Polycentric or monocentric, which kind of spatial structure is better for promoting the green economy? Evidence from Chinese urban agglomerations

The green economy has gained worldwide attention, especially in the urban agglomerations where population and economic activities are highly concentrated. However, what kind of urban agglomeration spatial structure is more conducive to promoting the green economy? No clear conclusions have been made. To bridge this gap, by employing the data of 16 urban agglomerations in China in 2003–2017 and a comprehensive analytic framework including dynamic panel threshold model, this paper studies the impact of urban agglomeration spatial structure on the green economy and the three subsystems of green economy to shed light on which kind of urban agglomeration spatial structure better drives the green economy. The main findings are shown below: (1) urban agglomeration spatial structural evolution is closely related to green economy, while in the research period, most urban agglomerations are not located in the optimal range of the spatial structure that drives the green economy. (2) Towards polycentric spatial structure is contributive to green economic growth; however, the excessively polycentric could not benefit green economy. (3) The evolution of urban agglomeration spatial structure exerts heterogeneous impacts on the three subsystems when green economy is decomposed into economic subsystem, resources subsystem, and environmental subsystem. Towards polycentric is more conducive to the improvement of economic subsystem and resource subsystem, while the tendency to monocentric drives the environmental subsystem. (4) Lastly, the conclusions enlighten the urban agglomeration development planning and spatial mode for approaching a better performance in green economy.


Introduction
Urban agglomerations (The term urban agglomeration is closely linked to the term of urban cluster. One prevailing viewpoint is that a typical urban agglomeration usually consists of at least 3 cities.), accounting for over 75% of total domestic economic outputs, have become the most dynamic and promising areas for China's economic development now and in the future (Fang 2015). However, the urban agglomerations also produce over 75% of the total pollution outputs, which consequently overload the ecological environment of the urban agglomerations (Fang et al. 2017). Compared with city individual, material and energy exchanges between urban agglomerations and other places (i.e., areas that do not belong to urban agglomerations) are more extensive and deeper, posing difficulties for urban agglomerations to solve increasingly severe resources and environmental constraints (Huang et al. 2021a, b;Miao et al. 2021) and making green economy of urban agglomerations more complicated than ever before.
In China, on the one hand, urban agglomerations are the most developed economic regions. On the other hand, urban agglomerations are also facing serious resource and environmental risks. Then, could a "multi-win" situation be achieved (i.e., economic growth, resources saving, and environmental protection are obtained simultaneously)? In other words, could the green economic growth be obtained in the urban agglomerations? In fact, the Chinese government has been Responsible Editor: Ilhan Ozturk pursuing the construction of a resource-saving and environment-friendly society for many years and has set up a "two-oriented society experimental zone" in the Chang-Zhu-Tan urban agglomeration (one of the urban agglomerations in China). Nevertheless, the problem of green development in China's urban agglomerations has not yet been fundamentally resolved. Presently, China is in the stage of accelerating the development of urbanization, which is stylized with a change in city size distribution as well as the evolution of urban spatial structure. Chinese government is also pursuing green development and high-quality growth. Therefore, the following issues emerge. How should the problems and difficulties presented in the process of urban agglomeration green development be solved? Does the evolution of urban spatial structure in China affect the green development? Can the three aspects of economic growth, resource conservation, and environmental protection be simultaneously achieved through an appropriate urbanization development mode? To address the aforementioned issues effectively, more and more scholars are focusing on urban spatial structure (e.g., the spatial distribution of population and employment) and are endeavoring to explore what kind of urban spatial structure can be beneficial to the urban development, i.e., exploring the growth effect caused by the urban spatial structure evolution. Admittedly, the existing findings enlighten this article theoretically and empirically. However, as of now, the integrated effects caused by the spatial structural evolution have not attracted sufficient attention. The topic about what impact the rapid spatial structure evolution of urban agglomerations have on the development of green economy are still not effectively revealed or addressed.
Although a bit of literature has paid attention to similar topic (Pili et al. 2017;Liu et al. 2020a;Miao et al. 2021), the evidence is still weak. It is obvious that bridging this gap is necessary for China, where many urban agglomerations are being constructed and green development is urgently required. It helps to reveal the relationship between the spatial structural evolution of urban agglomerations and the green economy.
Particularly, in recent years, polycentric spatial structure (one of the evolutionary stages of urban spatial structure) has drawn scholars' attention. With increasing concern about climate change, more and more attention has been paid to environmental problems, and the polycentricity has been regarded as an urban form to promote sustainable development (Vandermotten et al. 2008). However, whether spatial structure, especially polycentric, can effectively improve regional competitiveness and promote regional balanced development and environmentally sustainable development still lack empirical evidence. This is a research topic worth discussing, because different cities may adopt completely inconsistent or differentiated strategies when facing the economic and environmental problems. For example, policymakers may adopt "promotion tournaments" strategy in pursuing economic growth; however, they perhaps take "free-riding" behavior in environmental governance. Therefore, the development of urban agglomerations and the evolution of their spatial structure may have different effects on the three dimensions of economy, resources, and environment. Such guess requires empirical evidence, through which how urban agglomeration spatial structure affects green economy can be clearly shown. Until now, few papers show focus on this.
Taken together, this paper tries its best to reveal a relationship between the evolution of urban agglomeration spatial structure and green economy in current Chinese context (Fig. 1).
The main contribution of this paper is threefold. First, it explores the impact of urban agglomeration spatial structure on green economy, such research until now only has received a bit of evidence. By doing this, this paper can reveal which spatial structure is better, polycentric or monocentric? This is essential in determining better strategies that are for future planning in terms of urban agglomerations. Second, this paper divides the green economy into three subsystems and shows how the urban agglomeration spatial structure affects them. This helps to have a clearer picture of whether urban agglomeration can achieve economic growth, resource conservation, and environmental protection together. It is also a supplement to existing research about the growth effect of urban spatial structure. Third, this article makes another contribution to the existing papers by simultaneously using the linear model and panel threshold model in an empirical framework, through which some new findings are found compared with the traditional empirical cases. Previous studies usually asserted spatial structure's influence on economic growth or pollution emissions from linear perspective. However, the linear perspective might not be the best case for exploring the growth effects stem from the spatial structure of urban agglomerations. Actually, a threshold may be triggered and occur when the spatial structural evolution goes on. Using a panel threshold model helps to obtain more clear insights in the growth effect caused by spatial structural evolution of urban agglomerations.
To fulfill the above contribution in this study, the following research questions are investigated: Is there evidence of spatial structure's influence on green economy in the urban agglomerations over the sample period? If so, further, when the green economy is subdivided into three different subsystems, whether the impacts on three subsystems show heterogeneities? Moreover, after the threshold model is conducted, what new findings could be gotten? Could the empirical findings confirm the superiority of the threshold model compared to the linear model?
"Literature review" section describes the existing views. "Study areas, key variables, and econometric strategies" section depicts the selected study areas, ways to get key variables, and construction of empirical models. "Econometric results" section explores the relationship between spatial structure and green economy empirical results. Finally, concluding remarks are shown in "Concluding remarks and future research recommendations" section. The specific research framework is shown in a graphical way (Fig. 2).

Literature review
In the past few years, the growth effects caused by the change of urban spatial structure have attracted scholars' attention, and two main research fields summarized from the existing papers are as follows: first, a prevailing field about the economic growth effect, that is, the researches on whether and how urban spatial structure affect the economic efficiency and economic growth gap (Meijers and Burger 2010;Garcia-López and Muñiz 2012;Liu et al. 2017a;Zhang et al. 2017a;Li et al. 2018;Nijman and Wei 2020). Second, a research field concerning the resources and environmental effect caused by the evolution of urban spatial structure, that is, how does the urban spatial structure affect the resources utilization and pollution emissions (Clark et al. 2011;Burgalassi and Luzzati 2015;Hankey and Marshall 2017;Muñiz and Sánchez 2018;Han et al. 2020;Lee and Lee 2020;Liu et al. 2020a).
After a review of the existing papers, this article finds that, when they analyze the growth effects of urban spatial structure, most of the papers focus on the growth effect in a single perspective, e.g., "how does the evolution of urban spatial structure affect the economy" and "how does the evolution of urban spatial structure affect the environment" are researched separately. Although a single research objective is necessary for a deeper cognition in its own field, an integrated objective is still needed, because ignoring or weakening any aspects is not conducive to the green economy.
As the urbanization goes on, the polycentric spatial structure, one of the urban spatial structures, emerges in policymakers' urban planning more than ever before, which also is beloved and advocated by many scholars (Meijers and Burger 2010;Liu et al. 2017b). Specifically, the extant studies focus on discussing the relationship between urban spatial structure and transportation (Gardrat 2021) and urban spatial structure and air pollution dispersal (Burgalassi and Luzzati 2015;Yuan et al. 2018;Yang et al. 2020); moreover, some of the extant papers assert that polycentric spatial structure may outperform the monocentric spatial structure in some kinds of growth effects. For instance, a polycentric structure is more conducive to improvements in total factor energy efficiency (Yu 2021), and it decreases the mean carbon dioxide concentrations of city regions ). However, the previous studies usually focus on city individual, when it comes to a perspective of city spatial distribution in a larger space, e.g., urban agglomerations, does it still hold? Little clear evidence has been made by now. Such issue needs to be solved, because the circumstance, background, and context change over time and space, and strategies may change from a single city to city cluster. For example, due to the existence of "promotion tournaments" (i.e., pursuing political promotion for one governor by means of achieving better economic performance than other governors, in other words, the better the economic performance one governor has, the higher possibility of promotion in political areas he/she has), neighboring cities may adopt mutually competitive strategies to develop the economy (Zhou 2007). Thus, urban agglomeration may have a positive effect on the economy, and the economic growth of individual cities in turn affects the development of urban agglomeration. This forms a positive interaction between the spatial structural evolution of urban agglomeration and economic growth. However, the competition pattern (promotion tournaments) does not seem to be suitable for the environmental aspect, especially environmental policy. The extant literature has pointed out that there are "externalities" in environmental pollution and environmental governance, and the externalities may trigger the "free-riding" behavior in environmental governance (Sigman 2005;Konisky and Woods 2010). Therefore, the development of urban agglomerations and the evolution of their spatial structure may have different effects on the three dimensions of economy, resources, and environment.
In summary, exploring spatial structure's influence on green economy should be attempted to check out which is better, polycentric or monocentric. It is essential in developing countries, especially in China, where urbanization construction and sustainable development are attracting increasing attention.

Study areas
Since the implementation of economic reform and urban agglomerations development planning, the urban agglomerations in China have experienced rapid economic growth and rapid urbanization. It makes a continuous change in city size and ranking, high-speed increase in energy consumptions, and pollution emissions. In existing references, number for the urban agglomerations in China varies across scenarios, for instance, 20 urban agglomerations asserted in existing papers (Fang 2015;Fang et al. 2017) and 19 urban agglomerations mentioned in the 13th Five-Year plan of Chinese government. This paper follows the former one, and the 20 urban agglomerations are mapped in Fig. 3. It should be noted that this paper excludes four urban agglomerations, i.e., Northern Tianshan Mountain, Ningxia Yellow River, Lan-Xi, and Qianzhong that are labeled in Fig. 3, because of limited statistical period for data. Thus, the remaining 16 urban agglomerations are used as the study areas.
Two key variables and corresponding data processing Key variable 1: spatial structure of urban agglomerations Evaluating the spatial structure of urban agglomerations is the basic work. Methods for assessing spatial structure (i.e., monocentric/polycentric) differ in the previous papers. Following Meijers (2008), one of the prevailing indices, Pareto exponent, is employed to calculate the spatial structure of urban agglomerations, which measures how quickly size declines when ordering cities from largest to smallest (measuring the overall degree of disparity in the size distribution): where Rank represents the urban population rank of each city that belongs to each urban agglomeration. Citysize is the total urban population of each city. Coefficient β is the monocentric index: β > 1 represents the monocentric spatial structure; β < 1 means the polycentric one; β = 1 denotes the Pareto distribution.
Admittedly, the Pareto exponent has some flaws for different fitting degree (R 2 ) in different prefecture regions and may not comparable for a disparate number of sub-cities (Meijers and Burger 2010;Li et al. 2018). Therefore, the improved method in extant papers (Meijers and Burger 2010;Liu et al. 2017b) is used to calculate the monocentric index β; that is, according to Eq. (1), the top two, top three, and top four cities in each urban agglomeration are regressed, respectively (i.e., calculate the slope of the regression line of city rank-size distribution in each urban agglomeration), and then the three values are averaged to get the monocentric index β. Figure 4 highlights the differences and changes of the monocentric index of 16 urban agglomerations according to the Eq. (1), and the value 1 means the Pareto distribution line. (2) Monocentric urban agglomerations account for nearly a half (right hand in the figure); some urban agglomerations experience a decreasing monocentric score, i.e., towards the polycentricity (e.g., Yangtze River Delta urban agglomeration), while some other urban agglomerations that initially appeared as polycentric have become monocentric (e.g., Beibu Gulf urban agglomeration).

Key variable 2: green economy development level of urban agglomerations
Now, a comprehensive evaluation indicator system is constructed to calculate the green economy development level of the 16 urban agglomerations. Since the green economy first proposed by Pearce et al. in Pearce et al. 1989, its connotation has gradually enriched, and papers related to the research perspectives and methods of green economy are substantial. For example, approaches to evaluate the development of green economy are classified as comprehensive evaluation (Wang et al. 2019;Wu et al. 2021;Abid et al. 2021), efficiency measurement (Ringel et al. 2016;Miao et al. 2019;Pan et al. 2019), cost-benefit analysis (Söderqvist et al. 2015;Carroll and Couzo 2021;Li et al. 2021), and life cycle assessment (Hoogmartens et al. 2014;Röck et al. 2020;Gupta et al. 2020). In a paper titled Green economy and related concepts: An overview, published by Loiseau et al. (2016), the authors concluded that over half of the keywords related to "green economy" belong to the semantic fields of economy, environment, and resources (e.g., issues named economic development, growth, cost, climate change, renewable resources, energy consumption). Actually, it is difficult to get a comprehensive and systematic indicator system to measure the development of green economy because of abundant connotations of green economy itself (Gregorio et al. 2018). This paper follows the conclusion made by the previous scholars (Loiseau et al. 2016;D'Amato et al. 2017D'Amato et al. , 2019 to deal with the connotation of green economy. That is, the following three subsystems, economy, resource, and environment, are used to evaluate the green economy of Chinese urban agglomerations. Selecting indicators used for evaluating the green economy is the primary procedure. However, due to the lack of statistical data, constructing a database for cities is always not easy. Based on the existing papers (Xie et al. 2016;Haider et al. 2018;Tian and Sun 2018;Merino-Saum et al. 2018;Verma and Raghubanshi 2018;Zhang et al. 2018;Wu et al. 2021), this paper constructs an evaluation indicator system (Table 1) containing three levels: the first one is the target level, which represents green economy; the second one is standard level, including the three subsystems: economy, resources, and environment; the third one is the indicator level, containing a total of 19 indicators.
Next, this paper proceeds with the method for calculating the indicator system. In extant literature, several comprehensive evaluation methods are used. Such as principal component analysis method, factor analysis method, entropy weight method, and TOPSIS method. Here, the projection pursuit model (PPM) is used to evaluate the green economy development level based on the indicator system (Espezua et al. 2014). The PPM can avoid the loss of useful indicator information, bringing a relatively full reflection of things that are evaluated (Wei et al. 2016). Especially, when managing data characterized by high-dimensional nonlinear and non-normal, the PPM is a highly accurate statistical method (Wei et al. 2016). Steps for modeling are shown below.
First, the indicators contained in the evaluation system are standardized (Table 1).
Second, a projection indicator function is constructed. Suppose that a = {a 1 , a 2 , ⋯, a n } is n-dimensional unit vector, and Z i denotes the projected characteristic value of Z ij , i.e., i = 1, 2, ⋯m, j = 1, 2, ⋯n, which can be depicted as follows: Next, the projected objective function of green economy is as follows, which contains more information compared with Z i : where S(a) is the standard deviation of Z i and D(a) is the local density of Z i ; formulas are as follows: where E is the mean value ofZ i ; Ris the window radium of the local density usually taken as 0.01; r ij = |Z i − Z j |is the distance between a certain-two projected characteristic values; u(t) is unit step function (indicator function), and The optimal projection direction a j will be calculated, which refers to the weight of each indicator. Thus, the  (2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015)(2016)(2017)(2018) published by Chinese National Bureau of Statistics; "/" means division. The selected indicators are divided into "+" (rising) and "-" (constrained) based on their attributes. Among them, the "+" means an indicator that positively drives the green economy, a higher value usually means a stronger ability for green economy; and the "-" indicates the environmental and resources cost paid for the economic growth, i.e., a lower value implies a better performance of green economy comprehensive evaluation value Z i of green economy for each city and the urban agglomerations can be obtained by putting a j into formula (3). Scores of the three subsystems, economy, resource, and environment, can be also calculated based on formula (3). Figure 5 presents the score of green economy and its three subsystems in 16 urban agglomerations from 2003 to 2017 calculated by the PPM. As can be seen, first, the average value of green economy rises from 0.4269 in 2003 to 1.0733 in 2017, indicating an improvement in green economy. Second, the values of three subsystems of green economy differ a lot. The economic subsystem and resources subsystem witness a continuous rise, and the environmental subsystem shows only slight increasement; the ranking of resources subsystem exceeds the environmental subsystem in the second half.

Baseline linear model
To empirically check the effect of urban agglomeration spatial structure on green economy, these articles econometric models start with a baseline panel regression model shown below. As for the control variables mentioned in Eq. (8), it includes foreign direct investment (FDI), research and development investment (R&D), and urbanization rate (Urban). Reasons for selecting them are as below. For the FDI, the close relationship between FDI and economic growth, environmental quality has been proven (Newman et al. 2015;Huang and Zhou 2020). Therefore, FDI should be considered a factor affecting the green economy. For the R&D, although owing to the heterogeneity of R&D, not all the R&D bring new technology or contribute to green economy, the indigenous R&D, especially the energy-saving R&D still plays a significant role in decreasing carbon intensity (Huang et al. , 2021a. Moreover, R&D is a critical driving force to technology progress, which is closely related to economic growth, energy efficiency improvement, and pollution reduction. Finally, for the urbanization rate, it may influence green economy because of its effects on the pollution emissions, agglomeration economic effects, and resources utilization intensity (Zhang et al. 2017a, b;Huang and Wang 2020).
As mentioned in Meijers and Burger (2010), there are probably endogeneity problems when analyzing the impact of spatial structure on economic productivity; therefore, this paper sets up another two models to address the endogeneity problems in empirical test. First, it employs an empirical model with a time lag for the all the explanatory variables based on Eq. (8) and shown as below.
Second, a dynamic panel model improved by previous papers (Arellano and Bond 1991;Blundell and Bond 1998) is another convincing way to alleviate the endogeneity problems in regression analysis. Therefore, based on Eq. (8), a dynamic panel model, in which one period lagged of the green economy development level (GE it -1 ) is captured, is set to check the effects of spatial structure on green economy, and corresponding model is shown below.
Dynamic panel threshold model Traditional linear regression method fails to tackle structural breaks (Huang et al. 2019). In this study, it is likely that the effects of urban agglomeration spatial structure on green economy may vary across the monocentric index and show different characteristics. In other words, different monocentric index range may bring various green economic growth effects, and there is probably a nonlinear relationship between spatial structure and green economy. To verify such hypothesis, a panel threshold model originally proposed by Hansen (1999) and Hansen (2000) could be used. It can investigate the changes in the impact that the independent variable has on green economy development level at different intervals. This is helpful to demonstrate whether there is a significant change in the effect of monocentric index on green economy in different intervals, so as to reveal a better spatial structure of urban agglomeration. First, the threshold model with one threshold value is shown below: where 1(·) represents the indicator function. When the expression in parentheses is false, the value is 0; otherwise, the value is 1. Mono it is the threshold variable, γ is the threshold value, β 1 is the threshold coefficient when Mono it is lower than γ, and β 2 is the threshold coefficient when Mono it is higher than γ. Control variables are same as those in Eq. (8). β j represents the coefficients of control variables.
It should be noted that there may be endogeneity problems in empirical test as asserted in previous context of this paper. Thus, the empirical tests based on Eq. (11), the static threshold model, may be biased. To solve such issue, this paper employs the dynamic panel threshold model developed by the existing papers (Kremer et al. 2013;Seo and Shin 2016) that extend Hansen's (1999) static model for endogenous regressors. Dynamic models are advantageous over static models, because they easily capture more information on the evolution of urban agglomeration spatial structure, and also, the dynamic panel threshold model could not only endogenously determine the threshold value based on the characteristics of the constraint variables, but also better deal with the potential endogeneity problem. The dynamic model with single threshold is as follows: where GE it -1 denotes the one period lagged of the green economy development level, γ means the threshold value, and the generalized method of moments (GMM) estimation is used in order to allow for the endogeneity.
Further, if the single threshold holds, the multi-threshold needs to be checked, and then, the dynamic threshold model with a multi-threshold, such as double threshold model, can be shown below:  Notes: t-statistics are in parentheses; *, **, and *** stand for significance at 10%, 5%, and 1%, respectively; P value of AR (2) indicates no second-order correlation Data sources of the variables of econometric regressions Table 2 presents the critical information of the variables used in econometric models.

Econometric results
Empirical results 1: how does spatial structure affect the green economy? index induces a 0.3371% decrease in green economy, that is, towards the monocentric spatial structure constrains the improvement of green economy. Since the decrease in monocentric index means a polycentric trend, therefore, it indicates that the evolution to polycentric of urban agglomeration spatial structure in China contributes to the green economy than that in monocentric one.

Baseline linear model results
To ensure a robust result, another three regressions are made, all of which also could alleviate the endogeneity to some degree. The first two regressions are a one-orderlagged and two-order-lagged of explanatory variables based on the linear model (Eq. (9)), respectively, and the results are shown in columns (2) and (3); the third regression is checked based on dynamic model (Eq. (10)) with the prevailing SYS-GMM estimation; it is clear that all the coefficients present robust results. Additionally, the three control variables are all significantly and robustly related to green economy, indicating their effects on green economy.

Dynamic threshold model results
This section proceeds to estimate the threshold model to check the nonlinear effect of urban agglomeration spatial structural evolution on green economy, through which the validation of spatial structure's effect on green economy can be further examined. To check the threshold effect, the bootstrap-based testing procedure is used to obtain an approximation of the Fstatistics and P-values. For each of the bootstrap tests, 500 bootstrap replications are used. As shown in Table 4, for the monocentric index, F statistics are significant at least 10% level for single threshold, double thresholds, and triple thresholds, indicating that there are three thresholds, which probably brings structural breaks and different effects varies across scenarios. The results indicate that there are at least three thresholds in the relationship between monocentric index and green economy, implying that the green economy is sensitive to the urban agglomeration spatial structural evolution. Table 5 shows the regression results of monocentric index. As can be seen, when monocentric index≤0.8436, coefficient of monocentric index to green economy is −0.9206; when 0.8436<monocentric index≤0.9671, coefficient value is −0.6322; when 0.9671<monocentric index≤1.5849, coefficient value is −0.8854; when monocentric index>1.5849, coefficient value is −0.8037; meantime, such four coefficients are all statistically significant at the 1% level. Overall, for urban agglomerations, different monocentric index ranges exert different impacts on green economy, as the monocentric index value increases, its effects on green economy vary. When 0.8436<monocentric index≤0.9671, the monocentric index exerts the best impact on green economy, indicating that a polycentric urban agglomeration (i.e., when the monocentric index is 0.8436~0.9671, an urban agglomeration can be regarded as polycentric according to the Pareto exponent) is more conducive to the green economic growth.
From the above analysis, it can be seen that there is a nonlinear relationship between the spatial structure and the green economy of urban agglomerations; different stages of spatial structure evolution have different effects on the green economy; on the whole, there is an optimal spatial structure to promote green economic growth in urban agglomerations. Then, from the perspective of promoting green economic growth, among the 16 urban agglomerations, which urban agglomerations have always been in the optimal spatial structure? Which ones are gradually moving away from the optimal spatial structure? And which ones are gradually approaching the optimal spatial structure? To address these questions, Fig. 6 is drawn. In the figure, the dots are the trajectories of the monocentric index of 16 urban agglomerations from 2003 to 2017, and the two horizontal blue dotted lines are the optimal range for achieving green economy. The optimal range is obtained through the threshold regression model results (see "Dynamic threshold model results" section). From Fig. 5, three main findings are shown below: (1) During 2003-2017, five urban agglomerations are very close to the optimal range, such as Pearl River Delta and Mid-southern Liaoning urban agglomerations; (2) some urban agglomerations tend to be far from the optimal range, such as Guanzhong and Beibu Gulf urban agglomerations; (3) some urban agglomerations are moving towards the optimal range, but there is still much room for improvement, such as Jinzhong, Chengyu, and Hu-Bao-E-Yu urban agglomerations. In short, during the study period, the positive effect of the evolution of the spatial structure of Chinese urban agglomerations on green economy has not been fully stimulated.
Empirical results 2: how does spatial structure affect the three subsystems in green economy?

Baseline linear model results
Now, this paper proceeds with detailed research about the three subsystems. To ensure a robust result, for each   Notes: t-statistics are in parentheses; *, **, and *** stand for significance at 10%, 5%, and 1%, respectively subsystem, three regressions are made, i.e., no-lagged independent variable, one-lagged independent variable, and twolagged independent variable based on the baseline linear model, respectively. Corresponding results are shown in Table 6. Specifically, as shown in columns (1)-(3), the variable monocentric index is negatively correlated with economic subsystem at least 5% level, indicating that the increase in monocentric index in urban agglomerations constrains the economic growth, which verifies that the tendency to monocentric will not contribute to the improvement in economic growth, such conclusion is in line with the previous study (Hou and Sun 2016). Coefficients in columns (4)-(6) witness the negative relationship between monocentric index and resources subsystem, indicating that a 1% increase in monocentric index brings 0.0504~0.0755% decrease in resources subsystem, which also implies that the trend to  Notes: t-statistics are in parentheses; *, **, and *** stand for significance at 10%, 5%, and 1%, respectively monocentric does not benefit the resource utilization. As for the effect of monocentric index on environmental subsystem, from the positive coefficients in columns (7)-(9), this paper argues that, unlike the other two declarations, increase in monocentric index is positively correlated with the environmental protection, implying that the increase in monocentric index may benefit the environmental protection in some degree.

Dynamic threshold model results
Next, this article explores the threshold regression to check the possible nonlinear effects for better insights in seeking the effects of spatial structural evolution on the three subsystems. Table 7 demonstrates the test of threshold effect, and the F statistics are all significant for single threshold, double thresholds, and triple thresholds. It is evident that the effects of spatial structure evolution on the three subsystems are sensitive to the changes in monocentric index. Table 8 illustrates the estimated results for the three subsystems one by one. First, for the economic subsystem, all the regression coefficients are statistically significant. Specifically, when monocentric index≤0.8436, coefficient value is −0.8759; when 0.8436<monocentric index≤0.9671, coefficient value is −0.5949; when 0.9671<monocentric in-dex≤1.5849, coefficient value is −0.8628; when monocentric index>1.5849, coefficient value is −0.7574; Overall, for urban agglomerations, different monocentric index ranges exert different impacts on economic subsystem, as the monocentric index value increases, its effects on economic subsystem vary. When 0.8436<monocentric index≤0.9671, the monocentric index exerts the best impact on economic subsystem. It indicates that a polycentric urban agglomeration (the monocentric index 0.8436~0.9671) is more conducive to the economic growth.
Third, for the environmental subsystem, when monocentric index≤0.5964, coefficient value is −0.076; after the monocentric index exceeds the threshold value 0.5964, coefficient is insignificant any more but vary from negative to positive, when monocentric index>1.2143, coefficient value is 0.0288 at the 10% significance level, indicating a positive correlation between the monocentric index and the environmental subsystem. It also implies that a polycentric urban agglomeration spatial structure probably triggers the pollution emissions. Similar findings could be found in existing papers, such as polycentricity is significantly positively correlated with CO2, PM2.5, and PM10, and polycentricity alone does not reduce pollution emissions (Burgalassi and Luzzati 2015;Liu et al. 2020b).
In summary, based on the results of linear and nonlinear models, the following main findings are obtained: (1) Although the polycentric spatial structure shows better performance than the monocentric spatial structure in terms of promoting the green economy in urban agglomerations, polycentric spatial structure does not always boost the development of green economy. In other words, excessively polycentric spatial structure will constrain the green economy; (2) promoting the green economy requires the coordinated improvement of the three subsystems of economy, resources, and environment. However, it can be seen from the findings that the impact of spatial structural evolution on the environmental subsystem is not like the economic and resources subsystems; i.e., to get a better performance of economic growth and efficient resources utility, the polycentric spatial structure of urban agglomeration is prior to the monocentric one, whereas to achieve a better performance of environmental protection and pollution control, the monocentric spatial structure seems to be the first choice rather than the polycentric one. Therefore, to promote green economic growth through the construction of urban agglomerations, it is necessary to comprehensively consider multiple aspects. Urban agglomerations should not simply follow a monocentric spatial structure or a polycentric spatial structure.

Concluding remarks
Understanding whether and how urban agglomeration spatial structure affects green economy is of great importance for exploring the growth effects of urban agglomeration. Analyzing such issues could reveal whether urban agglomeration achieves economic growth, resources saving, and environmental protection simultaneously. However, as of now, theoretical and empirical evidence regarding to this has not received strong supports. To bridge this gap, this paper conducts a comprehensive study to shed light on how the evolution of urban agglomeration spatial structure affects the green economy.
The conclusions of the linear model compared with the dynamic threshold model that employed in this paper reveal differences in assessing spatial structure's effect on the green economy. This means that the linear model does not capture the nonlinear effects stemmed from the existence of the differentiated spatial structure ranges; therefore, the threshold model is probably the better econometric model to evaluate the spatial structure's influence on the green economy. Specifically, this paper's findings not only support the existing studies, but also have new discoveries. First of all, this paper uses a general linear model to conclude that towards polycentric spatial structure of urban agglomerations is beneficial to green economic growth. Further, the nonlinear regression results reveal that although it can be clearly known from the linear regression results that the polycentric trend is conducive to the development of green economy, there is an optimal range in polycentric spatial structure. In other words, higher polycentric value does not necessarily mean a better green economy performance. Thus, through the findings, this paper improves the conclusions in the existing linear regression literature.
Some concluding remarks are given below. First, in general, towards polycentric is contributive to green economy, while the excessive polycentric could not benefit the green economic growth. From the perspective of economic growth and resource intensive utilization, a polycentric urban spatial distribution should be constructed so as to avoid the excessive concentration of resources and the reduction of resource efficiency caused by the dominance of one central/large city. However, excessive polycentricity may also lead to the loss of economic efficiency and resource utilization and hinder the green economic growth. In particular, this paper also finds that, from the perspective of achieving better environmental protection quality and urban pollution control, the urban agglomerations stylized by monocentric have comparative advantages than polycentric ones. Therefore, the construction of urban agglomerations should not weaken the status and hierarchy of core cities. On the contrary, it is still very important to consolidate the status of existing core cities. In summary, for a certain urban agglomeration, its spatial structure is relatively stable, and therefore, the policymakers should give enough considerations to this to avoid a policy bias. In other words, since the spatial structure of urban agglomerations is not easy to adjust in the short term, it is necessary to demonstrate as clearly as possible which choice the urban agglomerations prefer in the next stage: economic growth, resource conservation, or pollution control? For instance, for urban Notes: z-statistics are in parentheses; *, **, and *** stand for significance at 10%, 5%, and 1%, respectively; coefficients of control variables and one-lag of explained variables of the three subsystems are not shown and available on request agglomerations with more developed economy but relatively serious pollution, the monocentric index can be appropriately increased to obtain better pollution abatement, while for urban agglomerations with relatively backward economy but higher environmental quality, the monocentric index can be moderately reduced (i.e., towards the polycentric spatial structure) to enhance the flow of factors of production and the market competition and thereby to speed up the economic development and expand the economic size. These are probably conducive to driving the green economy of urban agglomerations. Second, most urban agglomerations in China are not currently in the optimal spatial structure ranges for green economic growth. The spatial structural evolution of urban agglomerations presents obvious heterogeneous characteristics, and the monocentric index of some urban agglomerations has experienced two different trajectories (far away or close to the optimal range). Therefore, it is necessary to formulate a reasonable urban agglomeration spatial pattern according to its own development level or stage, so as towards the green economy.

Future research recommendations
This paper leaves some unaddressed issues for future research. It only presents the relationship between urban agglomeration spatial structure and green economy. However, the mechanisms behind the empirical results are still not fully clear and need thorough examination in future study. Another limitation is in the miss of some useful indicators because of the inefficient data collection; just as asserted by Verma and Raghubanshi (2018), application of indicators and subsequent assessment of urban sustainability will be most influenced by data availability. For example, the green patent, which is probably treated as a valuable indicator for assessing green economy, is not employed because of the difficulties in obtaining relatively complete data. Lastly, evaluating the green economy performance is not easy owing to its dynamic and complicated feature, just as noted by Benson et al. (2021), "meanings of the green economy changes in a changing world." Although this paper endeavors to overcome this towards a better research, some unchecked or unobserved aspects are out of the sightseeing.
Author contribution The idea and original writing for the article are conducted by Yue Huang; organization, critical feedback, and supervision are made by Ruiwen Liao. All authors have read and approved the manuscript. Availability of data and materials Available upon request.

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Competing interests The authors declare no competing interests.