How Does the Spatial Structure of Innovation Agglomeration Affect Energy Efficiency? From the Role of Industrial Structure Upgrading

Abstract

This paper employs the instrumental variable method and the intermediary model to explore the influence of monocentric and polycentric spatial structures of innovation agglomeration on energy efficiency. This paper uses data from 2010 to 2021 in China, and also panel data regression models were used. The findings indicate that the monocentric spatial structure of provincial system innovation agglomeration is primarily concentrated in northeastern and western regions of China, whereas the polycentric spatial structure is mainly distributed in eastern coastal areas. A monocentric spatial structure inhibits the enhancement of energy efficiency, but there is an environmental paradox of excessive resource agglomeration. In contrast, a polycentric spatial structure and its strengthening tendency facilitate the improvement of energy efficiency. A monocentric spatial structure has an inhibitory impact on the improvement of energy efficiency in the three sectors of agriculture, industry, and construction, while a polycentric spatial structure aids it. A monocentric spatial structure further hinders the improvement of energy efficiency by impeding the upgrading of the industrial structure, while the upgrading of the industrial structure driven by the polycentric spatial structure plays a role in enhancing energy efficiency. The policy recommendations of this paper are intended to help coordinate the pace of innovation development between cities, adjust the spatial structure of innovation agglomeration between regions, and promote the upgrading of the comprehensive industrial structure, thereby improving overall energy efficiency.

1. Introduction

The rapid development of the global economy has increased the energy demand from all sectors of society. The energy demand of nearly 14 billion tons of oil equivalent in 2018 represents a substantial increase from 12 billion tons of oil equivalent 10 years ago—an annual growth rate of nearly 3% [1]. This pattern of economic growth is accompanied by an extreme escalation in the demand for energy resources, which imposes significant pressure on the environment. In the face of the dual crisis of excessive energy consumption and continuous environmental deterioration, it is necessary to transform modes of production and consumption and enhance energy efficiency. At a time when energy reform is advancing worldwide, innovation is widely acknowledged as one of the main effective measures for improving energy efficiency [2].

The impact of innovation on energy efficiency is a consistently hot topic within the academic community. Numerous scholars have made significant contributions to the study of the influence of innovation on energy efficiency or energy intensity at the national, provincial, industrial, and enterprise levels. Specifically, at the national level, some scholars have discovered that scientific and technological innovation can assist in enhancing energy efficiency, based on a national sample of countries in the Middle East and South Africa [3]. Secondly, at the provincial level, many scholars have proposed that innovation can aid in improving energy efficiency [4] or green total factor energy efficiency [5] and promote the coordinated development of energy systems and environmental systems [6]. Thirdly, at the industrial level, certain studies based on industrial data have found that technological innovation has a positive driving effect on energy efficiency [7], and the application of products with innovation marks [8] and the implementation of innovative projects [9] are evidently conducive to reducing the energy intensity of industry. Fourthly, at the firm level, some studies have identified that the introduction of R&D technologies [10], process innovation [11], and the application of communication technologies [12] have significantly enhanced energy efficiency. Furthermore, the weakening effect of enterprise innovation based on innovation output representation on energy intensity is more pronounced than that based on innovation input representation [13]. In brief, the literature indicates that innovation can contribute to energy efficiency at various levels.

However, the mechanism by which innovation influences energy efficiency is complicated. Firstly, at the level of spatial heterogeneity, can the objective of “innovation-driven energy efficiency improvement” meet expectations? In reality, for a provincial system consisting of cities of varying size, the impact of innovation on energy efficiency is not merely attributed to the scale of innovation but also to the spatial structure of urban innovation agglomeration. The scarcity of resources means that innovation activities exhibit certain geographical agglomeration and spatial distribution disparities at the city level, and a spatial structure of “monocentricity” or “polycentricity” arises due to distinct development stages [14]. According to the research logic of spatial economics, it is probable that different spatial structures of innovation agglomeration will have dissimilar impacts on energy efficiency, and unreasonable spatial structures of innovation agglomeration not only fail to enhance energy efficiency but generate energy consumption, resulting in “negative externalities” [15] or “environmental paradoxes” [16] due to innovation agglomeration. Secondly, at the level of sectoral heterogeneity, given the precise geographical and economic distance between urban and rural areas, it remains unknown whether there is heterogeneity in the effect of the spatial structure of innovation agglomeration on energy efficiency between different sectors such as agriculture and industry. Thirdly, at the level of transmission mechanisms, the impact of innovation on energy efficiency is often not instantaneous but further influenced by the corresponding path. Hence, we must ask: what is the specific influence of the spatial structure of innovation agglomeration on energy efficiency? Is there sectoral heterogeneity in this effect? What is the transmission path for how the spatial structure of innovation agglomeration affects energy efficiency? These issues will be the central concerns of this article. The purpose of this paper is to explore the influence of monocentric and polycentric spatial structures of innovation agglomeration on energy efficiency during the period 2010–2021 in China.

Based on the above, the main research contents of this paper are as follows: first, the heterogeneity of innovation agglomeration at the city level in the provincial system is taken as the starting point. The impact of the monocentric and polycentric spatial structure of innovation agglomeration on energy efficiency is taken into account and verified by static panel estimation and instrumental variable estimation. Second, starting from the heterogeneity of energy efficiency, the impact of a monocentric or polycentric spatial structure of innovation agglomeration on energy efficiency is considered. Thirdly, the transmission mechanism of industrial structure upgrading and its influence on the energy efficiency of the innovation agglomeration spatial structure are analyzed. The existing results are then enriched from a theoretical point of view, with a view to providing empirical evidence for the development of innovation-driven strategies and energy efficiency improvement strategies for relevant departments.

2. Theoretical Analysis and Hypothesis

Innovation agglomeration is the key breakthrough point to achieve high-quality economic development, and the effective agglomeration of innovation elements is the necessary condition to achieve innovation-driven development. In today’s era of globalization and rapid technological development, innovation has become a core factor driving economic growth. The phenomenon of innovation agglomeration, that is, the high concentration of innovation activities in a specific region, has become a new focus of global economic competition. Innovation agglomeration refers to the phenomenon that innovation activities, innovation resources and innovation subjects are highly concentrated in a specific geographical area or field. Such agglomeration can bring about a range of economic and social effects, including but not limited to knowledge spillover, talent exchange, technological progress, and industrial upgrading. Innovation agglomeration is the key driving force of modern economic development. It accelerates the generation and application of new ideas and technologies by promoting knowledge sharing, technology exchange and talent flow. Within the provincial system, the urban unit serves both as a locale for innovative activities and a spatial agent for the enhancement of energy efficiency. However, under the condition of spatial heterogeneity, substantial disparities exist in innovation activities among different urban units, and they are manifested through the monocentricity or polycentricity of the spatial structure. The monocentric spatial structure resembles the rigid vertical structure of hierarchical differentiation and frequently presents a spatial structure of “strong provincial capital” or “one city dominance.” Nevertheless, the polycentric spatial structure leans towards the “flattening” of urban scale distribution [17]. However, it is unclear which kind of innovation agglomeration spatial structure brings about the improvement in energy efficiency in provincial systems. Our prediction is that a polycentric spatial structure will bring about such effects [15]. This structure represents continuous interaction and cooperation between urban units and is also an advanced way for each urban unit to achieve regional innovation through the mode of “cooperation in competition and competition in cooperation” within the spatial scope. Overall, there is a spatial correlation between energy efficiency and spatial scale, but different spatial structures of innovation agglomeration have varying impacts on the energy efficiency of provincial systems (Figure 1).

(1)

The Influence Logic of a Monocentric Spatial Structure of Innovation Agglomeration on Energy Efficiency

Although the energy utilization efficiency of the core city is enhanced, from the perspective of spatial equilibrium, this spatial structure is not conducive to the improvement of the energy efficiency of the edge city and even accumulates negative externalities and environmental paradoxes, resulting in decreased overall energy efficiency for the province [18]. In fact, the imbalance of innovation and development across space is not a historical accident. Innovation, as the engine of economic development, involving the formation and development of new models, new technologies, and new forms of business, urgently requires a mature market that can host new products and services. Therefore, innovation activities often converge in areas with high return rates [19]. Generally speaking, a provincial capital, as the central city, has more advantages than other small and medium-sized cities in terms of location advantages, resource endowment, and industrial structure and so is prone to the phenomenon of “single centralization” factor agglomeration [20]. However, this “single-centered” spatial structure of innovation agglomeration is obviously contrary to the requirement of the coordinated development of innovation in the provincial system. The “siphon effect” or “Matthew effect” is caused by the excessive agglomeration development of central cities [20], which in turn induces a spatial structure of “obesity” in large cities and “emaciation” in small and medium-sized cities, making the two-level differentiation significant and leading to secondary energy efficiency loss. In this process, there are a series of prominent problems in the construction of the urban innovation environment, such as a lack of public understanding, an imperfect talent incentive mechanism, an imperfect working mechanism, and lagging top-level design at the regional innovation level, which is not conducive to the improvement of the energy efficiency of the provincial system. This leads to our first hypothesis to be tested.

Hypothesis 1:

The monocentric spatial structure of innovation agglomeration has an inhibiting effect on the improvement of overall energy efficiency in a provincial system.

(2)

The Influence Logic of an Innovation–Agglomeration Polycentric Spatial Structure on Energy Efficiency

The excessive concentration of innovation in a single city exerts a restraining influence on the overall energy efficiency enhancement of a provincial system. Therefore, it is necessary to optimize the spatial structure of innovation agglomeration and promote energy efficiency by taking the coordinated development of innovation in each city of the province as the entry point [14]. A polycentric spatial structure of innovation agglomeration provides conditions for the coordinated development of cities, which helps to alleviate the negative externalities and efficiency losses caused by monocentricity [16]. Specifically, on the one hand, the polycentric spatial structure of innovative development avoids the unreasonable allocation of spatial elements and the loss of energy efficiency resulting from its monocentric development. On the other hand, the polycentric spatial structure of innovation development not only shortens the vertical distance of the vertical structure but also facilitates the improvement of horizontal connections and cooperation among urban units [18]. Innovation and development experience is better transferred between adjacent small and medium-sized cities, giving full play to the positive spatial diffusion effect of innovation elements and promoting the improvement of energy efficiency. This leads to our second hypothesis to be tested.

Hypothesis 2:

The polycentric spatial structure of innovation agglomeration will promote the improvement of the overall energy efficiency of the provincial system.

(3)

Theoretical analysis of the transmission mechanism of the impact of agglomeration spatial structure on energy efficiency

The aforementioned theoretical analysis indicates that the spatial structure of innovation agglomeration has an impact on energy efficiency. But what is the specific pathway? In reality, the spatial structure of innovation agglomeration indirectly affects energy efficiency by influencing the upgrading of the industrial structure. Specifically, certain studies have discovered that the adjustment of the industrial structure driven by technological innovation can assist in reducing energy loss due to the interaction between regional technological innovation, industrial structure, and energy efficiency [21]. Furthermore, within the two sets of causal relationships in the process of “innovation–industrial structure upgrading–energy efficiency,” not only is innovation conducive to promoting industrial structure upgrading [22], but industrial structure upgrading is also beneficial for enhancing energy efficiency [23]. Then, from the perspective of spatial heterogeneity, we must assess whether the influence path “spatial structure of innovation agglomeration–industrial structure upgrading–energy efficiency” is valid—that is, whether the two spatial structures of innovation agglomeration, monocentricity and polycentricity, indirectly affect energy efficiency by influencing the path of industrial structure upgrading [24]. In fact, based on the above theoretical analysis, it is not difficult to infer that a monocentric spatial structure of innovation agglomeration within a provincial system is prone to causing excessive geographical agglomeration of innovation resources [25]. This is not conducive to the optimization of the overall industrial structure of the provincial system and thus has an inhibitory effect on energy efficiency. On the contrary, a polycentric spatial structure of innovation agglomeration is conducive to the rational distribution of innovation elements, which is beneficial to the upgrading of the industrial structure of a provincial system and the further enhancement of energy efficiency. Therefore, the following hypothesis is proposed.

Hypothesis 3:

The monocentric spatial structure of provincial system innovation agglomeration indirectly inhibits the enhancement of energy efficiency by impeding the upgrading of the overall industrial structure, whereas the polycentric spatial structure indirectly promotes the improvement of energy efficiency by facilitating the upgrading of the overall industrial structure.

3. Model Identification and Data Sources

3.1. Model Building

In order to compare and analyze the effects of monocentricity and polycentricity on energy efficiency of the spatial structure of urban innovation agglomeration in the provincial system, the following equation was constructed. The panel data model was as shown:

$$E{E}_{it}={\alpha }_0+\alpha \cdot K_{it}+{\displaystyle \sum _{k=1}^m{\phi }_k\cdot }{X}_{kit}+{\mu }_i+{\upsilon }_t+{\epsilon }_{it}$$

(1)

$$I{S}_{it}={\beta }_0+\beta \cdot K_{it}+{\displaystyle \sum _{k=1}^m{\delta }_k\cdot }{X}_{kit}+{\mu }_i+{\upsilon }_t+{\epsilon }_{it}$$

(2)

$$E{E}_{it}={\chi }_0+\chi \cdot K_{it}+\gamma \cdot I{S}_{it}+{\displaystyle \sum _{k=1}^m{\vartheta }_k\cdot }{X}_{kit}+{\mu }_i+{\upsilon }_t+{\epsilon }_{it}$$

(3)

In Equation, $i$ and $t$ represent the province and year, respectively (and the same below); $EE$ represents the explanatory variable to reflect energy efficiency; and $K$ represents the core explanatory variables, i.e., the monocentricity index and the polycentricity index of the spatial structure of innovation agglomeration. $\alpha$ represents the total effect of the impact of the monocentricity index or the polycentricity index on energy efficiency; $X_k$ is incorporated into the model $K$ term control variables, ${\phi }_k$ is the corresponding estimation factor; ${\alpha }_0$ is an intercept term; ${\mu }_i$ and ${\upsilon }_t$ represent the provincial fixed effect and annual fixed effect, respectively; and ${\epsilon }_{it}$ is a random distractor.

In order to verify the transmission mechanism of industrial structure upgrading and its influence on energy efficiency of the innovation agglomeration spatial structure, according to Wen Zhonglin (2014) [26], the best method is recursive mediation. $IS$ indicates the upgrading of the industrial structure, the meaning and the formula of other specific variables and parameters.

3.2. Variables and Data Descriptions

3.2.1. Explanatory Variables

This paper adopted the characterization of the measured energy efficiency ($EE$) index proposed by Wang Ke et al. of the Beijing Institute of Technology (2021) [27]. The specific calculation process was as follows: Firstly, through the single-element energy efficiency measurement method, namely the proportion of real added value and energy consumption, the energy efficiency indexes of agriculture, industry, transportation, construction, and services in each provincial system from 2010 to 2021 were calculated separately. Then, in order to eliminate the influence of extreme values, the energy efficiency index of each sector was standardized by using the logarithmic power function as in Equation (4). Aggregate energy efficiency indices across sectors were transformed into provincial energy efficiency indices:

$$E{E}_i={\displaystyle \sum _{j=1}^5{\omega }_{ij}\cdot \frac{G_{ij,2015}}{E_{ij}}}$$

(4)

Among them, $E{E}_i$ is the energy efficiency index of the province, and ${\omega }_{ij}$ the proportion of the actual added value of $i$ the department in the province $j$ after standardization. $D{E}_{ij}$ = $G_{ij,2015}/E_{ij}$ indicates the energy efficiency index $i$ of the sector within the province $j$, where $G_{ij,2015}$ represents the actual value added corresponding to the base period of 2015 and $E_{ij}$ is the corresponding energy consumption. The energy efficiency index measurement data were mainly from national and local energy statistical yearbooks (https://data.stats.gov.cn/ (accessed on 3 March 2023)).

3.2.2. Core Explanatory Variables

To compare the monocentricity index ($MO$) and the polycentricity index ($PO$), the relevant data came from the Enterprise Big Data Research Center of Peking University. $\mathrm{vcpe}$ comprehensively calculates the total score of innovation and entrepreneurship, along with the per capita and unit area scores of cities above the prefecture level in each province according to the numbers of trademark authorizations, appearance patents, utility model patents, authorized invention patents, investments, foreign investments, and new enterprises.

(1) Uni-centralization index. Single centralization reflects the proportion of the first city within the provincial system; its construction method is as follows. $M{O}_{it}$ represents the monocentricity index of innovation agglomeration, while $D{I}_{ijt}$ represents the province $i$ in section $t$. The year is based on the per capita score of innovation and is ranked first in terms of scale $j$, which is the total index per capita of the city.

$$M{O}_{it}={\displaystyle \frac{max(D{I}_{i1t},D{I}_{i2t},\cdots ,D{I}_{int})}{{\displaystyle \sum _{j=1}^{n}D{I}_{ijt}}}}$$

(5)

(2) Polycentricity index. Polycentricity reflects the development gap between other cities and the first city and is constructed in the same way

$$\begin{gathered} P{O}_{imt}=Ln({\displaystyle \frac{{\displaystyle \sum _{j=2}^{m}D{I}_{ijt}}}{D{I}_{i1t}}}) \\ (m=2,4) \end{gathered}$$

(6)

In order to enhance the comparability and extensibility of the polycentricity index, the two-digit city polycentricity index ($P{O}_{i2t}$) and the four-digit city polycentricity index ($P{O}_{i4t}$) were calculated, respectively. The larger the polycentricity index value, the higher the degree of polycentricity of innovation agglomeration in the province. In addition, the mean values of the two-digit and four-digit city polycentricity indices ($P{O}_{24}$) were used to more completely describe the heterogeneity of the spatial structure of innovation agglomeration polycentricity.

(3) Other variables. (1) The intermediary variable to be tested was industrial structure upgrading ($IS$). The ratio of the added value of secondary and tertiary industries to the added value of domestic production in each province was used. (2) In the process of selecting control variables, the ratio of total imports and exports to GDP was used to characterize the introduction of technology (TI) with reference to relevant studies [28,29]. The ratio of construction output value to GDP and the ratio of urban construction land area to total urban area were used to characterize the contribution of the construction sector ($CW$) and the scale of urban construction ($LA$). The population size was measured by the number of people in urban areas ($LnPU$), and the ratio of urban population to total population was used to represent the urbanization rate ($UL$). The logarithmic value of the railway traffic volume was used to characterize the transport pressure ($LnRT$). Data on variables such as industrial structure upgrading, technology introduction, contribution of the construction sector, urban construction scale, and urbanization rate are from the China Macroeconomic Database, and data on transportation pressure are from the China Transportation Database.

(4) Endogeneity and Instrumental Variables. We considered that endogeneity might exist between the spatial structure of innovation agglomeration and energy efficiency. There could be an inverse causal relationship between the spatial structure of innovation agglomeration and energy efficiency. The improvement of energy efficiency might change the spatial structure of innovation agglomeration, while the spatial structure of innovation agglomeration influences energy efficiency. Important factors affecting energy efficiency might be overlooked, resulting in a biased model setting. In view of this, this paper intends to employ the instrumental variable method to identify the impact of the spatial structure of innovation agglomeration on energy efficiency. Lin Boqiang and Tan Ruipeng (2019) [30] utilized topographic relief as an instrumental variable of economic agglomeration and proved its validity. However, as a manifestation of economic agglomeration, it is theoretically feasible to use topographic relief as an instrumental variable. In light of this, terrain relief ($TR$) is selected as the instrumental variable to alleviate the endogeneity problem. The data on topographic relief were obtained in accordance with the method proposed by Feng et al. [31].

(5) Data Description and Exposition. To ensure the comprehensiveness and accessibility of the data, in conjunction with the data requirements for the calculation of the monocentric and polycentric indices of urban innovation agglomeration, the provinces of Tibet, Ningxia, and Qinghai, which have a small number of municipalities and cities in the sample, were excluded. Eventually, 23 sets of provincial panel data from 2010 to 2021 were selected.

Table 1. Descriptive statistics of variables.

Variable	Symbol	Mean	Standard Deviation	Minimum	Maximum	Observational Measurements
Energy efficiency	$EE$	0.563	0.102	0.323	0.765	207
Monocentricity index	$MO$	0.181	0.087	0.079	0.605	207
Two-digit polycentricity index	$P{O}_2$	−0.185	0.206	−1.177	−0.003	207
Four-digit polycentricity index	$P{O}_4$	0.798	0.252	−0.509	1.091	207
Mean of polycentricity index	$P{O}_{24}$	0.306	0.226	−0.843	0.544	207
Upgrading of industrial structure	$IS$	0.892	0.038	0.802	0.965	207
Technology introduction	$TI$	0.049	0.050	0.010	0.263	207
Construction sector Contribution	$CW$	0.306	0.136	0.055	0.770	207
Rate of urbanization	$UL$	0.531	0.088	0.338	0.707	207
Transport pressure	$LnRT$	9.210	0.827	7.944	11.354	207
The scale of urban construction	$LA$	0.338	0.137	0.107	0.708	207
Population size	$LnPU$	7.855	0.507	6.830	8.990	207
Terrain undulation	$TR$	0.983	0.909	0.013	3.529	207

presents the statistical results of the specific variables.

3.3. Index Values of Provinces

The energy efficiency of the eastern coastal provinces is significantly higher than that of the central and western provinces. The annual average energy efficiency indices of Jiangsu (0.73), Zhejiang (0.65), Fujian (0.70), and Guangdong (0.67) exceed 0.65, while those of Shanxi (0.39), Inner Mongolia (0.42), Heilongjiang (0.46), Guizhou (0.48), Gansu (0.46), Xinjiang (0.37), and other provinces have an annual average energy efficiency under 0.50. From the perspective of dynamic development, except for Heilongjiang, Gansu, and Xinjiang, the energy efficiency of the remaining 20 provinces tends to strengthen. The provinces with a high degree of monocentricity of innovation agglomeration are mainly distributed in northeast and western regions, such as Jilin (0.23), Heilongjiang (0.21), Guizhou (0.44), Yunnan (0.23), Xinjiang (0.32), and other provinces, with an annual average value more than 0.20. The degree of innovation agglomeration monocentralization in the eastern coastal provinces is low. In addition, except for the three northeastern provinces, the degree of monocentricity is gradually weakening. Similar to the energy efficiency index, eastern provinces such as Jiangsu, Zhejiang, and Guangdong have a high degree of polycentricity of urban innovation agglomeration, while Guizhou, Shanxi, Heilongjiang, Shaanxi, and Yunnan have a low degree of polycentricity—especially Guizhou, where the minimum value of the polycentricity index is −0.84 (due to the obvious difference between the polycentricity index of Guizhou Province and other provinces, for the convenience of display, some of the polycentricity index data of Guizhou Province are ignored, but this does not affect the analysis.). This indirectly indicates that the phenomenon of a “strong provincial capital” in Guizhou is obvious.

4. Empirical Results and Analysis

4.1. Baseline Regression Estimates

Before estimation, the variance inflation factor test was used to eliminate the multicollinearity issue among explanatory variables. According to the results of Hausman’s test, it was appropriate to employ the fixed-effect panel model.

Table 2. Baseline estimates.

Variable	Monocentricity		Polycentricity
			Two cities		Four Cities
	(1)	(2)	(3)	(4)	(5)	(6)
$MO$	−0.350 ***	−0.224 **
	(0.092)	(0.089)
$P{O}_2$			0.064 **	0.044 *
			(0.028)	(0.025)
$P{O}_4$					0.065 ***	0.045 **
					(0.023)	(0.022)
$TI$		−0.478 **		−0.478 **		−0.460 *
		(0.236)		(0.238)		(0.238)
$CW$		0.259 ***		0.269 ***		0.268 ***
		(0.054)		(0.054)		(0.055)
$UL$		2.386 ***		2.393 ***		2.408 ***
		(0.471)		(0.480)		(0.478)
$LnRT$		−0.020		−0.022		−0.019
		(0.019)		(0.019)		(0.019)
$LA$		0.385 *		0.288		0.348
		(0.219)		(0.215)		(0.219)
$LnPU$		−0.570 ***		−0.530 ***		−0.553 ***
		(0.164)		(0.165)		(0.166)
$C$	0.602 ***	3.646 ***	0.548 ***	3.397 ***	0.485 ***	3.451 ***
	(0.018)	(1.029)	(0.008)	(1.037)	(0.019)	(1.030)
Vintage effect	Yes	Yes	Yes	Yes	Yes	Yes
Province effect	Yes	Yes	Yes	Yes	Yes	Yes
$N$	207	207	207	207	207	207
$R^2$	0.320	0.555	0.285	0.546	0.294	0.549

Note: *, **, and *** represent significance at the 10%, 5%, and 1% levels, respectively, with the standard error in parentheses.

reports the estimation of energy efficiency by the monocentricity and polycentricity of the spatial structure of innovation agglomeration. On the one hand, based on the results of columns (1)–(2), it can be observed that the impact of the monocentric spatial structure of innovation agglomeration on energy efficiency is significantly negative, and passes the significance test of at least 5% regardless of whether control variables are added. This indicates that the “dominance of one city” in innovation agglomeration involves negative externalities and environmental paradoxes for the surrounding cities, thereby exerting an inhibitory effect on the improvement of the energy efficiency of the provincial system. Thus, Hypothesis 1 was validated. On the other hand, according to the results of columns (3)–(6), the positive impact of the polycentricity index on the energy efficiency of the two cities and the four cities passes the significance level of at least 5% without considering the control variables, and the polycentricity index of the two cities and the four cities passes the significance levels of 10% and 5%, respectively. At this point, then, Hypothesis 2 was verified. These results suggest that the energy efficiency of the provincial system has improved with the diffusion of urban innovation agglomeration to sub-central cities, and the effect of the polycentric spatial structure on energy efficiency has increased from 10% in the two cities to 5% in the four cities. To a certain extent, this indicates that, with the strengthening of the degree of polycentricity of the spatial structure of innovation agglomeration, the diffusion effect of innovation activities is enhanced, and the energy efficiency of the provincial system increases, which is conducive to resolving the environmental paradox caused by excessive innovation agglomeration.

4.2. Tool Variable Estimates

Considering that there might be endogenous issues such as reverse causality and omission of crucial explanatory variables in the setting of the benchmark model, the lagged period of the provincial topographic relief and the core explanatory variables were selected as the instrumental variables, and the TSLS and GMM instrumental variable methods were employed for estimation, as presented in

Table 3. Tool variable estimation results.

Variable	TSLS			GMM
	(1)	(2)	(3)	(4)	(5)	(6)
$MO$	−0.251 **			−0.265 ***
	(0.101)			(0.101)
$P{O}_2$		0.074 **			0.077 **
		(0.030)			(0.030)
$P{O}_4$			0.104 **			0.112 **
			(0.052)			(0.051)
Control variables	Yes	Yes	Yes	Yes	Yes	Yes
Vintage effect	Yes	Yes	Yes	Yes	Yes	Yes
Province effect	Yes	Yes	Yes	Yes	Yes	Yes
$N$	184	184	184	184	184	184
$R^2$	0.945	0.943	0.943	0.945	0.943	0.943

Note: *, **, and *** represent significance at the 10%, 5%, and 1% levels, respectively, with the standard error in parentheses.

. The results of the two instrumental variable estimation methods were clearly similar. From the GMM estimation results, the impact coefficient of the monocentricity index on energy efficiency in column (4) was −0.265 and passed the 1% significance level, indicating that the monocentric spatial structure of innovation agglomeration is not conducive to the improvement of energy efficiency. However, the influence coefficients of polycentricity on energy efficiency in the two and four cities in columns (5)–(6) were 0.077 and 0.112, respectively, and both passed the 5% significance level, revealing that the polycentric spatial structure of innovation agglomeration is conducive to the improvement of energy efficiency, and the strengthening of the degree of polycentricity is also beneficial for enhancing energy efficiency. In addition, regarding the validity test of instrumental variables, the corresponding p-values were all greater than 0.2178—that is, the null hypothesis that “all endogenous variables are exogenous” was not rejected, thereby indicating that the instrumental variables selected in this paper were valid.

4.3. Robustness Test

To ensure robustness, this paper focuses on the measurement error of the monocentricity index and the polycentricity index of the spatial structure of innovation agglomeration. In this paper, the monocentricity index and the polycentricity index were, respectively, measured in reference to the idea of primacy proposed by Zhong Shunchang et al. (2021) [14] and the Herfindahl–Hirschman index (HHI).

(1) Single-centralization index measurement error. The primacy degree reflects the proportional relationship between the first city and the second first city, where, $m=2,3,4$, measuring the firstness of the second, third, and fourth cities of innovation ($P{A}_2$, $P{A}_3$, and $P{A}_4$), so as to judge the agglomeration dynamics of innovation activities in the first city.

$$P{A}_{imt}={\displaystyle \frac{D{I}_{i1t}}{{\displaystyle \sum _{j=2}^{m}D{I}_{ijt}}}}$$

(7)

(2) Multicentricity index measurement error. The HHI is mainly used to calculate the equilibrium characteristics of polycentricity index distribution, and the value range is in the range of 0–1; the larger the value, the lower the degree of polycentralization. $H{P}_{imt}$ is the agglomeration polycentricity index for innovation; $m=2,4$ include $H{P}_2$ and $H{P}_4$; $HH{I}_{imt}$ represents the former within province $m$; $D{I}_{ijt}$ is as above; and $D{I}_{it}$ refers to the first $t$ year $i$. The total per capita index of innovation scale within the provincial system ranks first, with $m$ the sum of the indexes of cities.

$$H{P}_{imt}=1-HH{I}_{imt}=1-{{\displaystyle \sum _{j=1}^m\left(\frac{D{I}_{ijt}}{D{I}_{it}}\right)}}^2$$

(8)

Based on this, a robustness test is carried out according to the redefined monocentricity and multi-centrality index, and the results are shown in

Table 4. Robustness test.

Variable	Monocentricity Index						Polycentricity Index
	Two Degrees of First Place		Three First-Place Degrees		Four First Degrees		Two Digits		Four Digits
	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
$P{A}_2$	−0.041 ***	−0.030 **
	(0.016)	(0.014)
$P{A}_3$			−0.069 ***	−0.049 **
			(0.023)	(0.020)
$P{A}_4$					−0.088 ***	−0.067 ***
					(0.028)	(0.026)
$P{H}_2$							0.505 ***	0.398 **
							(0.178)	(0.161)
$P{H}_4$									0.693 ***	0.494 **
									(0.243)	(0.212)
Control variables	not	Yes	not	Yes	not	Yes	not	Yes	not	Yes
Vintage effect	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
Province effect	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
$N$	207	207	207	207	207	207	207	207	207	207
$R^2$	0.292	0.551	0.302	0.554	0.303	0.556	0.296	0.554	0.297	0.553

Note: *, **, and *** represent significance at the 10%, 5%, and 1% levels, respectively, with the standard error in parentheses.

. Regardless of whether the control variables are considered, the estimation coefficients in columns (1)–(6) are significantly negative and pass the significance level of at least 5%, which again verifies the inhibition effect of the monocentric spatial structure of innovation agglomeration on the improvement of energy efficiency. In addition, the estimation coefficients in columns (7)–(10) are all significantly positive and at least at the 5% level, which also proves that the spatial structure of innovation agglomeration polycentricity is conducive to promoting the improvement of energy efficiency. The estimation coefficients of the polycentricity index of the second and fourth cities are compared, ($H{P}_2$ = 0.398; $H{P}_4$ = 0.494); the higher the degree of polycentricity of innovation agglomeration, the more conducive to improving energy efficiency. Therefore, the baseline estimates can be considered reliable.

4.4. Sectoral Heterogeneity Analysis

Differences in the impact of $MO$ monocentricity and polycentricity of the spatial structure of innovation agglomeration $P{O}_{24}$ on the energy efficiency of agriculture, industry, construction, transportation, and service were further explored; the results are as shown in

Table 5. Sectoral heterogeneity analysis.

Variable	Monocentricity					Polycentricity
	Agriculture	Industry	Building	Transport	Service	Agriculture	Industry	Building	Transport	Service
	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
$MO$	−0.497 **	−0.219 *	−0.433 **	0.0466	0.155
	(0.200)	(0.117)	(0.198)	(0.203)	(0.193)
$P{O}_{24}$						0.957 *	0.536 *	0.834 *	0.109	−0.003
						(0.489)	(0.277)	(0.485)	(0.480)	(0.457)
Control variables	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
Vintage effect	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
Province effect	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
$N$	207	207	207	207	207	207	207	207	207	207
$R^2$	0.249	0.588	0.324	0.152	0.147	0.239	0.589	0.261	0.152	0.144

Note: *, **, and *** represent significance at the 10%, 5%, and 1% levels, respectively, with the standard error in parentheses.

. We discovered that a monocentric spatial structure of innovation agglomeration is negatively correlated with energy efficiency, while a polycentric spatial structure is positively correlated with it. This is manifested in the sectors of agriculture, industry, and construction, while in the transportation and service sectors, the correlation is not significant. In fact, in-depth reflection reveals that the activities of the transportation and service sectors mainly occur in central cities and are not location-bound. Hence, a monocentralized spatial structure of innovation agglomeration does not inhibit energy efficiency. However, agriculture, industry, and construction are often not located in central cities and have fixed locations, being far away from innovation resource centers. Therefore, the monocentricity of innovation agglomeration has an inhibitory effect on the energy efficiency of these three sectors. The situation is the opposite for the impact of the polycentric spatial structure on the energy efficiency of the five sectors, which contributes to the improvement of energy efficiency in agriculture, industry, and other sectors distributed in non-core development areas.

4.5. Mechanism Analysis

In order to verify the transmission mechanism of the industrial structure and its influence on the energy efficiency of the innovation agglomeration spatial structure, estimates are made according to Equations (1)–(3); the results are presented in

Table 6. Transmission mechanism testing.

Variable	Monocentricity			Polycentricity
	Energy Efficiency	Industrial Structure	Energy Efficiency	Energy Efficiency	Industrial Structure	Energy Efficiency
	(1)	(2)	(3)	(4)	(5)	(6)
$MO$	−0.611 ***	−0.245 ***	−0.442 ***
	(0.071)	(0.025)	(0.083)
$P{O}_{24}$				1.550 ***	0.525 ***	0.985 ***
				(0.302)	(0.113)	(0.291)
$IS$			0.689 ***			1.076 ***
			(0.190)			(0.172)
Control variables	Yes	Yes	Yes	Yes	Yes	Yes
$N$	207	207	207	207	207	207

Note: *, **, and *** represent significance at the 10%, 5%, and 1% levels, respectively, with the standard error in parentheses.

. Herein, columns (1)–(3) give test results on the conduction effect of the industrial structure. In the first column, the influence coefficient of the monocentricity index on energy efficiency is −0.611, passing the 1% significance test, and the total effect is significant. In the second column, the impact coefficient of the monocentricity index on the industrial structure is −0.245 and significant. In the third column, the impact coefficient of the monocentricity index on energy efficiency is −0.442 and significant, indicating that the direct effect is significant. Meanwhile, the influence coefficient of the industrial structure on energy efficiency is 0.689 and significant, indicating that the indirect effect is significant. The value of −0.245*0.689 is consistent with −0.442 in sign, which indicates that the industrial structure plays a partial mediating role in the process of the monocentricity index affecting energy efficiency, accounting for approximately 27.63% of the total effect. Specifically, the monocentric spatial structure of innovation agglomeration will impede the upgrading of the industrial structure of the provincial system, and subsequently inhibit the improvement of the energy efficiency. Similarly, the industrial structure plays a partial mediating role in the process of the polycentricity index affecting energy efficiency, accounting for about 36.45%, which indicates that the polycentric spatial structure of innovation agglomeration is conducive to promoting the upgrading of the industrial structure of the provincial system, and has a promoting effect on the improvement of energy efficiency. At this point, Hypothesis 3 can be verified.

5. Discussion

First, the pace of spatial innovation development among cities should be coordinated. The improvement of energy efficiency is a regional spatial public issue, and a coordinated spatial development pattern across cities and departments is key. In the context of the current energy revolution, it is urgent to form a collaborative development model of innovation among urban units within the province. It will also be important to challenge the status quo of the “strong provincial capitals” of innovation resources, advocate for multi-center development of innovation, encourage the positive diffusion effect of innovation activities, and break the unbalanced spatial development pattern driven by the “siphon effect.” Simultaneously, it is necessary to rationally allocate certain innovation resources to agriculture, industry, and other sectors on the periphery of the city, and increase the positive driving effect of the degree of polycentricity of innovation agglomeration on energy efficiency.

Second, the spatial pattern of innovation across regions should be adjusted. The “one-sided” approach to innovation and development is not conducive to the overall improvement of energy efficiency. There is innovation agglomeration in northeastern and western regions such as Guizhou, Xinjiang, Jilin, Heilongjiang, and Yunnan, which have been mainly monocentric for a long time. On the one hand, it is necessary for local governments to rationally allocate resources to cities with lagging innovation and development, promote the formation of polycentric cities for innovation and development, and increase the availability of innovation resources. On the other hand, it is necessary to promote the benign interaction between primary and secondary cities, strengthen the exchange of innovation and development between cities and regions, and strive to form a spatial structure of coordinated development of innovation and development. This can be achieved by actively attracting investment, expanding investment, and increasing R&D investment.

Third, the upgrading of the comprehensive industrial structure should be promoted. This serves as an intermediary step in the process of improving energy efficiency within the innovation agglomeration spatial structure. Simultaneously, as far as industrial development itself is concerned, the upgrading of the industrial structure is also one of the crucial factors in the continuous improvement of energy efficiency. Therefore, the government should expand the scope of innovation space and promote the upgrading of the industrial structure to improve energy efficiency. At the same time, relevant enterprises should aim for energy efficiency improvement through industrial optimization measures such as independent innovation, technology research and development, attracting talent capital, and expanding the development of the environmental protection industry.

Innovation agglomeration and energy efficiency are linked together. For future research, we can further explore the development model based on time and place by deepening the measurement indicators of innovation agglomeration degree, energy efficiency measurement methods and regional differences between them.

6. Conclusions

The conclusions of this paper are as follows: There is distinct heterogeneity in the spatial structure of innovation agglomeration in China’s provincial system. The monocentric spatial structure is mainly distributed in northeastern and western regions such as Guizhou, Xinjiang, Jilin, Heilongjiang, and Yunnan, presenting a spatial development pattern with a strong siphon effect of innovation resources in the first city. The polycentric spatial structure is mainly distributed in eastern coastal areas such as Jiangsu, Zhejiang, and Guangdong, where innovation activities are closely related between cities and have strong diffusion. However, in general, the monocentric spatial structure is on the wane, while the polycentric spatial structure continues to strengthen. The monocentric spatial structure of urban innovation agglomeration is not conducive to the enhancement of the energy efficiency of provincial systems, while the polycentric spatial structure is. The heterogeneity analysis revealed that the negative and positive correlations of the monocentric and polycentric spatial structures of innovation agglomeration with energy efficiency, respectively, were only established in the three sectors of agriculture, industry, and construction and had not been verified in the transportation and service sectors. The monocentric spatial structure of the city is not conducive to the upgrading of the provincial industrial structure, thereby inhibiting the improvement of energy efficiency, while the polycentric spatial structure promotes the upgrading of the industrial structure, thus facilitating the improvement of energy efficiency. Regarding the novelty of this paper, this paper answers the question of how the spatial structure of innovation agglomeration affects energy efficiency, from industrial structure upgrading to a polycentric spatial structure, and how its strengthening tendency facilitates the improvement of energy efficiency. A monocentric spatial structure has an inhibitory impact on the improvement of energy efficiency in the three sectors of agriculture, industry, and construction, while a polycentric spatial structure aids it. A monocentric spatial structure further hinders the improvement of energy efficiency by impeding the upgrading of the industrial structure, while the upgrading of the industrial structure driven by the polycentric spatial structure plays a role in enhancing energy efficiency