1. Introduction

2. Literature review

3. Research methodology, sample, and data

3.1. Variable measures

3.1.1. Measurement: Relative degree centrality and betweenness centrality

First, in terms of network model setting, we employ the L-space model, that is, there is no multiple connections between two nodes. Second, since some cities may have opened more than one HSR station, we define a HSR city as a node in order to avoid double counting. Then, we use the improved degree and betweenness centrality formula [12] to measure the importance of cities in HSR network. This formula is a standardized result and has two advantages for this study :(1) the influence of network size change is eliminated in variable selection, which reduces the endogeneity problem of dynamic analysis; (2) nodes are placed in a broader network perspective, which highlights the interaction and comparative advantage between nodes. Specifically, degree centrality reflects the ability of direct link between a node itself and other adjacent nodes. It can be defined as Equation (1)

$$RD{C}_{ij}=\frac{1}{N-1}·{\displaystyle \sum }_{j=1,i\ne j}^n{K}_{ij}$$

(1)

Where N refers to all cities with HSR that year, n = N-1, $K_{ij}$ represents the HSR connection between city j and city i, If i and j are directly connected through a HSR line, $K_{ij}$ = 1, otherwise, $K_{ij}$ = 0.

Betweenness centrality refers to the number of shortest paths passing through a node. It assesses the capacity of a node's indirect control over other nodes and potentially the entire network, defined as Equation (2)

$$RB{C}_i=\frac{2}{N^2-3N+2}·{\displaystyle \sum }_{f\ne i\ne t}^n\frac{{\alpha }_{od}^i}{{\delta }_{od}}$$

(2)

Where ${\alpha }_{od}^i$ represents the number of HSR connections through city i among all the shortest HSR connections from city o to city d, ${\delta }_{od}$ represents all the shortest HSR connections from city o to city d.

3.1.2. Measurement: Quality of urbanization

Drawing on the research of Wang et al. [48], quality of urbanization is mainly divided into five aspects: population, economy, space, environment, and society. For population urbanization, quality of urbanization not only seeks to improve the urbanization rate, but also takes into account the urban population density and the non-primary industrial population which reflect the utilization efficiency of urban resources and the employment structure respectively. In terms of economy, per capita GDP and the proportion of output value of secondary and tertiary industries are two common indicators to measure the quality of economic development, reflecting individual contribution and structure composition of regional economic development respectively. Besides, GDP density of non-agricultural industries are supplemented to reflect the space utilization rate of economic growth. For the space, how to give full play to the value of land resources and improve land utilization is another key issue of urbanization quality. The capita road areas and capita living areas are two good indicators of urban congestion. The proportion of built-up area and per capita built-up area respectively reflect the construction scale and utilization efficiency of urban space. Regarding the environment, sustainable development clearly emphasizes "ecological civilization" and seeks a "green and environmentally friendly " development mode. Therefore, per capita green space area, green coverage rate of built district, domestic garbage treatment rate, and wastewater treatment rate are included in the urbanization evaluation system to reflect the urban greening construction and waste treatment. In addition, the quality of urbanization has put forward higher requirements on education, medical care, culture, and resident income, so as to improve the level of social security and the quality of resident life. As a result, per capita education expenditure, the number of beds per 1,000 people, and other indicators are included in the social aspects. Finally, considering the five aspects, we construct the corresponding the quality of urbanization index system at city level which contains 18 indicators, as shown in Tab. 1.

The quality of urbanization is measured by panel entropy weight method (PEWM). PEWM can effectively extract the information, avoiding the randomness, presumption and other deviation problems caused by determining the weight due to subjective factors. By this method, the indicator weights are determined based on the full period sample data rather than a single period sample, which makes the data comparable in time dimension. The specific calculation steps are as follows:

Standardization, as shown in Equations (3) and (4)

$$\mathrm{Positive}\mathrm{indicator}\text{:}{A}_{tij}=\left(X_{tij}-\min \left\{X_j\right\}\right)/\left(\max \left\{X_j\right\}-\min \left\{X_j\right\}\right)$$

(3)

$$\mathrm{Negative}\mathrm{indicator}\text{:}{A}_{tij}=\left(\max \left\{X_j\right\}-X_{tij}\right)/\left(\max \left\{X_j\right\}-\min \left\{X_j\right\}\right)$$

(4)

Where t is the year, i is the city, j is the index, $A_{tij}$ is the value after standardization, $X_{tij}$ is the initial value. and $\max \left\{X_j\right\}$ and $\min \left\{X_j\right\})$ represent the maximum and minimum value of the index j in all of the years and the cities studied.

Calculation of the proportion of $A_{tij}$, as shown in Equation (5)

$$B_{tij}=A_{tij}/{\displaystyle \sum }_{t=1}^m{\displaystyle \sum }_{i=1}^n{A}_{tij}$$

(5)

Where m and n are total years and total cities, respectively, equal to 11 and 273 in this article.

Calculation of entropy value and difference coefficient, as shown in Equations (6) and (7)

$$C_j=-\frac{1}{\ln mn}·{\displaystyle \sum }_{t=1}^m{\displaystyle \sum }_{i=1}^n{B}_{tij}·\ln \left(B_{tij}\right)$$

(6)

$$D_j=1-C_j$$

(7)

Where $C_j$ denotes the entropy value of index j, $D_j$ denotes the difference coefficient of index j.

Calculation of weight of each index and quality of urbanization, as shown in Equations (8) and (9)

$$W_j=D_j/{\displaystyle \sum }_{J=1}^r{D}_j$$

(8)

$$OQ{U}_{tij}={\displaystyle \sum }_{j=1}^r{W}_j·B_{tij}$$

(9)

Where r is the total number of indexes, equals to 18 in this paper, $W_j$ denotes the weight of index j, $OQ{U}_{tij}$ denotes the original value of quality of urbanization. Since the value is too small, we enlarged it (multiply 1000) and obtained the final quality of urbanization (QU).

Table 1. Evaluation system of urbanization quality.

Table 1. Evaluation system of urbanization quality.

Index I	Index II	Weight (%)	Unit
Populationur banization	$X_1$: Urban population density	35.44	Person/square kilometer
	$X_2$: Proportion of urban district population	35.40	%
	$X_3$: Proportion of employees in secondary and tertiary industries	0.40	%
Economy urbanization	$X_4$: Per capita GRP	1.81	Yuan
	$X_5$: Proportion of GRP of secondary and tertiary industries	1.18	%
	$X_6$: GDP density of secondary and tertiary industries	7.66	10 thousand yuan/km2
Space urbanization	$X_7$: Proportion of built-up area	7.00	%
	$X_8$: Per capita built-up area	0.78	Square meter
	$X_9$: Per capita living area in urban	0.54	Square meter
	$X_{10}$: Per capita road area in urban	0.79	Square meter
Environment urbanization	$X_{11}$: Per capita green area	0.48	Square meter
	$X_{12}$: Green coverage rate of built-up district	0.09	%
	$X_{13}$: Domestic garbage treatment rate	0.06	%
	$X_{14}$: Wastewater treatment rate	0.14	%
Society urbanization	$X_{15}$: Per capita education expenditure	2.13	Yuan
	$X_{16}$: Medical facility beds per 1,000 people	0.98	Set
	$X_{17}$: Books in public libraries per 100 people	4.51	Piece
	$X_{18}$: Average salary of urban employees	0.95	Yuan/Person

3.3. Sample and data

The sample includes 273 cities in China for the period 2009-2019, covering all prefecture-level cities and municipalities in mainland China except Tibet and 12 cities with severe data deficiencies. A few missing value data are processed by exponential smoothing method or mean value. In terms of sample interval selection, most scholars agree that 2008 was the first year of HSR opening in China, but we choose 2009 as the starting point for two reasons: first, as a major infrastructure construction, the effect of HSR often has a lag, so we treat all HSR opening years with a lag of half a year. Second, after that, only one HSR line (Nanjing to Hefei) opened in 2008, which cannot be regarded as “network”. In addition, since China suffered from a “covid-19” epidemic shock and strict mobility restrictions in 2020, which do not reflect the true benefits of high-speed railway, the data for that year are excluded. The HSR data are from the China Railway Yearbook from 2008 to 2019. Other data are collected from the China City Statistical Yearbook, China Regional Economic Statistical Yearbook, China Urban and Rural Construction Statistical Yearbook and provincial yearbooks. Table 4 shows the descriptive statistics for all variables.

Table 2. Descriptive statistics of various variables.

Table 2. Descriptive statistics of various variables.

Variable	Economic implications	N	Unit	Mean	Std. dev	Min	Max
qu	quality of urbanization	3003	-	0.1809	0.1870	0.0176	2.7341
hsr_dum	high-speed railway dummy	3003	-	0.4179	0.4933	0.0000	1.0000
hsr_l	high-speed railway lines	3003	-	0.6044	0.8911	0.0000	6.0000
hsr_rdc	relative degree centrality	3003	%	0.7269	1.2490	0.0000	16.6670
hsr_adc	absolute degree centrality	3003	-	0.8578	1.1538	0.0000	6.9187
hsr_rbc	relative betweenness centrality	3003	%	2.2888	5.3738	0.0000	45.7290
hsr_abc	absolute betweenness centrality	3003	-	269.4749	724.5421	0.0000	8738.812
rtec	technology support	3003	%	0.0026	0.0024	0.0001	0.0415
rfin	financial development	3003	%	2.3732	6.4232	0.0044	128.5692
rmar	market factors	3003	%	0.3812	0.1083	0.0264	1.0126
rfdi	foreign direct investment	3003	%	0.0180	0.0198	0.0000	0.4599

4. Empirical results

4.1. The spatio-temporal evolution characteristics of HSR network

Table 3 shows the development of HSR network in the first 19 HSR cities in 2009 and 2019, including the number of HSR lines, relative degree and betweenness centrality. In terms of cities, China’s high-speed railway network mainly originates from metropolis, including two municipalities (Beijing and Tianjin), seven provincial capital cities (Shijiazhuang, Wuhan, Jinan, etc.) and cities with strong economic strength such as Qingdao, Zibo, Weifang (the top 40 of GDP), while 7 medium and small cities (out of 100 in GDP) are embedded in the HSR network. In terms of HSR lines, in addition to Yangquan, Jinzhou, Huludao, Liu’an four small cities, other cities have opened two or more high-speed rail lines. Hefei, Jinan and other metropolis have opened four high-speed rail lines, while Tianjing, Nanjing and Shenyang even have reached five. Only from the absolute number of HSR lines, the results clearly show that large cities gain the most from the HSR networking process. However, in the global network perspective, the result takes a shocking reversal. In terms of relative degree centrality, the absolute advantage of the lines does not translate into an absolute advantage of the network location. The relative degree centrality of all cities tends to decrease and eventually converge. This is not a local phenomenon, and the decline of national average (from 8.77 to 1.11) and variance (from 3.85 to 0.51) also strongly supports this result. According to the Equation (1), it can be well explained from the speed and layout of China ' s HSR construction. (1) China 's HSR network has expanded very rapidly, with an average of 20 cities opening high-speed rail each year, significantly increasing the base of HSR network nodes (2) Most of China's HSR lines are long-distance inter-provincial lines such as the Beijing-Shanghai line (through 3 municipalities and 4 provinces) and the Beijing-Kowloon line (through 2 municipalities and 7 provinces), which have many stations but a single connection. In terms of betweenness centrality, the law seems not so obvious. Some cities have obvious line advantages (e.g., Hefei), but the degree centrality is much lower than that of single-line cities (e.g., Huludao). One possible explanation is that these cities have a critical geographical location or are located in mandatory routes. Both results show that the absolute amount of HSR infrastructure (such as HSR lines) is not a complete reflection of the importance of the city's location, which supports our improved measurement.

Figure 1 shows the spatial distribution of changes in location importance in relative degree and betweenness centrality from 2009 to 2019. In order to more clearly present the dynamic change process, we further equate this period into three time points, 2009, 2014, and 2019. The evolution of relative degree centrality is shown in (a)-(c) of Figure 1, while (d)-(f) demonstrate the evolution of relative betweenness centrality. From these maps, some conclusions can be drawn: (1) In terms of overall evolutionary trends, the development of China's high-speed railway has gone through three major spatial evolution stages, namely "point distribution - corridor distribution - network distribution". The locational position of HSR cities is becoming more and more balanced. We can see that in the period 2009-2014, most of the cities have increased their locational importance (both degree centrality and betweenness centrality) due to the opening of high-speed railway. During this period, along the four horizontal and four vertical HSR trunk lines, a clear agglomeration of high-location cities has been formed. However, with the further expansion of the HSR's scale from 2014 to 2019, the locational advantages of these cities are rapidly fading. (2) From a regional perspective, both degree centrality and betweenness centrality are higher in cities in the Eastern and Central regions, indicating that the eastern and central regions are the pivotal zones for the development of high-speed railway. (3) For changes in two types of centralities, relative degree centrality continues to decline, but relative intermediary centrality is rising. This means that more and more high-speed railway cities are playing the role of "interchange" rather than "destination", and the role of each city in the high-speed railway network will become more and more prominent.

Table 3. HSR development in the initial HSR cities.

Table 3. HSR development in the initial HSR cities.

City	hsr_l		hsr_rdc		hsr_rbc
	2009	2019	2009	2019	2009	2019
Beijing	1.0000	3.0000	5.5560	1.5000	0.0000	3.1010
Tianjing	1.0000	5.0000	5.5560	2.0000	0.0000	20.1610
Shijiazhuang	1.0000	3.0000	5.5560	2.0000	0.0000	10.9280
Qinhuangdao	1.0000	2.0000	5.5560	1.0000	0.0000	17.7990
Nanjing	1.0000	5.0000	5.5560	3.5000	0.0000	45.7290
Hefei	2.0000	4.0000	11.1110	1.0000	1.9610	5.0090
Wuhan	1.0000	2.0000	5.5560	3.0000	0.0000	9.7540
Huanggang	1.0000	2.0000	11.1110	1.5000	1.9610	4.0860
Ji'nan	1.0000	4.0000	5.5560	2.0000	0.0000	23.8520
Qingdao	1.0000	4.0000	5.5560	1.5000	0.0000	4.5030
Zibo	1.0000	2.0000	11.1110	1.5000	1.3070	6.1910
Weifang	1.0000	2.0000	11.1110	1.0000	1.3070	5.3370
Taiyuan	1.0000	3.0000	5.5560	1.5000	0.0000	6.5380
Shenyang	1.0000	5.0000	5.5560	3.0000	0.0000	9.0960
Panjin	1.0000	2.0000	16.6670	2.5000	1.9610	7.8020
Yangquan	1.0000	1.0000	11.1110	1.0000	0.6540	6.3740
Jinzhou	1.0000	1.0000	11.1110	2.0000	0.0000	7.9510
Huludao	1.0000	1.0000	16.6670	1.5000	1.9610	17.0950
Liu'an	1.0000	1.0000	11.1110	1.0000	2.6140	4.4090
national mean	1.0526	1.6244	8.7722	1.1117	0.7224	5.2822
national sd	0.2294	1.0107	3.8470	0.5128	0.9470	7.6108

4.2. Spatial autocorrelation test and model determination

This paper examines the spatial agglomeration characteristics and evolution trend of urbanization. As shown in Tab.4, Moran’s I value are all significantly positive at the 1% level, showing that China’s urbanization quality has significant positive autocorrelation during 2009-2019. From the development trend, we can also find that the positive effect is gradually strengthened. This means that China's overall development is more closely linked in space, and the cross-influence of urban development is stronger.

For the selection of best models, at first, the Lagrange Multiplier (LM) and robust LM tests are adopted to examine whether SEM or SLM is more accurate [57]. Both models have been proved to be appropriate for the regression analysis. Then, we run a further LR & Wald test and discovered that neither SEM nor SLM cannot nested in SDM. So, SDM is more representative. Additionally, the P-value in Hausman test was 0.0000, showing that FE model is more appropriate in this case. Combining with above test results, we construct a spatial Durbin regression model with individual and time fixed effects for all our estimations in this paper.

Table 4. Moran’s I of the quality of urbanization in China.

Table 4. Moran’s I of the quality of urbanization in China.

Year	2009	2010	2011	2012	2013	2014	2015	2016	2017	2018	2019
Moran's I	0.055	0.052	0.058	0.054	0.055	0.055	0.062	0.061	0.065	0.047	0.063
P-value	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000

Note: the global autocorrelation test results are based on the geographical distance weight matrix.

4.3. HSR network and the quality of urbanization

We use five HSR proxy variables including dummy variables, absolute and relative degree centrality, absolute and relative betweenness centrality to test the impact of high-speed railway on urbanization quality from non-network, local network and overall network. Cities with a higher centrality indicate a higher importance in the HSR network.

Table 6 reports the estimation results of the whole sample with a MLE method. Odd and even models represent regression results without and with control variables respectively. In models (3)-(6), the coefficients of hsr_rdc and hsr_adc are both negative, suggesting that increase in degree centrality is detrimental to improving the quality of urbanization. Among them, coefficients of hsr_rdc have passed the test of significance at the 1% level while coefficients of hsr_adc does not, further indicating that location changes in global network have a more pronounced impact on the quality of urbanization than changes in local network. In models (7) -(10), the coefficients of hsr_rbc and hsr_abc are both positive, showing that rising betweenness centrality is conducive to promoting the urbanization quality. Of these, only one of the four models, model (10) has passed the significance test and the estimated coefficient of hsr_abc was just 0.0001, demonstrating that the effect of locational change arising from betweenness centrality on urbanization is limited. Since the HSR network actually reduces the relative degree centrality and improves the relative betweenness centrality, all above results show that HSR network can indeed enhance the quality of urbanization. This well verifies hypothesis 1. Meanwhile, by comparing the regression results of models (5) and (8), we can also see that the direct connectivity effect of HSR network would be more pronounced than the intermediary effect. However, it is worth wondering why a decline in the importance of a city drives urbanization instead.This can be explained as follows: With the expansion of high-speed rail network, the line advantage of a single city, especially the HSR hub city (with more lines), will be gradually diluted, which makes the siphon effect of large cities gradually weakened, and the majority of small and medium-sized cities usher in a good opportunity for development [58]. Due to ignoring this dilution effect, the positive effect of high-speed rail has not been effectively reflected in the perspective of non-network and local network. The coefficients of hsr_dum in model (1) and (2) even reache a completely opposite conclusion. Thus, all the evidence demonstrates the necessity of relative index measurement again.

Regarding the impact of control variables, estimation results shows that only the coefficient of rtec is significantly positive across all models. This means that technical support has a relatively stable role in promoting the quality of urbanization, whether based on the network perspective or non-network perspective. Technological innovation often relies on breakthroughs in basic scientific research, so it can result in a systemic rather than a unilateral change [50]. Therefore, for an urban system, the improvement of technological level can promote its overall development from multi-aspects.

Table 6. The result of overall regression.

Table 6. The result of overall regression.

Variables		Dependent variable: Quality of urbanization
		hsr_dum			hsr_rdc			hsr_adc			hsr_rbc			hsr_abc
		(1)	(2)		(3)	(4)		(5)	(6)		(7)	(8)		(9)	(10)
hsr		-0.0087**	-0.0097***		-0.0052***	-0.0047***		-0.0001	-0.0010		0.0002	0.0004		0.0001	0.0001**
W×hsr		0.0326***	0.0067		0.0384***	0.0198*		0.0100***	-0.0055		0.0014*	-0.0007		0.0001	-0.0001**
rtec			4.1260***			4.1080***			4.1606***			4.1530***			4.0645***
rfin			0.0000			0.0000			0.0000			0.0000			0.0000
rmar			-0.0788***			-0.0806***			-0.0807***			-0.0808***			-0.0841***
rfdi			-0.2950***			-0.2940***			-0.2903***			-0.2910***			-0.2821***
rho		0.6600***	0.2800**		0.7770***	0.2810**		0.6686***	0.2858**		0.7640***	0.2880**		0.7471***	0.2939**
sigma2		0.0031***	0.0030***		0.0031***	0.0030***		0.0031***	0.0030***		0.0031***	0.0030***		0.0031***	0.0030***
city FE		YES	YES		YES	YES		YES	YES		YES	YES		YES	YES
year FE		YES	YES		YES	YES		YES	YES		YES	YES		YES	YES
N		2730	2730		2730	2730		2730	2730		2730	2730		2730	2730
logL		4008.9755	4059.2649		4011.5885	4062.8970		4005.8872	4056.2412		4002.2400	4056.5197		4003.6787	4059.3856
Vif		1.0000	1.1100		1.0000	1.0700		1.0000	1.1100		1.0000	1.0700		1.0000	1.0700
LM-sar		226.672***	89.904***		679.041***	176.317***		222.179***	86.823***		616.320***	165.752***		604.148***	170.270***
(Robust)		0.475	7.478***		54.134***	3.527***		1.536	10.985***		10.747***	0.543		44.508***	0.768
LM-sem		484.604***	357.409***		627.286***	277.912***		523.487***	393.390***		636.837***	311.785***		641.398***	309.710***
(robust)		258.407***	274.983***		2.378	105.122***		302.844***	317.553***		31.264***	146.576***		44.508***	140.208***

Notes: ^⁎ P < 0.1. ^⁎⁎ P < 0.05. ^⁎⁎⁎ P < 0.01.

4.4. HSR network and the quality of urbanization: dynamic analysis

The rolling-window regression is applicable when the correlation between variables is time-varying. This method divides the whole sample into several sub-samples by setting a fixed rolling window (time span T), and then examines the impact of each period separately. Drawing on this idea and combining with the spatial econometric model, this paper examines the dynamic impact of the HSR network on the quality of urbanization in one-year steps. Since Table 6 shows that the mediating effect of the HSR network is not significant, this section only explores the direct effect (i.e., relative degree centrality). To visually verify the presence of a nonlinear characteristic, we present the estimation results including coefficients and significance for all HSR variables in the form of line graphs.

Figure 2 reports the rolling regression results of the impact of the HSR network on urbanization at different window size settings. As shown in Figure 2a, the estimated coefficients under all windows show a clear downward trend (from positive to negative to smaller negative values), indicating that the HSR network does have a non-linear effect on the quality of urbanization. This finding supports our hypothesis 2.

Specifically, at the beginning of the construction of the HSR network, the increased importance of cities in the HSR network is conducive to promoting urban development. This can be interpreted as a "leader advantage", where the first cities to open high speed railways (often large cities) have an extremely obvious transportation and location advantage over other cities, so resources tend to flow to these cities, creating a stronger centripetal force effect [6]. This conclusion has been validated by most studies [59,60]. However, as more and more cities are connected to the HSR network, this centripetal effect is gradually weakening and being replaced by a centrifugal effect [61]. High-speed rail is no longer the "patent" of large cities. A more equitable distribution of transport resources fully mobilizes the development of small and medium-sized cities and promotes balanced regional development [62]. More importantly, this centrifugal force effect will be further strengthened with the further expansion of the size of the high-speed rail network. All these findings provide strong evidence for the new economic geography theory [45].

Based on the above estimation results, we can roughly divide the process of China's HSR network into three periods. From the results of Figure 2b, these three periods can be further identified as: 2010-2012, 2013-2015, and 2016-2019 with estimated coefficients of +0.0037, -0.0066, and -0.0203, respectively. The corresponding HSR coverage ranges are 0-25.27%, 33.33%-53.48%, and over 61.17%, respectively, showing a strong “stage characteristic” of HSR network development. However, it is worth noting that when data in 2019 are added to the sub-sample interval, the estimated coefficient rebounds significantly, indicating that the centrifugal force effect is also weakening to some extent. As shown in table 7, there are only 11 new HSR cities in 2019, the second-lowest of all years. This means that the size of China's HSR network (number of nodes) has gradually stabilized and its scale effect is diminishing. In conclusion, our study shows that network size does play a crucial role in the impact of HSR on urban development, rather than being a negligible factor.

Table 7. The HSR cities and coverage from 2009 to 2019.

Table 7. The HSR cities and coverage from 2009 to 2019.

YEAR	2009	2010	2011	2012	2013	2014	2015	2016	2017	2018	2019
HSR cities	19	41	57	69	91	110	146	167	172	186	197
New HSR cities	19	22	16	12	22	19	36	21	5	14	11
HSR coverage	0.07	0.15	0.21	0.25	0.33	0.40	0.53	0.61	0.63	0.68	0.72

Notes: The total number of cities is equal to 273

4.6. HSR network and the quality of urbanization: robustness test

Regarding the robustness test, scholars often choose lagged variables and proxy variables to replace the original variables, or change the time length of the sample. However, these methods are not applicable in this paper for two reasons. (1) Centrality is a proprietary measure of node importance in network analysis and is difficult to substitute. (2) Our study emphasizes the heterogeneity of the temporal dimension. Therefore, we still draw on the approach commonly used in spatial econometric analysis, which is to replace the spatial weight matrix, to perform robustness tests. In this paper, another spatial weight matrix is the adjacency matrix. The results of all sample and sub-urban agglomerations based on adjacent distance weight matrix are shown in table 9. From the result, we can find that almost all coefficients do not change in sign. As a result, the empirical findings can be considered reliable.

Table 9. The regression result based on adjacent distance matrix.

Table 9. The regression result based on adjacent distance matrix.

variables	Dependent variable: Quality of urbanization
	overall regression					Urban agglomerations		Non-urban agglomerations
	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)
hsr_dum	-0.0068*
hsr_rdc		-0.0061***				-0.0061***		-0.0009
hsr_adc			-0.0008
hsr_rbc				0.0007**			0.0011**		-0.0009***
hsr_abc					0.0001***
W×hsr	0.0294***	0.0095***	0.0118***	0.0002	0.0001	0.0088***	0.0002	0.0032***	0.0012***
Control	YES	YES	YES	YES	YES	YES	YES	YES	YES
city FE	YES	YES	YES	YES	YES	YES	YES	YES	YES
year FE	YES	YES	YES	YES	YES	YES	YES	YES	YES
N	2730	2730	2730	2730	2730	2080	2080	650	650

Notes: ^⁎ P < 0.1. ^⁎⁎ P < 0.05. ^⁎⁎⁎ P < 0.01.

5. Discussions and conclusions

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