Mathematical Problems in Engineering
Volume 2021 (2021), Article ID 4028236, 13 pages
https://doi.org/10.1155/2021/4028236

Research Article

Research on the Impact of Expressway on the County Economy Based on a Spatial DID Model: The Case of Three Provinces of China

Xueming Xu1,2 and Changping Liu³

¹Beijing Key Laboratory of Traffic Engineering, Beijing University of Technology, Beijing 100124, China
²CCCC Highway Consultants Co., Ltd., Beijing 100088, China
³Beijing Transport Institute, Beijing 100073, China

Correspondence should be addressed to Xueming Xu; xuxueming@hpdi.com.cn

Received 7 July 2020; Revised 31 March 2021; Accepted 13 May 2021; Published 21 May 2021

Academic Editor: Emilio Jiménez Macías

Copyright © 2021 Xueming Xu and Changping Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract.

Infrastructure construction results in transportation cost and regional economy changes. Based on the exogenous infrastructure change of a county highway opening as a natural experiment, this paper uses the spatial difference-in-differences (DID) model to analyze the impact of highway construction in three different provinces of China from 2004 to 2017. It was proved that highway connectivity had no significant or negative impact on the economy of the counties in three provinces that the highway passes through. In addition, highway connectivity was claimed to have obvious spatial spillover effects, which could promote the economic development of the whole region. For counties belonging to provinces in different regions and stages of economic development, we establish a spatial DID model that integrates time and space dimensions to study the impact of expressways on county economic development, to make up for the traditional DID model’s dependence on SUTVA assumptions, and to obtain spatial spillover effects.

1. Introduction

The role of transportation infrastructure in promoting and guiding economic development is recognized across the world, in which the expressway, as effective infrastructure to improve transport efficiency, has played a huge role in promoting the development of the regional economy. Therefore, it has attracted the attention of governments and scholars [1]. China began expressway construction in 1984. After more than 30 years of development, the total mileage of expressways in China reached 142,600 km by the end of 2018, which meant that it ranked first in the world. A large-scale highway system requires a huge amount of construction and operating expenses. As a result, it is particularly important to analyze the impact of expressways on economic development.

Recent research has analyzed the impact of transport infrastructure construction on the economy at the national, state, or interprovincial level, while its impact from a smaller intercounty perspective has rarely been analyzed. The county economy is not only the basic unit of the national economy but also an important part of the economy in China. In terms of the total economic output, the gross domestic product of 2079 counties in 2017 totaled 43.635461 trillion yuan in China, accounting for 52.4% of the total GDP in that year. In terms of the growth rate, the Chinese county economy grew at an average annual rate of 16.04% from 2003 to 2015, while the Chinese economy grew at an average annual rate of 9.81% during the same period [2]. It can be concluded from the above data that the county economy not only accounts for more than half of the Chinese total economic volume but is also an important factor through which the country can maintain rapid economic growth. Therefore, it is important to analyze the impact of highway construction on economic development from the perspective of the county economy.

The main contributions of the paper can be summarized in the following three aspects. First, we select the counties of different provinces in different locations and stages of economic development in China to ensure that the research objects have sufficient coverage and relevance; at the same time, the panel data time span reaches 14 years, which can realize local economic development changes. Secondly, a parallel trend test was fully carried out to ensure that the control group and the experimental group have the common trend to ensure that the impact of highway construction is reflected. Third, the economic geography matrix is introduced as the spatial weight matrix, which reflects the influence of distance and economic development, making the research more reasonable.

The rest of the paper is organized as follows. Section 2 provides relevant literature review. Section 3 describes the necessary background. Section 4 contains model structure and data in detail. Section 5 shows the method and result of the parallel trend test. Section 6 contains setting of the spatial weight matrix. Section 7 shows and discusses the empirical results. The last section concludes.

2. Literature Review

As an important part of infrastructure, transport infrastructure plays an important basic and leading role in economic development. With the deepening of research on economic growth theory in recent years, the impact of transport infrastructure as an important research topic has received plenty of attention.

Aschauer adopted the Cobb–Douglas production function (C–D production function). Through an analysis of the time series and cross-sectional data from 1945 to 1985 in the United States, Aschauer claimed that government investment in infrastructure has contributed to the growth of the total economic output [3]. Using the data of the counties of California from 1968 to 1988, Boarnet believed that the areas with better transportation infrastructure would attract the resources of the surrounding areas, which would result in negative spillover effects [4]. Khadaroo and Seetanah studied the association between transport capital and economic growth for Mauritius from 1950 to 2000 and found that transport infrastructure has significantly contributed to the economic performance [5]. Khadaroo and Seetanah used the ARDL approach to analyze data of Mauritius from 1960 to 2004 and found that transport infrastructure availability is seen to have contributed to the relative attractiveness of the country towards FDI [6]. Pradhan et al. analyzed the impact of transport infrastructure on India’s economic growth from 1970 to 2010 and found that there was a two-way causal relationship between transport infrastructure and economic growth: the expansion of transport infrastructure and the growth of total capital led to a substantial growth of the Indian economy [7]. Therefore, it was suggested that transport policies be retained to stimulate the growth of transport infrastructure investment and promote economic growth. Sanchez et al. investigated the data from OECD countries and found that transport infrastructure promoted economic growth by indirectly increasing environmental consumption, but did not directly generate economic growth [8]. Chi studied the effectiveness of transport infrastructure investment in improving the economy and found that expanding transport infrastructure investment may be an effective way to improve the economic level of developing European economies [9]. Crescenzi et al. assessed the relationship between government regional quality and profits of different types of road infrastructure in the European Union (EU) region and concluded that although the government preferred highways, the benefits were lower than that of secondary roads [10]. Kalra et al. conducted an empirical analysis on the relationship between transport infrastructure and economic growth in India and found that there was both a short-term and a two-way causal relationship between GDP and transport infrastructure [11]. Mohmand et al. believed that the development of transport infrastructure could directly or indirectly affect economic growth [12]. Additionally, transport infrastructure construction could bring trade and investment opportunities to previously underdeveloped regions, as well as goods transport, services, and employment opportunities through these multiplier effects. Yapicioglu et al. conducted questionnaires on public entities, private clients, consultants, and contractors in the construction industry in six Nigerian states [13]. They found that while transport policies improved transport infrastructure investment, they also promoted sustainable economic development. Saidi et al. discussed the impact of transport energy consumption and transport infrastructure on economic growth in the Middle East and North Africa [14]. They found that the development of transport infrastructure had a positive impact on the economic growth in all regions, while transport energy consumption promoted economic growth in only a few regions. Tong and Iop discussed the relationship between GDP and road transport infrastructure density of 12 cities in Inner Mongolia and analyzed the relationship between economic growth and road transport infrastructure [15]. They found that the promotion of road transport infrastructure to economic growth is permanent, and the impact of road transport infrastructure on economic growth increased gradually and then weakened gradually after reaching the peak. Wang et al. used the nearest neighbor distance method, kernel density estimation, regression analysis, global autocorrelation, local autocorrelation, and other spatial methods to study the spatial distribution characteristics and growth mechanisms of 238 megacities in China [16]. Baumsnow et al. investigated the effects of the recently constructed Chinese national highway system on local economic outcomes [17]. They found that, with the development of expressways, the economic output and population of advantageous areas increased, while the interests of hinterland areas declined, which had an impact on the regional economic structure. Herzog estimated inter-regional transportation’s effect on the local economic activity by studying the Interstate Highway System and found that interstates’ effects were highly heterogeneous and that additions to early Interstate plans were less valuable than the system’s core [18].

Summarizing recent research findings, Liu and Zhou used Chinese county-level panel data for the first time to investigate the impact of highway construction on the county-level economy from 1997 to 2008 [19]. They found that expressways have a significant positive impact on the county economy. However, Faber analyzed the county-level economic data to discuss the highway built in China from 1998 to 2003 and the county-level economic data from the 1997–2006 period [20]. It was found that the highway had a significant negative effect on connecting the small counties. Dong and Liu concluded that the connectivity of national highways had a significant positive impact on the economy of the counties through which the national expressway passed from 2004 to 2013 [21]. They also claimed that the farther away one is from a major city, the smaller the county seat is affected by the positive driving effect. The spatial spillover effects of expressways were not taken into account in the above discussion, although it was proved that the traffic infrastructure has significant externalities. Therefore, the spatial spillover effects of expressways need to be fully considered. Moreover, the difference-in-differences (DID) model used in the above research has relatively strict application conditions, and it is evident that the characteristics of traffic infrastructure conflicted with the conditions; thus, such research methods need to be improved.

3. Theoretical Basis of the Spatial DID Model

3.1. The DID Model

The DID model is widely used in econometrics to quantitatively evaluate the implementation of public policies or projects [22]. Its core idea is to realize an effective analysis of the implementation effect of a policy or project through the natural experimental construction of “difference before and after” and “with or without contrast.” Its theoretical model is shown in the following formula:

where β is the DID estimator, Y is the outcome variable in the study, “treat” and “control” represent the experimental group and control group, respectively, and “before” and “after” represent preintervention and postintervention, respectively. The DID method effectively eliminates the impact of nonproject factors, so it is widely used to assess the impact of policy or project implementation on the regional economy.

The form of the DID model is shown as follows:

where Dit and Tit are virtual variables, the value of which can only be 0 or 1. They represent whether the object is the treatment group or the control group and whether the time is before or after implementation.

The DID model takes the implementation time of the public policy or project as a clear sign to distinguish before and after the intervention, and there is a clear single time point. However, within the scope of the study, when there are inconsistencies in the policy implementation or project completion time in different regions, it is necessary to introduce a multiperiod DID model.

The multiperiod DID model takes the interaction terms of Dit and Tit in the DID model as the symbol of policy or project implementation. In the multiperiod DID model, there is only the interactive term of the product of two virtual variables, while the separate terms of Dit and Tit are not included. The form of the multiperiod DID model is as follows:

The problem of an inconsistent implementation time can be solved effectively by using the multiperiod DID model, and the application range of the DID model can be greatly improved. In addition, the sample size can be greatly increased by stages. Even if the final policy or project covers all of the objects, the objects in the period in which the policy or project has not yet been implemented can still be used as the control group.

3.2. Application of the DID Model in Transportation

Based on the above characteristics, the DID model has been widely used to evaluate the impact of traffic infrastructure construction. By using the data of 287 prefecture-level and above cities in China from 2006 to 2010, Wang and Nian used the DID model to empirically test whether the opening of a high-speed railway had a significant impact on the development of the regional economy [23]. By constructing a DID model, Li et al., respectively, took the location entropy of the tertiary industry as the agglomeration economic index to econometrically analyze the impact of a high-speed railway on the urban agglomeration economy [24]. Taking the Yangtze River Delta urban agglomeration as an example, Fang and Sun used the DID model to analyze the impact of high-speed railway construction on the per capita GDP growth rate and the gap between urban and rural areas in the Yangtze River Delta urban agglomeration [25]. Based on the transaction data of 600,000 new houses in Shanghai, Fan et al. used the progressive DID model to analyze the impact of a subway on the housing area and price [26]. Liu, Faber, and Dong Xiaofang used the DID model to analyze the impact of an expressway on regional economic development.

In the above research, domestic and foreign scholars have used double cross-section or panel data to analyze the impact of major traffic infrastructure on the study area by using the DID model or the multiperiod DID model.

3.3. The Spatial DID Model

There is an important assumption when using the DID model, which is the effectiveness of the stable unit treatment value assumption (SUTVA) [27]. This assumption assumes that the potential result of an object will not be affected by others which are being processed [28]. The violation of SUTVA, which is also known as “intervention” or “social interaction,” has been a popular research theme of economics and many other disciplines [29]. Traffic infrastructure projects have significant externalities, which need to be paid attention. Therefore, the spatial DID (SDID) model has been introduced. Through the spatial econometric model, the spatial interaction of processing utility between objects is described, which effectively solves the problem in the traditional DID model. The spatial DID model fully considers the possibility that the project affects the spatial correlation and allows spatial interaction in the implementation effect of the project. Spatial interaction refers to the direct and indirect effects of policy or project implementation. The indirect effect is referred to as the “spillover effect” or the “network effect.” The specific form of the spatial DID model is related to the selection of the spatial lag term, which is introduced in combination with the spatial econometric model below.

After the spatial DID model was proposed, it was applied in many fields, including the impact of traffic infrastructure construction. Dubé et al. used the spatial DID model to analyze the impact of rail transit project construction on the housing prices in the affected area [30]. They took the development of the new rail transit system in the suburbs of Montreal, Canada, as an example and compared it with the traditional DID model. Chagas et al. analyzed the effects of sugarcane yield on respiratory diseases in Brazil using a spatial DID model and proposed a separation method for the effects on production and nonproduction areas [31]. Sunak et al. applied the spatial DID model to analyze the influence of a wind farm on the room under a different landscape influence degree [32]. Based on census data, Zhou et al. used the spatial DID model to discuss whether rail transit promoted the diffusion of industry in Beijing [33].

4. Spatial DID Model Setting, Variable, and Data

4.1. Spatial DID Model Setting

The most commonly used spatial econometric models include the spatial autoregressive model (SAR), the spatial error model (SEM), and the spatial Durbin model (SDM). Considering the inter-regional interaction in economic development and the impact of highway connectivity on economic development, this paper chose the spatial Durbin model (SDM) as the main analysis model and conducted a comparative analysis of the spatial autoregressive model (SAR) and the spatial error model (SEM). According to the construction of the multiperiod DID model, which was introduced in the previous section, the interaction item Dt, which characterizes the highway connection, is added to the spatial measurement model to form various forms of the spatial DID model. The spatial Durbin DID model is as follows:

The spatial autoregressive DID model is as follows:

The spatial error DID model is as follows:

where Yt is the explained variable, which refers to the economic development of the county in a certain year. This paper used the GDP of the county in the current year to present the changes in the economy. Dt is a virtual variable indicating whether the county is connected to the highway in that year. If it is connected in that year, it is set to 1; otherwise, it is 0. The function of Dt is equivalent to the interactive term of the traditional DID model. Xt is a covariable, which is mainly a statistical index related to the economic development of each research object. WYt is an endogenous interaction effect between the explanatory variables. WXt is an exogenous interaction effect between the explanatory variables. Wu is an interaction effect between the interference terms of different observation units. ρ is a spatial autoregressive coefficient. λ is a spatial autocorrelation coefficient. θ and β represent fixed and unknown parameter variables to be estimated. ε is an independent random error term constant. ιN is a unit vector.

The purpose of this article is to study the impact on economic development after the expressway is connected. It is undoubtedly appropriate to use the DID model for this comparison. The expressway has the function of connecting different areas, and the spatial spillover effect brought about by the construction results is also inevitable. In this case, spatial DID is a more appropriate method.

From the limitation of the method, there is a certain presetting for the setting of the influence form of the spatial indirect effect. And, it has an additive relationship with the direct effect, but whether it is an additive relationship in practice still needs further argumentation and analysis.

4.2. Variables and Data

In order to enhance the representativeness of the study, this paper chose Guangdong province, Hubei province, and Qinghai province as representative provinces of China. Guangdong province, Hubei province, and Qinghai province are located in the eastern, central, and western regions of China, respectively, and can thus represent different geographical locations. In 2017, Guangdong, Hubei, and Qinghai provinces ranked 1st, 7th, and 30th, respectively, in the total GDP of 31 provincial administrative regions in mainland China. Therefore, these three provinces can also reflect three different levels of economic development in China.

In this study, the time of the connected expressway in the county was determined by the statistical data of the opening time of the highway section provided by the local transport authority and the situation of the regional road network. Other economic statistics were obtained from the China County Economic Research Database in CSMAR (Guotai’an CSMAR database) and the 2004–2017 China County Statistical Yearbook.

As described above, the representative interaction item in this paper is the highway connectivity, and the values of this term for Guangdong, Hubei, and Qinghai provinces are shown in Table 1. It can be seen in the table that the connected highways of the counties of Guangdong, Hubei, and Qinghai have been rising over the years. In 2017, the proportion of connecting expressway counties in Guangdong and Hubei exceeded 90%, while it only exceeded 55% in Qinghai province.

Table 1: Statistics of connected highway counties for 2004–2017.

Year
Guangdong
Hubei
Qinghai

Sample counties
78
67
39

2004
31
17
8

2005
37
22
8

2006
40
23
9

2007
42
27
9

2008
42
30
9

2009
44
41
9

2010
54
45
9

2011
54
50
9

2012
54
51
10

2013
58
51
10

2014
59
62
10

2015
68
62
11

2016
70
64
13

2017
73
65
22

The explained variable is the GDP of each county, and the covariates are the population, the fixed asset investment, the fiscal expenditure, and the fiscal revenue of each county.

The descriptive statistics of the main variables are shown in Table 2. In terms of the average GDP, for Guangdong, it is 1.74 times higher than that of Hubei and 9.01 times higher than that of Qinghai. It can be seen that there are significant differences in the economic development of the three provinces. In addition, in order to reduce the heteroscedasticity of the data, a natural logarithm was used for all variables except the dummy variables. Examples of data are shown in Table 3.

Table 2: Descriptive statistics of the main variables.

Province
Variable Name
Observed
Mean
Variance
Min
Max

Guangdong
GDP (10,000 yuan)
1092
2,232,373
3,506,064
48,577
30,589,219

Population (10,000 people)
1092
77
47
7
247

Investment in fixed assets (10,000 yuan)
1092
846,435
1,236,250
4151
10,782,942

Financial revenue (10,000 yuan)
1092
117,068
233,925
2013
2,248,715

Financial expenditure (10,000 yuan)
1092
233,964
275,213
10190
2,743,406

Hubei
GDP (10,000 yuan)
938
1,278,927
1,253,906
43,543
7,171,791

Population (10,000 people)
938
66
33
8
165

Investment in fixed assets (10,000 yuan)
938
997,944
1,230,851
6626
7,993,968

Financial revenue (10,000 yuan)
938
65,093
85,384
832
980,543

Financial expenditure (10,000 yuan)
938
200,473
165,795
7488
831,728

Qinghai
GDP (10,000 yuan)
546
247,665
419,003
3108
3,272,383

Population (10,000 people)
546
12
12
1
49

Investment in fixed assets (10,000 yuan)
546
201,685
388,073
3161
2,922,300

Financial revenue (10,000 yuan)
546
12,100
25,241
73
210,302

Financial expenditure (10,000 yuan)
546
94,988
92,424
535
697,936

Table 3: Descriptive statistics of the main variables.

Province
County
Year
GDP (10,000 yuan)
Population (10,000 people)
Investment in fixed assets (10,000 yuan)
Financial revenue (10,000 yuan)
Financial expenditure (10,000 yuan)
Expressway Connection

Guangdong
Dongyuan
2004
242,357
52
127,567
6833
53,237
0

2005
245,098
53
139,740
10,257
62,442
1

2006
316,992
54
203,670
15,703
73,389
1

2007
417,860
52
242,902
20,166
97,459
1

2008
512,531
54
145,533
22,789
107,439
1

2009
511,182
57
162,857
26,045
125,383
1

2010
595,479
57
218,948
30,741
145,208
1

2011
743,345
59
185,261
40,021
173,153
1

2012
794,021
55
185,261
47,406
191,835
1

2013
863,663
56
571,838
60,272
231,619
1

2014
979,803
59
668,479
73,540
295,969
1

2015
1,006,351
59
752,427
79,807
323,145
1

2016
1,046,923
59
917,610
83,063
393,346
1

2017
1,137,344
59
1,112,709
88,127
402,662
1

Fengshun
2004
263,915
67
19,353
6376
41,655
1

2005
314,213
67
68,323
9431
46,566
1

…

Hubei
Danjiangkou
2004
408,179
49
17,467
15,058
15,058
1

2005
421,648
49
81,079
16,861
45,892
1

2006
480,100
49
194,173
228,63
57,617
1

2007
545,100
50
148,877
25,462
72,882
1

2008
676,300
50
242,090
30,444
98,355
1

2009
757,106
50
358,945
45,158
183,822
1

2010
921,359
46
493,961
119,758
265,885
1

2011
1,083,752
46
698,792
157,918
329,081
1

2012
1,300,165
46
970,683
275,883
379,843
1

2013
1,507,151
46
1,282,892
221,465
429,533
1

2014
1,658,103
46
1,595,100
115,348
311,557
1

2015
1,830,222
46
1,883,854
132,058
415,490
1

2016
1,986,835
46
2,278,400
129,504
445,362
1

2017
2,234,856
46
2,507,371
149,238
485,865
1

Yunmeng
2004
469,066
58
24,700
13,065
27,340
0

2005
469,623
58
99,471
13,376
30,488
1

…

Gansu
Dongxiang
2004
33,537
27
122
766
16,674
1

2005
43,921
27
151
738
21,083
1

2006
48,509
27
179
781
31,366
1

2007
54,146
27
233
970
46,654
1

2008
63,095
27
336
1224
67,234
1

2009
71,534
28
629
2090
86,135
1

2010
79,364
32
814
2281
104,517
1

2011
97,882
29
1192
2800
175,700
1

2012
119,574
32
1755
5519
197,341
1

2013
127,197
33
1899
10,689
188,671
1

2014
150,854
35
2289
12,268
193,393
1

2015
162,743
34
2613
6878
217,323
1

2016
173,012
35
2830
7602
241,730
1

2017
188,803
36
1148
8059
292,944
1

Liangdang
2004
16,719
5
15.35
448
7512
0

2005
19,990
5
18
461
9881
0

…

5. Parallel Trend Test Results

There is an important assumption for the establishment of the DID method: the control group and the experimental group have the same change trend λ t (common trend assumption), which is also known as the parallel trend assumption [34]. According to the method of Autor et al. [35], this paper estimated the DID model of the p-period and q-period before and after the opening of the expressway, which is shown as follows:

According to the number of samples and the general inspection needs, τ was selected to be 3, which means the relevant conditions of three years before and after the opening of the expressway were detected. Table 4 shows the parallel trend hypothesis test results. Only Hubei province has a weak correlation with the economy in the first three years before the connection, and there is no significant difference in the other two provinces. The p-value of Hubei is 0.094, which is close to rejection of the original hypothesis. The parallel trend of the three provinces is shown in Figure 1, and it can be seen that the coefficient of each province fluctuates around 0 before and after the high-speed connection, which means that the experimental group and the control group can be compared. Therefore, it is believed that the subjects are subject to the parallel trend hypothesis.

Table 4: Parallel trend test results.

Variables
Guangdong
Hubei
Qinghai

3 years prior
−0.0447 (−1.61)
−0.0394 (−1.68)
−0.106 (−0.54)

2 years prior
−0.015 (−0.41)
−0.0309 (−0.97)
0.0372 (0.19)

1 year prior
−0.00822 (−0.17)
−0.0401 (−1.25)
0.099 (0.37)

Connect year
0.0544 (1.20)
−0.0285 (−1.04)
0.105 (0.41)

1 year after
−0.0117 (−0.37)
−0.00143 (−0.05)
−0.105 (−0.54)

2 years after
0.0413 (1.29)
0.000272 (0.01)
−0.155 (−1.16)

3 years after
0.0277 (0.96)
−0.00641 (−0.23)
−0.0496 (−0.74)

Constants
14.41 (407.36)
14.35 (385.88)
12.22 (163.3)

Note. for , for , and for ; t statistics in parentheses.

(a)

(b)

(c)

Figure 1: The parallel trend of Guangdong, Hubei, and Qinghai provinces. (a) Guangdong. (b) Hubei. (c) Qinghai.

6. Spatial Weight Matrix

In spatial econometrics, the two most common forms of spatial weight are the adjacency matrix and the inverse distance matrix. Because the research object of this paper was the county economy, many areas were divided by the urban area of prefecture-level cities. The adjacency matrix was not suitable for this study, so the inverse distance matrix was considered. In addition, the economic distance matrix was also not used in this study due to the characteristics of the county economy.

The matrix form is shown in the following formula:

The distance dij between the two counties is calculated according to the following equation:

In the equation above, the longitude and latitude of county i and county j are (αi, βj) and (αi, βj), respectively, and R is the Earth radius.

The calculation of the distance between counties is shown in Figure 2. On this basis, the inverse distance matrix required in this paper could be obtained by taking the reciprocal of the square of the distance according to equation (8).

(a)

(b)

(c)

Figure 2: Schematic diagram of the distance matrix of counties by province. (a) Guangdong. (b) Hubei. (c) Gansu.

7. Empirical Research and Result Discussion

7.1. Spatial Correlation Test of Economic Growth

7.1.1. Moran’s Index (Moran’s I) of Counties

In order to analyze the spatial correlation of each region, this paper calculated Moran’s I of the natural logarithm of GDP of the counties of Guangdong, Hubei, and Qinghai over the years, as shown in Table 5, and the trend chart with time is shown in Figure 3.

Table 5: Moran’s index (Moran’s I) of the GDP of the counties of Guangdong, Hubei, and Qinghai in 2004–2017.

Year
Guangdong
Hubei
Qinghai

2004
0.494
0.315
0.453

2005
0.495
0.306
0.467

2006
0.486
0.315
0.45

2007
0.47
0.33
0.469

2008
0.462
0.349
0.442

2009
0.462
0.328
0.431

2010
0.441
0.327
0.44

2011
0.438
0.33
0.434

2012
0.46
0.325
0.424

2013
0.446
0.317
0.448

2014
0.452
0.313
0.459

2015
0.451
0.307
0.443

2016
0.453
0.304
0.434

2017
0.462
0.303
0.414

Figure 3: Chart of Moran’s I over time.

From Table 5 and Figure 3, it can be seen that Guangdong and Qinghai show a decreasing trend in general, while Hubei reached a peak in 2008 and then declined. The above trend shows that the spatial correlation of all regions is gradually decreasing, which means that the regional economic gap in each province displays a narrowing trend.

7.1.2. The Spatial Correlation of Residuals

The spatial correlation of residuals was regressed by the OLS method, and the Moran index of residuals was calculated. The results are shown in Table 6, where it can be seen that the data of the three provinces have a significant spatial correlation.

Table 6: OLS regression residual Moran index.

Province
Guangdong
value
Hubei
value
Qinghai
value

Results
5.516
0.000
112.477
0.000
92.711
0.000

7.2. Model Setting Test

In the space panel analysis, the specific model form needs to be tested. In this study, the LM and Robust LM tests were used to determine which of the models—the spatial lag model, the spatial error model, or the spatial Durbin model—were more suitable in this study. The Wald test and the LR test were used to determine whether the spatial Durbin model, the spatial lag model, and the spatial error model could be transformed from one another, and the Hausman test was used to determine whether it was better to use a fixed effect model or a random effect model.

7.2.1. LM and Robust LM Tests

The LM and Robust LM test results are shown in Table 7. It can be seen from the table that both LM and Robust LM reject the original hypothesis. Therefore, the results point to the SDM.

Table 7: The LM and Robust LM test results.

Index
Guangdong
value
Hubei
value
Qinghai
value

LM-error
28.851
0
112.477
0
92.711
0

Robust LM-error
15.18
0
70.034
0
69.639
0

LM-lag
26.59
0
66.034
0
27.328
0

Robust LM-lag
12.919
0
23.591
0
4.256
0.039

7.2.2. Wald Test and LR Test

The results of the Wald test and the LR test are shown in Table 8. It can be seen from the table that the original assumptions of θ = 0 and θ + ρ β = 0 are rejected. Besides, it is believed that the SDM will not degenerate into SAR or SEM.

Table 8: The Wald test results.

Index
Guangdong
value
Hubei
value
Qinghai
value

H0: θ = 0
87.04
0
69.99
0
33.75
0

H0: θ + ρβ = 0
46.37
0
87.83
0
51.53
0

The results of LR inspection are shown in Table 9. It can be seen that the LR test results are similar to the Wald test results, and SDM will not degenerate into SAR or SEM.

Table 9: The LR test results.

Index
Guangdong
value
Hubei
value
Qinghai
value

SDM/SAR
45.52
0
68.78
0
33.23
0

SDM/SEM
158.69
0
178.46
0
110.57
0

7.2.3. The Hausman Test

The Hausman test was considered for the SDM, and the results are shown in Table 10. It can be seen from the results that Guangdong, Hubei, and Qinghai all rejected the null hypothesis at a significance level of 5%. Therefore, a fixed effect model should be used for the SDM.

Table 10: The Hausman test results.

Index
Guangdong
value
Hubei
value
Qinghai
value

H0: random
115.51
0
17.22
0.016
25.25
0.0007

7.3. Model Estimation Results

The SDM was used to calculate the SDID model, and the results are shown in Table 11.

Table 11: The estimation results of the spatial difference-in-differences (SDID) model.

Variables
Guangdong
Hubei
Qinghai

secper
0.4649 (9.00)
0.6488 (9.17)
1.4044 (14.47)

total_pop_ln
0.1014 (2.32)
0.0494 (0.3)
−0.1797 (−2.97)

invest_ln
0.0402 (5.55)
0.0362 (4.56)
0.0394 (2.35)

fin_reve_ln
0.1035 (6.75)
0.0827 (6.41)
0.044 (2.16)

fin_exp_ln
0.1646 (6.58)
0.0232 (1.36)
−0.0434 (−1.49)

exp
−0.0127 (−0.87)
−0.0467 (−4.02)
0.0276 (0.6)

Wsecper
−0.1501 (−1)
−1.3039 (−6.82)
−0.2616 (−1.01)

Wtotal_pop_ln
0.0413 (0.25)
−1.6083 (−3.7)
−0.6312 (−3.56)

Winvest_ln
−0.0316 (−1.64)
0.0194 (0.84)
−0.022 (−0.64)

Wfin_reve_ln
−0.0127 (−0.34)
0.1518 (4.18)
−0.0172 (−0.5)

Wfin_exp_ln
0.0159 (0.32)
0.2135 (4.05)
0.152 (1.49)

Wexp
0.1492 (4.22)
0.109 (2.97)
0.3204 (2.22)

rho
0.2644 (5.02)
0.3997 (6.99)
0.3292 (4.55)

sigma2_e
0.0129 (23.26)
0.009 (21.46)
0.031 (16.38)

LogL
820.1518
870.7909
168.6213

Note., , and ; t statistics in parentheses.

In the spatial multiple coefficients’ model of the county economy in Guangdong, Hubei, and Qinghai provinces, the spatial effect coefficient ρ is significant at the level of 1%, which is also positive. The estimation results show that the provincial and county economies have obvious space spillover benefits. Additionally, the economic growth of one county has significantly improved the economic development of other counties.

In the spatial multiple difference model of the county economy in Guangdong province, the proportions of secondary industry, fixed asset investment, fiscal revenue, and fiscal expenditure are all significant at the 1% level, where the population is significant at the level of 5%. The spatial lags of the proportion of the secondary industry, population, investment in fixed assets, fiscal revenue, and fiscal expenditure are not significant, while the space after the expressway connectivity is significant at the 1% level.

In the spatial multiple difference model of the county economy in Hubei province, the proportion of secondary industry, investment in fixed assets, fiscal revenue, fiscal expenditure, and highway connectivity are all significant at the level of 1%. The value of the expressway connection factor is −0.0467. The population and fiscal expenditure are not significant. The spatial lags of the proportion of the secondary industry, the total population, fiscal expenditure, fiscal revenue, and highway connectivity are all significant at the 1% level, while the spatial lag of fixed asset investment is not significant.

In the spatial multiple difference model of the county economy in Qinghai province, the proportions of the secondary industry and the population are both significant at the level of 1%, while fixed asset investment and fiscal revenue are significant at the level of 5%, and fiscal expenditure and highway connectivity are not the same. It is claimed that fixed asset investment, fiscal revenue, fiscal expenditure, and expressway connectivity are all significant at 1%, and the value of the expressway connection factor is −0.0467, while the population and fiscal expenditure are not significant. The spatial lag terms of expenditure and fiscal revenue are not significant. The spatial lag terms of the population are significant at the level of 1%, and the spatial lag terms of highway connectivity are significant at the level of 5%.

It can be seen from the comparison that the relationship between the expressway connection and economic growth is not significant or plays a certain negative role, while the space spillover effect of the expressway connection is significant and positive. Although the connection of expressways has no direct positive impact on the economic growth of directly connected counties, it has a positive effect on the county economy in the entire region.

According to the study of spatial econometrics, the parameter estimation results obtained in Table 11 are biased. In order to more deeply understand the impact of highway connectivity on the county economy, the results needed to be further decomposed into direct and indirect effects (also known as spillover effects). During the analysis, the direct effect reflected the impact of highway connectivity on the economic growth of connected counties, while the indirect effect reflected its impact on the economic growth of other counties. The decomposition results of direct and indirect effects are shown in Table 12.

Table 12: Direct, indirect, and total effects.

Variables
Guangdong
value
Hubei
value
Qinghai
value

exp
−0.0127
0.382
−0.0467
0.000
0.0276
0.548

Wexp
0.1492
0.000
0.1090
0.003
0.3204
0.026

Direct effect
−0.0065
0.650
−0.0413
0.000
0.0494
0.308

Indirect effect
0.1963
0.000
0.1517
0.016
0.4940
0.033

Total effect
0.1898
0.000
0.1104
0.091
0.5434
0.032

It is shown from Table 12 that the direct and indirect effects of the three provinces’ highway connections on the county economy are not similar. The direct effect of Guangdong is close to 0, which is also not significant in the model. The value of the indirect effect is 0.1963, of which the total effect is 0.1898. The value of the direct effect of Hubei is −0.0413, of which the indirect effect is 0.1517 and the total effect is 0.1104. The direct effect of Qinghai province is positive, but not significant. The value of the indirect effect is 0.4940 and the total effect is 0.5434. From the above results, it can be found that the expressway connection has no significant impact on the economic growth of the connected counties and even has a certain negative impact. However, it has a significant space spillover effect on adjacent areas and benefits the overall regional economic growth. The indirect impact of the value is affected by many factors, such as the economic development situation of various places and the existing level of transportation infrastructure development.

8. Conclusion

Highways are designed to connect provincial capital cities with populations of more than 500,000. As a side effect, a large number of surrounding county towns are connected to large urban agglomerations, so county economies are affected by the spillover and siphon effects of larger cities. This article validated Faber’s research results [16]. The completion of an expressway will bring about a decline in the GDP growth rate of nontarget surrounding areas. However, from the perspective of the overall development of the county economy, the connection of an expressway has a significant spillover effect. The effect has a greater promotion effect on the overall regional economic growth, which is ignored by the traditional DID analysis method.

Both the economic development of the county and its relationship with related factors show obvious spatial correlations. The use of the spatial DID model can result in an improvement in terms of the dependence of the traditional DID model on the SUTVA assumption and can more accurately assess the impact of highway connection on the county economy.

The total effect of the expressway connectivity on the county economy in each province is positive, but the impact on the connected counties is negative or is even not significant, which is similar to the results of previous scholars’ estimations based on the DID model. The reason for this is considered to be related to the economic siphon effect formed after rapid transportation infrastructure construction. This verifies the two-stage conclusion of the impact of the decline in transportation costs in the new economic geography: the first stage widens the regional economy and income gap; in the second stage, the industry spreads to low-income regions. Therefore, it can be seen that roads and other transportation infrastructure have spatial spillover effects, but it is uncertain whether the spillover effects are positive.

Comparing the data from the Guangdong, Hubei, and Qinghai provinces, it has been shown that the impact of expressway connectivity on the county economy of Qinghai province is more obvious than that of the other two provinces, which is because of Qinghai’s relatively low level of economic development and proportion of expressway connectivity. This paper used a spatial DID model to eradicate the dependence of the traditional DID model on the SUTVA assumption and to effectively estimate the space spillover effect of highway connectivity. Therefore, it has more scientifically and comprehensively analyzed the impact of highway connectivity on the area.

The construction of highways requires the central and local governments at all levels to invest a lot of manpower, material resources, and funds, so it is of practical significance to effectively evaluate the economic effects of highways and other infrastructure construction. The research in this paper proves that counties with more connections can effectively promote the efficient flow of factors and the overall development of the county economy. At the same time, there is a certain degree of uncertainty regarding the impact of the overall development of expressways and its own industrial characteristics on specific counties. From the analysis results, it can be seen that the completion and opening of the expressway to traffic does not directly promote the economic growth of the connected counties, but it has a significant role in promoting the county economy in the province as a whole. According to the two-stage conclusion of the impact of declining transportation costs, the economy of lagging counties may experience a period of negative impact after they are connected to expressways. Therefore, the management department should adjust the industrial composition in time according to the different stages of county development to deal with the impact of the adjustment of regional economic distribution. Expressway construction has always been one of the important means for China to stimulate economic development, and the research results of this article provide evidence for the supporting role of expressways on the county economy, which will provide a basis for better expressway development policies.

Data Availability

The data used to support the findings of this study are included within the article.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

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