulation is calculated using the perpetual inventory method, with the base period established in 2003. PM2.5 data underwent secondary processing using ArcGIS software to enhance accuracy. Additional data were derived from the China Urban Statistical Yearbook and the China Urban Construction Statistical Yearbook.

4 Results

4.1 Baseline Regression

Table 3 reports the baseline regression results for public services, urban innovation, and GTFP. Columns (1) and (2) present the estimates for the effects of urban innovation and public services on GTFP, while Columns (3) and (4) show the corresponding standardized coefficients. Standardization removes differences in variable scales and allows clearer comparison of direct, indirect, and total effects. The results indicate the following: First, public services do not have a statistically significant direct effect on GTFP, as shown in Columns (1) and (3). This suggests that improvements in public service provision do not directly translate into higher GTFP. Second, the coefficients for urban innovation in Columns (1) and (3) are significantly positive, indicating that higher levels of urban innovation contribute to increases in GTFP. Third, Columns (2) and (4) show that public services have a significant positive effect on urban innovation. This implies that enhanced public service provision promotes innovation activity, which subsequently contributes to GTFP improvements.

Table 3:

Baseline regression

Variable (1) (2) (3) (4)
GTFP I GTFP I
I 0.5337** 0.1769**
(2.42) (2.42)
PS −0.0794 0.3646*** −0.0152 0.2102***
(−0.29) (2.67) (−0.29) (2.67)
N 3,808 3,808 3,808 3,808
R 2 0.255 0.866 0.255 0.866
Control variables YES YES YES YES
City fixed YES YES YES YES
Year fixed YES YES YES YES

  1. ***p < 0.01, **p < 0.05, *p < 0.1, the same below.

4.2 Mechanism Analysis

To accurately analyze and quantify the pathways and corresponding effects between public services, urban innovation levels, and GTFP, this paper computes the direct, indirect, and total effects among these variables. These calculations are based on the estimation results of the standardized regression presented in Columns (3) and (4) of Table 3, with detailed results provided in Table 4.

Table 4:

Path of action analysis.

Mechanism of action Parametric Measured results Total effect
Direct effect Urban Innovation → GTFP β3 0.1769 0.1769
Direct effect Public services → GTFP β4 Not significant 0.0372
Indirect effect Public services → Urban innovation β1 0.0663
Indirect effect Public services → Urban innovation → GTFP β1*β3 0.1769 × 0.2102 = 0.0372

The analytical results in Table 4 indicate that public services can indirectly enhance GTFP through urban innovation, demonstrating a significant mediating role for urban innovation. This finding verifies the proposition presented in this paper. As the direct effect is not significant, the measures of the total effect and the indirect effect are numerically consistent.

4.3 Robustness Tests

This paper employs three approaches to robustness testing. First, the study uses the Propensity Score Matching-Difference in Differences (PSM-DID) methodology to assess the impact of public service policies on urban innovation and GTFP. Columns (1) and (2) of Table 5 present the estimation results of the PSM-DID, while columns (3) and (4) report the estimation results of the parallel trend test, utilizing the same relevant control variables as in the benchmark regression. According to Table 5, the smart city pilot policy significantly increases the level of urban innovation, which subsequently contributes to GTFP. Additionally, none of the previous years of the policy show significant results, indicating that it passes the parallel trend test. Based on these findings, a placebo test is conducted by randomly selecting an equal number of cities as the real pilot cities to construct the experimental group and randomly setting the time of policy shocks for regression analysis. This process is repeated 500 times. The estimated kernel density of the estimated coefficients and the corresponding distribution of the p-value are depicted in Figure 1. The regression results demonstrate that the estimated coefficients from the randomization process are centered around the value of 0, with P-values predominantly greater than 0.1. This significant difference from the estimated coefficients of the actual policy shocks indicates the robustness of the policy shock estimation results presented in this paper.

Table 5:

Estimation results of PSM-DID.

Variable (1) (2) (3) (4)
GTFP I GTFP I
I 0.4261** 0.3128*
(2.11) (1.66)
did 0.0400*** 0.0393*
(3.81) (1.86)
Pre2 0.0069
(0.25)
Pre3 −0.0343
(−1.24)
Pre4 −0.0108
(−0.39)
Pre5 0.0057
(0.21)
Pre6 0.0239
(0.86)
N 2,673 2,673 2,673 2,673
R 2 0.354 0.844 0.380 0.845
Control variables YES YES YES YES
City fixed YES YES YES YES
Year fixed YES YES YES YES
Figure 1: Placebo test.
Figure 1:

Placebo test.

Secondly, to address the issue of variable measurement singularity, this paper employs alternative methods for measuring core variables. First, the calculation of green total factor productivity is adjusted using the SBM-Undesirable model, which accounts for non-expected output, to re-measure urban total factor productivity (GTFP2). The regression results, presented in columns (1) and (2) of Table 6, demonstrate that the benchmark regression estimates remain robust. Second, the paper uses the city’s new utility patent index (I 2) as an alternative measure for the level of urban innovation. The regression results, shown in columns (3) and (4) of Table 6, indicate that the positivity, negativity, and significance of the core explanatory variables are consistent with the benchmark regression.

Table 6:

Other robustness tests.

Variable (1) (2) (3) (4) (5) (6) (7) (8)
GTFP2 I GTFP I 2 GTFP I GTFP I
I 0.8923*** 0.6224*** 0.5502***
(3.43) (2.68) (2.77)
I 2 0.3969**
(2.42)
PS −0.6715** 0.3657*** −0.0734 0.4480*** −0.3174 0.4503*** −0.1802 0.3718**
(−2.05) (2.68) (−0.27) (4.07) (−0.98) (2.86) (−0.68) (2.57)
N 3,807 3,807 3,808 3,808 3,598 3,598 3,808 3,808
R 2 0.163 0.866 0.279 0.911 0.228 0.845 0.278 0.866
Control variables YES YES YES YES YES YES YES YES
City fixed YES YES YES YES YES YES YES YES
Year fixed YES YES YES YES YES YES YES YES

Finally, to address the issue of sample extreme values, this paper employs several methods. First, sub-provincial cities are excluded from the sample. Due to significant differences in administrative and economic development levels between sub-provincial and ordinary prefecture-level cities, these cities are omitted from the analysis. The regression results, shown in columns (5) and (6) of Table 6, indicate that the baseline regression results remain robust. Second, outliers are removed by trimming the top and bottom 1 % of samples for the core variables. The regression results, presented in columns (7) and (8) of Table 6, show that the sign and significance of the estimated coefficients for the core explanatory variables are consistent, affirming the robustness of the benchmark regression results. Third, the paper calculates the covariance of the benchmark model residuals (e) and the covariance of public services (PS) and urban innovation level (I), which are 1.0e-12 and −0.005357, respectively. These values are numerically close to zero, suggesting that the model’s endogeneity has been controlled within acceptable limits.

5 Further Analysis

The relationship between public services, urban innovation, and GTFP, along with their paths of action, has been discussed above. However, several questions remain unaddressed. First, from the perspective of productivity heterogeneity, how do public services and urban innovation levels differentially impact technological efficiency versus technological progress within GTFP? Second, considering public service heterogeneity, if public services are categorized into infrastructure public services and livelihood public services, which category exerts a greater influence on urban innovation and GTFP? Additionally, urban innovation appears more directly effective in attracting entrepreneurial factors such as inward investment, new enterprises (Chi et al. 2024), and registered trademarks, indicating that “urban innovation drives entrepreneurship.” This dynamic is also a significant pathway through which urban innovation can enhance GTFP. Which entrepreneurial factors are most attracted to urban innovation, and what role do public services play in this attraction? This section aims to address these questions.

5.1 Productivity Decomposition Effect

In this study, GTFP is dissected into two components: technical efficiency (EC) and technological progress (TC). These elements are incorporated as explanatory variables in the regression model, with findings detailed in Table 7. The results indicate that the coefficients of urban innovation, as estimated through the technical efficiency model, are statistically significant. Conversely, the coefficients derived from the technological progress model do not display significance. This discrepancy suggests that the augmentation of urban innovation in Chinese cities primarily bolsters GTFP via enhancements in technical efficiency, rather than through advancements in technological progress.

Table 7:

Productivity decomposition regression results.

Variable (1) (2) (3) (4)
EC I TC I
I 1.0976** 0.4771
(2.18) (1.62)
PS −0.5964 0.3624*** −0.4826 0.3605***
(-0.94) (2.65) (-1.31) (2.64)
N 3,808 3,808 3,808 3,808
R 2 0.063 0.866 0.046 0.866
Control variables YES YES YES YES
City fixed YES YES YES YES
Year fixed YES YES YES YES

5.2 Public Service Heterogeneity

To elucidate the impact of various public services on urban innovation and GTFP, this study classifies public services into two categories: infrastructure public services (PS2) – encompassing road transportation, energy, and communication – and livelihood public services (PS3), which include basic education, medical care, and environmental protection. This analysis computes the supply levels of both categories and explores their respective influences on urban innovation and GTFP. The regression outcomes, presented in Table 8, reveal distinct effects: Columns (1) and (2) demonstrate that infrastructure public services directly enhance GTFP, whereas Columns (3) and (4) indicate that livelihood public services indirectly boost GTFP by fostering urban innovation.

Table 8:

Public service heterogeneity regression results.

Variable (1) (2) (3) (4)
GTFP I GTFP I
I 0.5119** 0.5538**
(2.32) (2.53)
PS2 0.2798* −0.1085
(1.83) (−1.40)
PS3 −0.2547 0.3945***
(−1.18) (3.98)
N 3,808 3,808 3,808 3,808
R 2 0.260 0.865 0.252 0.866
Control variables YES YES YES YES
City fixed YES YES YES YES
Year fixed YES YES YES YES

5.3 Extended Discussion

In the presented analysis, the focus is predominantly on GTFP. However, scientific and technological innovators in urban areas are often more concerned with the market recognition and application of urban innovations. This includes factors such as the ability of urban innovations to attract new enterprises, the volume of capital drawn from inward and venture capital private equity (VCPE) investments, and the registration of new trademarks. These elements are crucial for leveraging urban innovation to enhance GTFP. In this study, we introduce four indices as explanatory variables for regression analysis: the number of new business registrations (I 3), the inward investment attraction index (I 4), the new trademark registrations index (I 5), and the VCPE investment index (I 6). The results, detailed in Table 9, show significant positive regression coefficients for the indices of new business registrations, inward investment attraction, and new trademark registrations on the level of urban innovation, indicating a substantial impact. Conversely, the coefficients for the VCPE investment index are not significant. The effects of public services on these indices are reported in Columns (2), (4), (6), and (8) of Table 9, revealing a significant positive influence of public service provision on urban innovation levels. This underscores that enhanced public services contribute significantly to urban innovation, which in turn promotes entrepreneurial activities such as new business registrations, inward investment, and trademark registrations.

Table 9:

Analysis of the effect of public services on urban innovation-driven entrepreneurship.

Variable (1) (2) (3) (4) (5) (6) (7) (8)
I 3 I I 4 I I 5 I I 6 I
I 0.9428*** 1.2640*** 0.9641*** −0.1048
(8.49) (7.55) (8.89) (−0.57)
PS −0.0363 0.3261** −0.0497 0.3515*** 0.0285 0.3236** 0.4031* 0.3611***
(−0.26) (2.39) (−0.23) (2.58) (0.21) (2.37) (1.75) (2.64)
N 3,808 3,808 3,808 3,808 3,808 3,808 3,808 3,808
R 2 0.827 0.865 0.645 0.866 0.838 0.865 0.657 0.866
Control Variables YES YES YES YES YES YES YES YES
City fixed YES YES YES YES YES YES YES YES
Year fixed YES YES YES YES YES YES YES YES

6 Conclusions and Insights

6.1 Conclusions

Using panel data from 272 prefecture-level cities in China from 2006 to 2019, this study applies a three-stage least squares model to examine how infrastructure-oriented and livelihood-oriented public services affect urban innovation and GTFP. The results show that public services promote GTFP primarily by enhancing urban innovation, while their direct effect on GTFP is not statistically significant. These findings are robust to multiple specification and stability tests, which supports the theoretical framework. Heterogeneity analysis further indicates that both types of public services improve GTFP mainly through technological efficiency. Infrastructure public services exert a direct positive impact on GTFP, whereas the effect of livelihood public services operates indirectly through their influence on urban innovation. Additional analysis on innovation-driven entrepreneurship shows that higher levels of urban innovation stimulate new business formation, inward investment, and trademark registrations, although the effect on venture capital and private equity investment (VCPE) is relatively weaker. In contrast, improvements in public service provision directly attract VCPE investment, underscoring the role of public services in strengthening urban entrepreneurial ecosystems.

6.2 Insights

The conclusions of this paper carry significant policy implications, proposing specific measures across three key areas: Firstly, for cities with inadequate livelihood public service provision, higher-level governments should employ policy tools such as horizontal and vertical transfers and financial subsidies, guided by the principles of stock adjustment and incremental focus. Adjustments to the distribution of financial and administrative powers between local and higher-level governments are necessary to ensure the provision of essential services such as healthcare and education, thereby facilitating rapid knowledge growth and enhancing GTFP. This policy direction aligns with global discussions on equitable urban service provision, particularly in rapidly urbanizing regions where human capital accumulation is a critical driver of productivity. Secondly, in cities with robust economic foundations and well-developed infrastructures, local governments and relevant enterprises should be encouraged to innovate and upgrade traditional infrastructure. There should be a concerted effort to develop “new infrastructure” to leverage the role of public services in boosting knowledge production and advancing GTFP. Thirdly, it is essential to systematically engage market and social forces in the provision of public services, establishing a “government-led, market-participating, social-supervising” public service supply system. The integration of market and social forces can alleviate financial burdens on local governments, expedite the enhancement of urban innovation levels, and improve GTFP. More broadly, this governance approach offers policy relevance for global urban sustainability agendas, highlighting how coordinated state–market–society collaboration can support innovation-driven productivity growth under green and inclusive development goals.

Corresponding author: Jiayu Chen, Jiyang College, Zhejiang A&F University, Zhuji, 311800, China, E-mail:
Pengzhen Liu, Heng Gu, Yueting Shao and Jiayu Chen are contributed equally to this work.

  1. Funding information: This work was supported by the Quzhou University Research Project [KYQD007225002].

  2. Author contributions: P.L. drafted the manuscript, Y.S. collected and processed the data, H.G. compiled the references, Y.S. and J.C. reviewed and critiqued the manuscript. All authors participated in the conception and design of the study, provided feedback on earlier versions of the manuscript, and approved the final version.

  3. Conflict of interest: Authors state no conflict of interest.

  4. Data availability statement: The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

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Supplementary Material

This article contains supplementary material (https://doi.org/10.1515/econ-2025-0182).

Received: 2025-06-17
Accepted: 2025-11-17
Published Online: 2026-02-02

© 2026 the author(s), published by De Gruyter, Berlin/Boston

This work is licensed under the Creative Commons Attribution 4.0 International License.

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https://doi.org/10.1515/econ-2025-0182
Keywords for this article
public services; urban innovation; green total factor productivity; knowledge production; theoretical derivation
Creative Commons
BY 4.0

Articles in the same Issue

  1. Review Articles
  2. Professional Development of ESP Teachers for Digital Transformation: Approaches, Challenges, and Policy Implications
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  4. Research Articles
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  8. Internet Use and Child Malnutrition: Evidence from Rural Areas in China
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