Introduction

Introduction

Amidst the backdrop of economic globalization and regional integration, regional economic circuits, often led by central cities, have emerged as a pivotal force in the global economy, fostering national competitiveness in global contests and regional division of labor. Such economic circuits have attracted substantial governmental attention in China, specifically with regard to transportation infrastructure, a crucial prerequisite for regional developmentFootnote 1.

Road transport, despite its ancient origins, remains central in modern governance. It stands out among other transportation modes due to its unmatched mobility, flexibility, and accessibility. With the advent of modern technology, constructing roads has become simpler and cost-effective, reinforcing road transportation’s prominence in connecting distant areas. China’s road system, which spans from national to village roads, epitomizes this accessibility. According to China’s recent “Outline of National Comprehensive Three-Dimensional Transportation Network Planning,” creating an all-encompassing transport network, with roads at its core, is a primary goal in economic circuitry.

Despite robust evidence suggesting that highway infrastructure fosters regional economic development more effectively than urban roads, certain studies have presented conflicting findings. Konno et al. (2021) empirically scrutinized road infrastructure productivity using a global database, revealing that although the spatial spillover effect was positively significant, the direct impact was significantly negative, with the overall effect being positive yet not significant. Similarly, Magoutas et al. (2023) postulated that highways’ aggregation effect might trigger a production factors’ exodus from less economically developed to more developed regions, potentially engendering negative implications for the former and provoking economic downturns.

Thus, this study endeavors to unravel the intricate role of road transportation networks in the economic advancement of the Chengdu-Chongqing twin-city economic circle. Through this investigation, we aspire to offer insights that will inform rational transport system planning and economic distribution policy formulation within the Chengdu-Chongqing twin-city economic sphere.

Literature review

The intricate interplay of transportation infrastructure and economic development

Research has extensively explored the link between transportation infrastructure and regional economic development, with roots tracing back to theories from Rodan and Rostow in the 1940s. The early hypotheses often simplified the dynamics of transportation and economics, potentially overlooking underlying complexities. Recent perspectives, such as those from Knowles et al. (2020), offer a more nuanced understanding, evaluating transport’s role in shaping urban development through various, evolving lenses.

Pioneering studies like those by Aschauer (1989) have explored this relationship further. His work utilized a neoclassical economic growth model to assess the implications of declining transportation infrastructure investments in the United States. These investigations unequivocally emphasized the pivotal role of transportation infrastructure in driving economic growth. Meanwhile, Sun et al. (2022) highlighted the significant contributions of land and water transport systems to China’s economic growth. Yet, with the dialog concerning economic impacts of transportation evolving, comprehensive analyses are emerging. These revisit and redefine concepts like Transit Oriented Development (TOD) in current and future planning contexts (Knowles et al., 2020; Yu et al., 2022).

Road traffic: the lifeline of economic vitality

Scholars, including Acheampong et al. (2022) and Zhou et al. (2022), have joined in a resounding academic consensus, underscored the crucial role of road traffic in driving economic growth and development across various nations. However, our understanding of road traffic’s role in economic development is not fully exhausted. Traditionally, research has majorly focused on the quantitative aspects of road transportation, such as mileage, road density, vehicle counts, and other similar metrics.

Acknowledging the substantial dynamics of evolving urban agglomerations, especially within China, it is vital to manage both intra and inter-city transit effectively and sustainably (Huang et al., 2020). Yet, this quantitative focus, while valuable, sometimes overlooks critical subtleties of road traffic, such as its quality, efficiency, and accessibility. For instance, Arbués et al. (2015) highlighted that the impact of road traffic on economic growth is not just a function of infrastructure scale but also of its utilization and accessibility. Studies by Banister and Berechman (2003) also suggest that the mere presence of road infrastructure is not enough; integration and accessibility within the broader transportation network and region are crucial.

Furthering this, Pradhan and Bagchi (2013) emphasized the role of road traffic efficiency and accessibility in shaping regional economic growth. Huang et al. (2020) expand this perspective, exploring various challenges and focal areas in developing transportation systems within Chinese urban agglomerations. They address aspects like travel behavior, demand management, system design, risk management, and sustainable development.

These investigations accentuate a crucial need to broaden the scope of research, to not merely focus on the quantity of road infrastructure, but to delve deeper into understanding the quality of road traffic, particularly its accessibility. In this regard, our study hopes to provide a more comprehensive and nuanced insight into the relationship between road traffic accessibility and regional economic development, thereby further enriching and expanding the theoretical and practical landscape of this domain.

Traffic accessibility: a measure beyond quantity

Introduced by Hansen (1959), traffic accessibility offers an innovative approach to evaluate interaction opportunities within a transportation network. Later, Morris et al. (1978) and Jie et al. (2007) refined the concept, interpreting accessibility as a function of individual preferences and the ease of transitioning between different locations within a transport system. However, discussions about accessibility often overlook the deeper influence of socioeconomic and environmental factors on its measurement.

Advancements in natural sciences and GIS technology have widened the applicability of accessibility, facilitating its use in regional traffic optimization and traffic equity evaluation. Moreover, it has emerged as an influential metric to evaluate the relationship between transportation and the economy (Chen et al., 2020; Chacon-Hurtado et al., 2020). Still, few studies consider accessibility as a representation of transportation development, especially regarding road traffic.

Recognizing these research gaps, our study will delve into road traffic accessibility within the Chengdu-Chongqing twin-city economic circle. Given the dominance of road traffic in China’s transportation infrastructure, this study promises to yield a comprehensive and nuanced understanding of the traffic network development and its consequential impacts on economic growth. Therefore, our research does not only enrich academic dialogue, but also equips policymakers with pertinent insights for strategic transportation planning and regional economic development.

Study area, data sources, and methods

Study area

Our study focuses on the Chengdu-Chongqing twin-city economic circle, positioned at the central-western intersection of China (Fig. 1). This hub of population, towns, and industries significantly influences the western region’s development, enhancing inland openings and augmenting national strength. The Institute of Geographical Sciences and Resources of the Chinese Academy of Sciences introduced the idea of the Chengdu-Chongqing Economic Zone in 2003. Successive regional development initiatives followed, like the “Regional Planning of Chengdu-Chongqing Economic Zone” (2011) and the “Development Plan of Chengdu-Chongqing City Cluster” (2016). According to these plans, the Chengdu-Chongqing twin-city economic circle encompasses the provinces of Sichuan and Chongqing, including 15 cities in Sichuan like Chengdu, Deyang, and Mianyang, and 29 districts and counties in Chongqing like Wanzhou, Fuling, and YuzhongFootnote 2. This region covers a total area of 185,000 square kilometers and is home to 104.49 million people. As of 2018, the gross regional product was 5.58 trillion yuan.

Fig. 1
figure 1

Study area.

Full size image

Situated strategically, the Chengdu-Chongqing circle intersects the “two horizontal and three vertical” urbanization pattern, including the Yangtze River and Baokun Passages. This location facilitates access to the east and west and connections to the north and south, making it an essential urbanization area in China. In light of the drive to promote interaction between the Yangtze River Economic Belt and the Silk Road Economic Belt, the Chengdu-Chongqing twin-city economic circle is set to become the fourth key development region in western China, alongside the Beijing-Tianjin-Hebei city cluster, the Yangtze River Delta city cluster, and the Guangdong-Hong Kong-Macao city cluster.

Currently, the Chengdu-Chongqing circle features an extensive highway network. According to the “Three-Year Action Plan for Integrated Transportation Development in the Chengdu-Chongqing Region Twin Cities Economic Circle (2020–2022)”, the region’s road network will expand. By 2022, plans include 16 new highways and several upgrades. Efforts to ease traffic between the Chengdu-Chongqing circle and neighboring areas are also underway.

Data sources

At the outset, it’s imperative to highlight the primary sources from which our dataset has been curated. The core data employed in this study originates from several comprehensive and authoritative yearbooks: the “Sichuan Statistical Yearbook-2019”, “Chongqing Statistical Yearbook-2019”, “China County Statistical Yearbook-2019”, and “China Traffic Statistical Yearbook”. All these sources consistently pertain to the year 2019, ensuring the temporal coherence and relevance of our analysis. Subsequent sections delve deeper into the specifics of the data extracted from these sources and the methodologies applied.

The analysis in this paper is based on ArcGIS-based raster cost distance, utilized to study the accessibility. Our data is pulled from the 1:250,000 scale geographic data of Sichuan Province and Chongqing Municipality. We utilized the ArcGIS platform for projection conversion, extracting data points like the road traffic network and urban nodes. The 2018 road traffic map of the Chengdu-Chongqing twin-city economic circle was vectorized, aligned, supplemented, and improved to extract the traffic network data from the basic geographic data at the 1:250,000 scale.

In alignment with the “Technical Standards of Highway Engineering of the People’s Republic of China (JTGB01- 2014)”, and considering the road network density and quality within the Chengdu-Chongqing twin-city economic circle, the actual operating speeds were set to 120 km/h for highways, 80 km/h for national highways, 60 km/h for provincial highways, and 40 km/h for county highways. Consequently, the time taken per kilometer for these respective highways was set at 30 s, 45 s, 60 s, and 90 s.

We then converted the Chengdu-Chongqing twin-city economic circle’s road transport network into a grid format with pixel dimensions of 1000 m × 1000 m, totaling 278,178 grids. From this, a grid map of road transportation costs in 2018 was constructed. The shortest travel time for each city node was calculated through the cost grid (with Sichuan Province being the seat of the municipal government and Chongqing City the seat of the county and district government), and the reachability of each city was calculated through the shortest travel time. The calculation process is as follows:

$$A_i = \frac{{\mathop {\sum}\nolimits_{j = 1}^n {T_{ij}} }}{n}$$
(1)

Where \(A_i\) is the accessibility of city i, the smaller its value, the higher the level of accessibility; \(T_{ij}\) is the shortest travel time from city node i to node j, n is the number of cities.

To explore the spatial impact of road accessibility on economic growth within the Chengdu-Chongqing twin-city economic circle, this study employs per capita gross domestic product (GDP) as the dependent variable. Road accessibility, which serves as a measure of the convenience of a transportation network and effectively illustrates the level of transportation network development in each region, is employed as an independent variable. The other control variables used in this study are as follows:

Urbanization level

Urbanization is a critical factor influencing China’s economic growth. It is represented by the urbanization rate, which is the proportion of the urban population to the total population of a region. In 2018, China’s urbanization rate stood at 59.58%, and it is projected to exceed 65.5% by 2025.

Industrial structure

The structure of industries within a region indicates the region’s economic dependence. We measure this using the sum of secondary and tertiary industries as a percentage of regional GDP. This metric underscores productivity levels, as these industries lean heavily on technological innovation and production efficacy than primary sectors.

Labor force

The labor force is an essential component of economic development. This study evaluates the labor force by considering the ratio of employees in secondary and tertiary industries to the total regional population. This ratio is utilized due to the shifting industrial structure and an aging society, resulting in the gradual depletion of low-end labor force employment opportunities and high-end talent.

Educational investment

The financial investment in education per capita is used as an indicator to evaluate the value that a region places on education, which is a crucial prerequisite for high economic development.

Trade openness

A region’s external economic engagement, termed trade openness, mirrors its international trade magnitude. We determine this by calculating the total regional import-export value against its GDP. Elevated trade openness can drive regional economic advancements, but simultaneously necessitates extensive transportation infrastructure development (Table 1).

Table 1 Descriptive statistics of the variables.
Full size table

Methods

Spatial autocorrelation analysis

The existence of spatial autocorrelation of variables needs to be determined before conducting spatial econometric analysis. Commonly used methods to accomplish this include Geary’s C index, Geti’s G index, and Moran’s I index. Among them, Moran’s I index is the most widely used. Moran’s I reflects the degree of similarity of attribute values in spatially contiguous or spatially neighboring regional units, and is used to test the spatial correlation of variables. The calculation formula is as follows:

$$I = \frac{{{{{\mathrm{n}}}}\mathop {\sum}\nolimits_{{{{\mathrm{i}}}} = {{{\mathrm{1}}}}}^{{{\mathrm{n}}}} {\mathop {\sum}\nolimits_{{{{\mathrm{j}}}} = {{{\mathrm{1}}}}}^{{{\mathrm{n}}}} {w_{ij}(x_i - \bar x)(x_j - \bar x)} } }}{{\mathop {\sum}\nolimits_{i = 1}^n {\mathop {\sum}\nolimits_{j = 1}^n {w_{ij}\mathop {\sum}\nolimits_{i = 1}^n {(x_i - \bar x)^2} } } }}$$
(2)
$$I = \frac{{\mathop {\sum}\nolimits_{{{{\mathrm{i}}}} = {{{\mathrm{1}}}}}^{{{\mathrm{n}}}} {\mathop {\sum}\nolimits_{{{{\mathrm{j}}}} = {{{\mathrm{1}}}}}^{{{\mathrm{n}}}} {w_{ij}(x_i - \bar x)(x_j - \bar x)} } }}{{S^2\mathop {\sum}\nolimits_{i = 1}^n {\mathop {\sum}\nolimits_{j = 1}^n {w_{ij}} } }}$$
(3)

Among them \(S^2 = {\textstyle{1 \over n}}\mathop {\sum}\nolimits_{i = 1}^n {\left( {x_i - \bar x} \right)^2}\), \(\bar x = {\textstyle{1 \over n}}\mathop {\sum}\nolimits_{i = 1}^n {x_i}\). xi denotes the observation of the ith region, \(S^2\) is the sample variance, n is the total number of regions, and \(w_{ij}\) is the (i,j) element of the spatial weight matrix. Moran’s I index takes values in the range [−1,1].

A positive Moran’s I index suggests a positive spatial autocorrelation. As the value approaches 1, it denotes stronger adjacency of similar values. In simpler terms, regions with high values are near other high-valued regions, while low-valued areas are adjacent to other low-valued ones. If Moran’s I index equals 0, there’s no spatial relationship, meaning high and low values are scattered randomly. Conversely, a negative Moran’s I index points to a negative spatial autocorrelation. As the value nears −1, there’s a greater contrast between neighboring areas, meaning high-valued regions are next to low-valued ones.

By performing local Moran’s I index analysis, a Moran scatter plot can be obtained for analyzing the local spatial characteristics among spatial units. Moran scatter diagrams generally divide the spatial units into four quadrants, numbered from one to four, as follows: high-value units surrounded by high-value units, low-value units surrounded by high-value units, low-value units surrounded by low-value units, and high-value units surrounded by low-value units. The local Moran’s I index is calculated as follows:

$$I = \frac{{(x_i - \bar x)}}{{s^2}}\mathop {\sum}\limits_{j = 1}^n {w_{ij}} (x_j - \bar x)$$
(4)

The implication of the local Moran index is similar to that of the global Moran index. A positive \(I_{{{\mathrm{i}}}}\) indicates that the high (low) values of region i are surrounded by the corresponding high (low) values; a negative \(I_{{{\mathrm{i}}}}\) indicates that the high (low) value of region i is surrounded by the low (high) values.

Spatial econometric model selection based on the LM test

Moran’s I index can only test the existence and magnitude of spatial autocorrelation, but cannot determine which spatial model to apply. Therefore, an LM test is required to determine the specific spatial model to be used. The LM-error test was first proposed by Burridge (1980); subsequently, Anselin (1988) proposed the LM-lag test, and Hua et al. (2022) improved the LM-error test and LM-lag test by proposing the robust LM-error (R-LM-error) test and the robust LM-lag (R-LM-lag) test, respectively. The corresponding equation is as follows:

$$LM - Error = \frac{{(e^\prime We/s^2)^2}}{T}$$
(5)
$$LM - L{{{\mathrm{ag}}}} = \frac{{[{{{\mathrm{e}}}}^\prime Wy/(e^\prime e/N)]^2}}{R}$$
(6)
$$Robust\,LM - Error = \left( {\frac{{e^\prime Wy}}{{s^2}} - \frac{{TR^{ - 1}e^\prime We}}{{s^2}}} \right)^2/(T - T^2R^{ - 1})$$
(7)
$$Robust\,LM - L{{{\mathrm{ag}}}} = \left( {\frac{{{{{\mathrm{e}}}}^\prime Wy}}{{s^2}} - \frac{{e^\prime We}}{{s^2}}} \right)^2/(R - T)$$
(8)

Among them \(R = {\textstyle{1 \over {\sigma ^2}}}(WX\beta )^T[I - X(X^TX)^{ - 1}X^T](WX\beta ) + T_W\sigma ^2\), \(T_W = tr(W^2 + W^\prime W)\), \(s^2 = e^\prime {\textstyle{e \over N}}\), e denotes the residual term after OLS model regression, W is the spatial weight matrix, σ2 is the variance and I is the unit matrix.

According to the Lagrange multiplier test, the spatial lag model is considered superior to the spatial error model if the present LM-lag is more significant than the LM-error, and the R-LM-lag is significant but the R-LM-error is not. In contrast, if the LM-error is more significant than the LM-lag and the R-LM-error is significant but the R-LM-lag is not, the spatial error model is considered to be better than the spatial lag model.

Spatial econometric model

The spatial lag model focuses on whether the variables in a region are diffused. The spatial lag model is similar to the autoregressive model in a time series, so the spatial lag model is also called the spatial autoregressive model. The calculation formula is as follows:

$$Y = \rho Wy + X\beta + \varepsilon$$
(9)

where Y is the vector of dependent variables; X is the matrix of explanatory variables; W is the matrix of spatial weights; and Wy is the spatial lagged dependent variable; ρ is the spatial regression coefficient, reflecting the degree of diffusion or spillover between adjacent spatial units; the parameter β reflects the effect of X on Y; ε is the vector of random error terms. The spatial lag model mainly verifies the spatial spillover effect of the dependent variables in a region, and also verifies that the influencing factors of the dependent variable act on other regions through a spatial transmission mechanism. Bring each variable into the spatial lag model, and get the following calculation formula:

$$\begin{array}{l}GDP_{pi} = \rho WGDP_{pi} + \beta _0 + \beta _1Acc_i + \beta _2Urb_i + \beta _3Ind_i\\ \quad \quad + \,\beta _4Lab_i + \beta _5Edu_i + \beta _6Tra_i + \varepsilon _i\end{array}$$
(10)

The spatial error model explores whether the error term (unobservable variable) in one region has an effect on the error term in the adjacent region. The calculation formula is as follows:

$$Y = X\beta + \varepsilon$$
(11)
$$\varepsilon = \lambda W\varepsilon + v$$
(12)

Y is the dependent variable, X is the explanatory variable, β is the coefficient of the independent variable to be estimated, W is the spatial weight matrix, ε is the random error term; λ is the spatial lag coefficient of the error term to be estimated, i.e., the spatial autocorrelation coefficient; and v is the error term of the error term, i.e., the error term of ε. Bring each variable into the spatial error model, and get the following calculation formula:

$$GDP_{pi} = + \beta _0 + \beta _1Acc_i + \beta _2Urb_i + \beta _3Ind_i + \beta _4Lab_i + \beta _5Edu_i + \beta _6Tra_i + \varepsilon _i$$
(13)

For the parameter estimation of the spatial lag model and the spatial error model, the traditional least squares estimation method is biased and inconsistent due to the existence of spatial correlation. In order to overcome this problem, Anseln developed the maximum likelihood estimation method for spatial econometric model estimation, and judged the suitability of the model by the value of the log-likelihood function (Log-Likelihood). The larger the absolute value of the log-likelihood function value, the better the model suitability, that is, the more suitable for interpretation and analysis based on empirical results.

Additionally, another challenge arises from the underlying relationships within the variables under consideration. An essential aspect to consider in our model is the potential endogeneity problem. As highlighted by Hong et al. (2011), there exists a bidirectional relationship between economic growth and transport infrastructure. Economic growth can lead to increased government revenue, driving a greater demand for improved infrastructure. In turn, better infrastructure can stimulate further economic growth. Such a bidirectional relationship means that our independent variable (transport infrastructure investment or quality) might be correlated with the error term in the model, leading to biased estimates. While our current model does not instrument for this potential endogeneity, future research could consider employing instrumental variable techniques or other methodologies to account for this.

Results

Analysis of the accessibility of the Chengdu-Chongqing twin-city economic circle

The Chengdu-Chongqing twin-city economic circle’s accessibility analysis reveals intriguing trends. The majority of areas within this zone have moderate accessibility, with only a few regions showcasing extremely high or low values. Notably, Suining stands out with the lowest accessibility value, clocking in at 3.449 h. In contrast, Wanzhou and Kaizhou, both under Chongqing Municipality, have the highest. This indicates the spatial accessibility distribution isn’t uniform.

From a broader view, Chongqing’s overall accessibility is less than Sichuan’s. A higher average accessibility in Chongqing (4.191 h) compared to Sichuan (3.946 h) suggests reaching destinations within Chongqing takes longer. Moreover, Chongqing has a broader accessibility range than Sichuan, as evidenced by its larger standard deviation (0.647 h compared to Sichuan’s 0.361 h). This variability might stem from infrastructure differences, geographical challenges, or urbanization rates. These insights are crucial for understanding spatial accessibility patterns in the Chengdu-Chongqing region, potentially guiding improvements in transportation and regional development.

Central regions unsurprisingly have higher accessibility than outer areas, showcasing a clear “core-periphery” pattern(see Fig. 2). This design sees accessibility diminish as one moves from the center to the edges. The first accessibility layer encompasses only Suining City, with values up to 3.500 h. The subsequent layer possesses a noticeable ring-shaped structure with varied radii, sheltering numerous “Chengdu-Chongqing Twin Cities” zones. The outermost rings, primarily southwest and northeast, feature areas like the Kaizhou and Wanzhou Districts. Especially the northeast ring, with accessibility surpassing 5.001 h, stands out as a high-access zone.

Fig. 2
figure 2

The spatial pattern of accessibility in the Chengdu-Chongqing twin economic circle.

Full size image

Spatial correlation analysis

Analysis of Moran’s I index

Spatial correlation can affect regression model outcomes. Thus, before applying spatial econometric models for estimation and testing, it’s essential to determine spatial correlation among variables. Considering the continuity of roads, this study suggests road development significantly impacts adjacent spaces but less so on non-adjacent ones. A neighboring space weight matrix is believed to capture spatial characteristics more accurately. Consequently, a first-order spatial weight matrix, based on the Queen neighborhood, is created. Tests show a Moran’s I index value of 0.210, significant at a 5% level. This indicates the Chengdu-Chongqing twin-city economic circle’s per capita GDP in 2018 had significant spatial correlation. Distribution was not random and was influenced by neighboring region innovations, highlighting a clear spatial clustering.

However, the global Moran’s I index does not illuminate the spatial clustering attributes of specific regions. To delve deeper into the local distribution characteristics of per capita GDP in terms of spatial units, this paper generates a clustering diagram using the local Moran’s I index, which facilitates an intuitive examination of the phenomenon, as displayed in Fig. 3.

Fig. 3
figure 3

GDP per capita clustering chart.

Full size image

As Fig. 3 illustrates, the spatial distribution of per capita GDP in the Chengdu-Chongqing twin-city economic circle exhibits a pronounced clustering phenomenon. The low-low agglomeration areas dominate, covering 47.2% of the total. Following this, the high-high agglomeration zones comprise 25%. Low-high and high-low agglomeration zones account for 19.5% and 8.3%, respectively. High-high agglomeration regions are primarily concentrated in Chongqing’s main city and its surrounding areas, while low-low agglomeration regions are dispersed throughout the northern and southern regions of the Chengdu-Chongqing twin-city economic circle.

LM test

We can further perform the Lagrange multiplier test. Moran’s I (error) represents the Moran’s I test on the residuals of the standard linear regression model. As indicated in Table 2, Moran’s I (error) is 0.216, with an associated probability of 0.002. This result leads us to reject the null hypothesis of “no spatial dependence in residuals” at the 1% significance level, suggesting that the residuals of the standard linear regression model demonstrate significant spatial dependence and thus the model should be discarded. The LM-error value stands at 3.848 and is significant at a 5% level. Meanwhile, the LM-lag is 0.011 and lacks significance. The R-LM-error is 4.947, significant at a 5% level, whereas the R-LM-Lag is 1.110 and is insignificant. Hence, it can be concluded that the spatial error model outperforms the spatial lag model.

Table 2 LM test.
Full size table

Model empirical analysis

In an effort to fully account for the spatial correlation observed in the economic development trajectory of the Chengdu-Chongqing twin-city economic circle and to bolster the validity of the research findings, this study employs ordinary least squares (OLS), spatial lag model, and spatial error model for analysis. To provide more insight, the disparities among the outcomes of the different models will be juxtaposed in the subsequent section.

Model comparison

The selection of appropriate spatial econometric models can be informed by LM tests, while the efficacy of these models can be further scrutinized by examining their respective log-likelihood (LogL), Akaike information criterion (AIC), and Schwarz criterion value (SC) outputs. Notably, a larger LogL value and smaller AIC and SC values are indicative of a superior model fit and a more accurate delineation of the relationships between the variables.

As highlighted in Table 3, the LogL value of the spatial error model in this study, standing at −360.631, surpasses those of the ordinary least squares (−362.992) and the spatial lag model (−362.986). Additionally, the AIC and SC values for the spatial error model, at 735.262 and 746.346 respectively, are lower than those yielded by both the ordinary least squares and the spatial lag model. Hence, in concordance with the previous LM test results, the spatial error model indeed emerges as the more robust model.

Table 3 Results of the three models.
Full size table

Spatial error model results

The GDP per capita in the Chengdu-Chongqing twin-city economic circle demonstrates a significant spatial effect, predominantly manifested as the spatial autocorrelation of error terms. Subsequent results reveal a spatial autocorrelation coefficient for the spatial error model of 0.535, significant at the 1% level. This finding suggests a robust spatial dependence of the regional error term, and a pronounced proximity effect of the error term. Consequently, utilizing either the classical linear regression model or the spatial lag model would likely yield biased outcomes.

In accordance with the spatial error model, the urbanization level and accessibility met the 10% significance test, educational investment passed the 5% significance test, while the labor force and industrial structure passed the 1% significance test. Of these, accessibility has a negative correlation with per capita GDP, while the remainder exhibit positive correlations with per capita GDP, aligning with initial expectations. Nonetheless, the influence of trade openness on per capita GDP contradicts the original hypothesis and did not pass the 10% significance test.

A notable positive relationship exists between the level of urbanization and per capita GDP. For each 1% increase in the urbanization rate, per capita GDP escalates by ¥315.642, implying that regions with higher urbanization rates generally have higher per capita GDP. The optimization of the industrial structure also effectively bolsters economic growth, with every 1% enhancement in regional industrial structure within the Chengdu-Chongqing twin-city economic circle correlating with a per capita GDP increase of ¥2,029.470. Furthermore, there is a significant positive relationship between education investment and GDP per capita, with a per capita GDP increase of ¥108,469.000 accompanying every ¥10,000 increase in per capita educational expenditure.

The labor force also exhibits a distinct positive relationship with the regional economy, as corroborated by this study. According to the spatial error model, a 1% rise in the proportion of the employed population within the Chengdu-Chongqing twin-city economic circle corresponds with a per capita GDP increase of ¥322,575.700. Accessibility, reflecting the travel convenience within each region, can be effectively enhanced to minimize travel costs and improve regional mobility of people and materials. However, this study found that within the Chengdu-Chongqing twin-city economic circle, accessibility bears a significant negative relationship with economic growth, and with every 1-h decrease in accessibility, the per capita GDP increases by ¥5,006.560.

Discussion

This study first analyzed the regional accessibility distribution features of the Chengdu-Chongqing twin-city economic circle. Through this analysis, we discovered that the distribution of road traffic accessibility in the Chengdu-Chongqing twin-city economic circle exhibits a “center-periphery” circular shape. Overall, the road traffic accessibility in Sichuan province slightly surpasses that of Chongqing city. This is mainly due to early planning and construction strategies. Central region cities radiated from the main urban areas of Chengdu and Chongqing. These cities had developed economies and well-built highways, resulting in higher geospatial accessibility. This concurs with findings by researchers such as Liu et al. 2009 and Bai et al. 2012, who established that accessibility is influenced by the city’s administrative level and its degree of development. Further, the generally lower accessibility of Chongqing can be attributed to the fact that most counties in Chongqing are located in the peripheral areas.

Interestingly, our subsequent research revealed that the spatial agglomeration relationship of the economy of the Chengdu-Chongqing twin-city economic circle has similar distribution characteristics to its accessibility distribution, i.e., high-value/low-value areas demonstrate certain coupling characteristics. This similarity could be attributed to the fact that central regional cities receive more benefits in terms of economic allocation and resources from the government and society. There’s a strong link between traffic accessibility and the economy, as noted by Yin (2014). Cities with better traffic promote economic growth, and a booming economy demands improved accessibility. Therefore, a coupling exists between the spatial agglomeration and accessibility distribution in the Chengdu-Chongqing twin-city economic circle.

In the final spatial error model analysis, we observed that the effect of trade openness on economic growth in the Chengdu-Chongqing twin-city economic circle was not as significant as we initially expected. Considering the overall level of trade openness in the Chengdu-Chongqing twin-city economic circle, we believe that the reason for this insignificance is that the overall level of trade openness in the Chengdu-Chongqing twin-city economic circle is currently too low. As the relationship between trade openness and economic growth has a non-linear relationship (Kong et al. 2021), when the overall level of trade openness is low, its effect on economic growth is not sufficient to be tested.

According to the spatial error model, the effect of road traffic accessibility in the Chengdu-Chongqing twin-city economic circle on economic growth is significant and positive. As per the “inverted U-shaped” curve between road traffic accessibility and economic growth proposed by Bo (2019), we believe that road traffic in the Chengdu-Chongqing twin-city economic zone is in a period of rapid development, and its impact on economic growth will continue to significantly promote. Given the importance of road transportation, this conclusion carries significance for the economic development of the Chengdu-Chongqing twin-city economic zone.

However, it is crucial to note that this study bears certain limitations. Firstly, only data from 2019 were collected for the study. Future studies will incorporate a time series and construct panel data for analysis, aiming to study the spatial effects of road accessibility on economic growth in the Chengdu-Chongqing twin-city economic circle with greater precision. Additionally, our model did not account for the impact of traffic congestion on travel times. Congestion, as a significant factor, can alter the relationship between road accessibility and economic growth. Future endeavors should aim to integrate congestion metrics or indicators into the research framework, offering a more holistic understanding of the relationship between road traffic accessibility and economic development.

On another note, although this study utilized a cost grid method to estimate the shortest travel times, it’s noteworthy to mention the potential use of real-world data sources such as floating car data. Floating car data, which represents real-time traffic flow collected through mobile or in-vehicle devices, can provide a more granular and accurate depiction of actual travel durations. While the cost grid approach offers a standardized, consistent, and easily replicable method for estimating travel times, incorporating floating car data in future studies could further refine and enhance the accuracy of these estimates. However, the availability and granularity of such datasets might pose challenges, especially for historical periods or less urbanized areas.

Conclusions and policy implications

In this study, we first evaluated the road traffic level of the Chengdu-Chongqing twin-city economic circle using GIS technology. We found that the road traffic level of cities or counties located in the central area of the Chengdu-Chongqing twin-city economic circle was significantly higher than that in the peripheral areas. Subsequently, we introduced spatial econometric models as an indicator to evaluate the level of traffic development through quantitative treatment of road traffic accessibility, and then analyzed the spatial effect of road traffic on economic growth in the Chengdu-Chongqing twin-city economic circle.

The spatial autocorrelation test indicated a significant spatial dependence of GDP per capita in the Chengdu-Chongqing twin-city economic circle. A Lagrange multiplier test further revealed that the spatial error model is more suitable for this study. To bolster the credibility of the study, we utilized the classical linear regression model, the spatial lag model, and the spatial error model for analysis and comparison, establishing that the spatial error model indeed proved to be the optimal model. The results from the spatial error model indicated that accessibility significantly and positively affects economic growth.

With the implementation of the “Planning Outline for the Construction of the Chengdu-Chongqing Twin-City Economic Circle” and the “Belt and Road” strategy, the Chengdu-Chongqing twin-city economic circle is gradually becoming the fourth growth pole in China’s economic development. To achieve this goal, we can draw the following conclusions from this study:

  1. 1.

    Emphasize regional transportation gradient construction: There are noticeable disparities in the highway traffic level among the regions within the Chengdu-Chongqing twin-city economic circle. Considering the importance of different cities or counties in regional development and their own economic conditions, the existence of such a gap in traffic development levels is inevitable. Therefore, subsequent traffic planning should focus on improving the traffic development level of the “Chengdu-Chongqing main city” linkage area, while also fostering the development of traffic in other areas.

  2. 2.

    Foster integrated regional transportation development: The existence of administrative boundaries has led to a gap in transportation between the Sichuan and Chongqing regions of the Chengdu-Chongqing twin-city economic circle, and the current sub-administrative planning and management model makes mutual benefit difficult to achieve. In future transportation planning of the Chengdu-Chongqing twin-city economic circle, the traditional administrative district management model should be revised from the perspective of integrated regional transportation development. This includes coordinating the regional transportation management mechanism, designing the overall layout, focusing on key development areas, and promoting the joint construction and sharing of the transportation network.

  3. 3.

    Concentrate on resource allocation and financial tilting: The clustering diagram indicates an uneven economic development in the Chengdu-Chongqing twin-city economic circle. Owing to the construction of the Chengdu-Chongqing twin-city economic circle, the Chengdu-Chongqing region must shift away from traditional thinking and gradually reallocate resources and financial investment to other cities and counties while continuing to develop the main urban areas of Chengdu and Chongqing. This can ensure coordinated and balanced economic development in the region.

  4. 4.

    Improve the regional economic support environment: In addition to transportation accessibility, factors such as the urbanization level, industrial structure, educational investment, and labor force also significantly contribute to regional economic growth. Therefore, establishing a robust regional economic support environment is an indispensable measure to realize the sustainable economic development of the Chengdu-Chongqing twin-city economic circle. Furthermore, a significant increase in the level of trade openness may have a certain impact on economic growth.