Spatiotemporal data evolution of regional economy based on spatial econometric models

Abstract

From the perspective of practical development, under the premise of stable macroeconomic growth in society, influenced by spatiotemporal factors, regional economies inevitably have differences and changes, which affect various aspects of social production and life. In order to understand the spatiotemporal data evolution characteristics of regional economy, promote common regional development and the implementation of coordinated economic development strategies, this article takes the Beijing Tianjin Hebei (BTH for short here) region as an example. By combining spatial econometric models (SEM for short here), this article collects and processes economic development data from 2013 to 2022 in the BTH region, and introduced a spatial weight matrix to conduct High-performance computing and analysis of its regional economic spatial correlation. Based on this, this article conducted in-depth research on the spatiotemporal data evolution characteristics of the BTH regional economy through the description and quantitative analysis of the influencing factors of the BTH regional economy. The empirical analysis results showed that the global Moran index (Global Moran’s for short here) of the BTH region was positive from 2013 to 2022, and the $Z$ -values were all greater than 1.96, indicating a significant spatial correlation in the BTH regional economy. There is an imbalance in economic development in the BTH region, but with the continuous development of the region, its economic balance has improved.

Keywords

Regional economies spatial econometrics evolution of spatiotemporal data BTH region

1. Introduction

As an important component of economic development theory, regional economy plays a crucial role in the overall level of social development. Taking the BTH region as an example, influenced by time and geography, the economy of the BTH region has undergone many changes while constantly growing. The economic development among various cities in the region is imbalanced and insufficient, which has become a common objective phenomenon in the process of regional development. The negative issues arising from these changes are clearly not conducive to the comprehensive, coordinated, and sustainable development of the social economy. From the perspective of practical development, the changes in the economy of the Beijing Tianjin Hebei region mainly include problems such as imbalanced and insufficient economic development among various cities within the region. For example, in urban areas, economic development is relatively fast, infrastructure and public services are relatively complete, while in rural areas, economic development lags behind, and problems such as insufficient infrastructure and public services have become common objective phenomena in the process of regional development. How to effectively analyze the evolution of regional economic data while fully considering spatial and temporal characteristics has become an important direction for regional development strategies. The SEM is an econometric model dealing with spatial correlation effects. It can be applied to the analysis of national, provincial, urban, and regional issues and can take into account both temporal and spatial changes. Through High-performance computing of spatio-temporal data, more accurate estimation results can be obtained. In the analysis of the spatiotemporal data evolution of regional economies, SEM can analyze the spatiotemporal pattern evolution and mechanism of regional economy from a two-dimensional perspective.

With the improvement of social development level, the evolution of regional economic spatiotemporal data is receiving increasing attention from scholars. Song Yaqing used a hyper relaxation measure model to estimate the green economy efficiency of various provinces and cities in the Yangtze River Delta region from 2005 to 2018, and explored the spatiotemporal evolution characteristics of the green economy by combining the Thiel index and Moran index (Moran’ I) [1]. Chu Nanchen built an indicator system to evaluate Russia’s urbanization development level in combination with the population economic sociology ecological environment model [2]. Ye Changsheng took 110 prefecture-level cities in the Yangtze River Economic Belt as the research area. He used exploratory spatial data to analyze the spatiotemporal evolution of urban resilience, promoting sustainable development of regional and national economies [3]. Liu Baiqiong proposed a contribution decomposition method, which divides the contributions of each region into economic contribution and population contribution [4]. At present, the evolution analysis of regional economic spatiotemporal data has made good progress, but with the complexity of the economic development (ED for short here) environment, the analysis methods also need to be appropriately improved and optimized. The current research methods used have limitations in fitting.

The SEM is concise and clear, allowing for unbiased parameter estimation. Wang Zhenbo used a SEM to study the green economic efficiency of 26 cities in the Yangtze River Delta from 2005 to 2015, and the results showed that the SEM had a good fitting effect [5]. Zhang Jie used the panel data and spatial analysis model of 31 provinces in China from 2008 to 2018 to study the correlation [6]. Under the SEM, the evolution analysis of regional economic spatiotemporal data has achieved further development, but most studies have not combined practical issues in regional development to provide more effective guidance for coordinated ED.

In order to deeply understand the spatiotemporal evolution laws of regional ED and promote its development towards a more balanced and healthy direction, this article combines SEM to conduct in-depth research on the spatiotemporal data evolution of BTH regional economy. Starting from the perspective of Beijing, Tianjin, Hebei city, this article reveals the spatiotemporal data, evolution laws, and characteristics of regional economy based on spatial econometric models. At present, there is still a lack of research on the analysis of economic development changes in various regions of Beijing, Tianjin, Hebei from a regional perspective, and there is a lack of dynamic analysis from spatial differences to spatial agglomeration. This article uses spatial econometric models as the calculation method to enrich the dynamic analysis of the evolution of regional economic spatiotemporal data. Through empirical analysis, the factors that affect the evolution of regional economic development have been deeply explored. This article finds through empirical analysis that there is a spatial positive correlation in the BTH regional economy, and there is a certain imbalance in ED. The SEM provides a comprehensive and effective analysis of the temporal characteristics and spatial evolution patterns of the regional economy and provides objective guidance for the formulation of practical policies and development strategies.

2. The evolution of regional economic spatiotemporal data under SEM

2.1 BTH regional economy

Regional economy is a whole that corresponds to the socio-economic system, that is, the economy of a specific region [7]. Specifically, it refers to a production complex generated by the interaction of internal and external factors in different spatial individuals at the level of economic development within a designated and divided administrative region. It is a comprehensive geographical concept of ED, with a geographical scope, objective law of ED as the standard, and economic activities and economic relations as the main content. Regional economy is not only the mutual influence of various economic and geographical factors within a region, but also a comprehensive reflection of the overall ED of the region. It is an organic whole composed of geography and economy, which can achieve economic correlation within a certain range. Regional economy is the key to achieving rational resource allocation and improving regional competitiveness.

In geographical space, the spatiotemporal characteristics exhibited by regional economies have a certain degree of complexity [8]. The BTH region plays a unique representative role and value in sustainable development such as society, economy, and environment.

The BTH region is mainly composed of two municipalities directly under the central government, Beijing and Tianjin, 11 prefecture-level cities in Hebei Province, and Anyang City in Henan Province. As one of the regions with the greatest potential for ED, BTH is the third largest promoting unit in China’s economic spatial development and holds an important position in the Bohai Rim Economic Circle [9]. In addition, due to its unique geographical location, the ED of the BTH region has received increasing attention. The BTH region is an important ecological, political, economic, and cultural center in China, characterized by regional continuity, integration, cultural similarity, and strong cultural characteristics. It serves as a crucial venue and means of entry for China into international competition to promote social modernization and development [10].

2.1.1 Geographic location and natural environment

BTH region is located in the hinterland of Bohai Sea rim in China to the east of Eurasia, adjacent to Yanshan Mountain in the north, North China Plain in the south, Taihang Mountain in the west and Bohai Sea in the east. It is a region with great potential and broad ED prospects [11]. Its north-south length is 750 kilometers, its east-west width is 650 kilometers, and its area is approximately 218000 square kilometers. The BTH region has a temperate monsoon climate with significant seasonal changes, characterized by high climate risk, less snowfall, and low temperatures. Its vegetation distribution has significant regional characteristics and vertical distribution characteristics [12]. The BTH region mainly uses arable land and forest land as the main land use methods, with arable land accounting for over 30% of the total construction land, while forest land accounts for about a quarter. In actual development, the BTH region has basically formed two distinct land use patterns: the northern mountainous area is mainly composed of forest and grassland, supplemented by wasteland, and the southern plain is mainly composed of cultivated land, supplemented by construction land.

2.1.2 ED

The economy of BTH region is developing rapidly, and the per capita GDP (Gross Domestic Product) of each city in the region is also continuously increasing [13]. The current GDP situation of BTH region is displayed in Table 1. By 2022, the total GDP of the BTH region has exceeded 10 trillion yuan, and its ED has reached a new level [14]. Compared with the proportion of total GDP in 2013, the proportion of total GDP in Beijing in the BTH region in 2022 has increased by about 10%, while the proportion of total GDP in Hebei and Tianjin has decreased.

Table 1
Current economic development status of BTH region in 2022

Area	GDP (100 million yuan)	Proportion (%)
Beijing	41610.9	41.49
Tianjin	16311.3	16.26
Hebei	42370.4	42.25
Total	100292.6	100

From the economic development status of the BTH region in 2022 in Table 1, it can be seen that the core cities in the BTH region have a relatively fast economic development speed. From the change in GDP proportion, Beijing’s advantage in economic development has further strengthened, while the economic development of Hebei and Tianjin is relatively weak. Beijing has certain advantages in high-end industries and technological innovation, while Hebei and Tianjin lack high-end industries and technological innovation capabilities, resulting in a relatively weak proportion of GDP.

2.1.3 Industrial structure

The industrial structure of the three industries in BTH would reach a level of 4.8:29.6:65.6 in 2022 [15]. From the proportion of its industrial structure, Beijing’s tertiary industry holds a core position in the industrial structure, with a specific proportion of 83.8%; Next is the secondary industry, which accounts for 15.9% of the total, while the primary industry in Beijing accounts for only 0.3%; Similar to Beijing, Tianjin’s industrial structure is also centered around the tertiary industry, with the tertiary industry accounting for 61.3%, and the secondary and primary industries accounting for 37% and 1.7% of the exhibition structure, respectively; The proportion of industrial structure in Hebei is relatively balanced, with the tertiary industry accounting for 49.4%, the secondary and primary industries accounting for 39.6% and 11%.

Compared with the industrial structure of BTH region in 2013, the industrial structure of each city achieved a certain optimization and adjustment in 2022. Overall, Beijing, Tianjin, and Hebei are all centered around the tertiary industry, especially Beijing, where the tertiary industry accounts for over 80% of the total structure. The industrial structure of Tianjin is also steadily optimizing. Since 2014, the output value of its tertiary industry has surpassed that of the secondary industry for the first time, and it has gradually achieved a transformation from “two, three one” to “three, two one” in industrial structure; the proportion of the tertiary industry in Hebei is slightly smaller than that in the Beijing Tianjin region, and its proportion is less than 50% [16]. It has also become the main industrial growth pattern of “321”. In terms of the share of the tertiary sector in the BTH region, the share of the tertiary sector in the total industrial structure of the BTH region has increased from 58.1% to 65.6% between 2013 and 2022, with an actual increase of 7.5%. The proportion of the tertiary industry in Beijing, Tianjin, and Hebei has increased by 4.3%, 7.2%, and 8.4%, respectively, compared to 2013, with the most significant increase in the proportion of the tertiary industry in Hebei [17].

2.2 SEM

The SEM mainly analyzes the value of a specific attribute of the observed object through High-performance computing to describe and explain its existence with space, time, and space-time characteristics, and then classify the objects with different spatial attributes [18]. Space, time, and spatiotemporal characteristics are also known as the “spatial effects” of spatial data. The classification of spatial effects mainly includes spatial dependence and spatial heterogeneity. Spatial dependency refers to the functional relationship between the specific values of a certain attribute of a geographical unit and the attribute values of other geographical units, which is known as spatial “isomorphism”. Spatial heterogeneity refers to that when analyzing the observed things, it should not use a certain unit of a certain region as the analysis object, but should analyze according to some attributes of the region or the whole country in various aspects, that is, spatial “heterogeneity”. When classifying spatial effects, two aspects need to be considered: first, the dependency between attribute values of the same type; the second is the dependency between attribute values of different categories. Traditional econometric models often overlook these two aspects, while SEM incorporate them. This method introduces the adjacency between spatial positions into the model by constructing a weight matrix, making the model more accurate and more conducive to analyzing some economic phenomena and their evolution characteristics.

Spatial econometrics introduces spatial dependence and spatial heterogeneity in data into the model, no longer emphasizes the classic assumptions of traditional econometrics, and abandons the practice of treating the data itself as fixed or random effects [19, 20]. The SEM is an organic combination of classical econometric methods and the spatial relationship of geographical location, that is, under the influence of time and space factors, the spatial analysis method is used to study the relationship and change laws between economic variables [21, 22].

In the process of analyzing the evolution of regional economic spatiotemporal data using SEM, it is first necessary to quantify the spatial relationships between each other. This step can be described using spatial weight matrices:

$\displaystyle W=\left[{{\begin{array}[]{*{20}c}{w_{11}}\hfill&{w_{12}}\hfill&{% {\begin{array}[]{*{20}c}\cdots\hfill&{w_{1n}}\hfill\\ \end{array}}}\hfill\\ {w_{21}}\hfill&{w_{22}}\hfill&{{\begin{array}[]{*{20}c}\cdots\hfill&{w_{2n}}% \hfill\\ \end{array}}}\hfill\\ {{\begin{array}[]{*{20}c}\vdots\hfill\\ {w_{n1}}\hfill\\ \end{array}}}\hfill&{{\begin{array}[]{*{20}c}\vdots\hfill\\ {w_{n2}}\hfill\\ \end{array}}}\hfill&{{\begin{array}[]{*{20}c}{{\begin{array}[]{*{20}c}\cdots% \hfill\\ \cdots\hfill\\ \end{array}}}\hfill&{{\begin{array}[]{*{20}c}\vdots\hfill\\ {w_{nn}}\hfill\\ \end{array}}}\hfill\\ \end{array}}}\hfill\\ \end{array}}}\right]$ (1)

As a spatial weight matrix, $W$ represents the matrix relationship between the independent variable and the dependent variable in space. In the application process of specific SEM, $W$ is obtained externally because the spatial weight matrix involves exogenous data information related to the interaction between regions, and generally can be analyzed without the need for a model. $w_{\textit{ij}}$ represents the general form of spatial weight matrix elements. On the main diagonal, the value of this element is equal to 0.

The distance can be expressed as:

$\displaystyle w_{ij}=d_{ij}^{-\theta}$ (2)

$d_{\textit{ij}}$ refers to the actual distance between regions, where the parameter $\theta$ is usually taken as a positive number.

The exponential function of distance is:

$\displaystyle w_{ij}=\exp\left({d_{ij}^{-\theta}}\right)$ (3)

Public boundary length:

$\displaystyle w_{ij}=\left({\frac{l_{ij}}{l_{i}}}\right)^{r}$ (4)

$l_{ij}$ refers to the length of the common boundary between regions $i$ and $j$ , while $l_{i}$ refers to the length of the boundary between individual regions. If $w_{ij}=$ 1, it means that there is a common boundary between the two regions; if $w_{ij}=$ 0, it means that there is no common boundary between the two regions.

Assuming that the BTH regional economy has significant spatial correlation, spatial static and dynamic panel data models can be used for estimation. The specific model settings are:

$\displaystyle r_{it}=\delta\mathop{\sum}\nolimits_{j}^{N}w_{ij}r_{jt}+s_{it}% \sigma+u_{i}+\varepsilon_{it}$ (5) $\displaystyle r_{it}=\gamma r_{i,t-1}+\delta\mathop{\sum}\nolimits_{j=1}^{N}w_% {ij}r_{jt}+\alpha\mathop{\sum}\nolimits_{j=1}^{N}w_{ij}r_{j,t-1}+s_{it}\sigma+% u_{i}+\varepsilon_{it}$ (6)

The definitions of variables in Eqs (5) and (6) are displayed in Table 2.

Table 2

Definition of formula variables

Sequence	Parameter	Meaning
1	${i}$	Individual area
2	${t}$	Time
3	${r}_{\text{it}}$	Explained variable
4	${s}_{\text{it}}$	Exogenous explanatory variable matrix
5	$\sigma$	Parameters to be estimated
6	${u}_{i}$	Individual fixed effects
7	$\varepsilon_{\text{it}}$	Mean value
8	$\gamma$	Time autoregressive coefficient
9	$\delta$	Spatial autoregressive coefficient
10	$\alpha$	Coefficient of spatial lag term

Among them, the value range of $i$ is $\left({1,\cdots,N}\right)$ ; The value range of $t$ is $\left({1,\cdots,T}\right)$ . To remove the instability in $r$ , the model can be rewritten in vector form:

$\displaystyle r_{t}=\gamma r_{t-1}+\delta Wr_{t}+\alpha Wr_{t-1}+s_{t}\sigma+u% _{i}+\varepsilon_{it}$ (7)

After deformation:

$\displaystyle\left({I-W}\right)r_{t}\!=\!\gamma\left({I\!-\!W}\right)r_{t-1}+% \delta W\left({I-W}\right)r_{t}+\alpha W\left({I-W}\right)r_{t-1}+\left({I-W}% \right)s_{t}\sigma\!+\!\left({I\!-\!W}\right)\varepsilon_{it}$ (8)

Due to $\left({I-W}\right)u_{i}=0$ , $u_{i}$ has been removed. Multiplying both sides of formula 8 by $k$ yields:

$\displaystyle k\left({I-W}\right)r_{t}=\gamma k\left({I-W}\right)r_{t-1}+% \delta kW\left({I-W}\right)r_{t}+\alpha kW\left({I-W}\right)r_{t-1}+k\left({I-% W}\right)s_{t}\sigma+k\left({I-W}\right)\varepsilon_{it}$ (9)

Among them, $k=\bigwedge_{N-1}^{-1/2}F_{N,N-1}^{T}$ and $\bigwedge$ are non zero eigenvalues, and ${F}$ is the eigenvector.

After organizing formula 9, it can be concluded that:

$\displaystyle r_{t}^{\ast}=\gamma r_{t-1}^{\ast}+\delta Wr_{t}^{\ast}+\alpha r% _{t-1}^{\ast}+s_{t}\sigma+\varepsilon_{t}$ (10)

The error correction model and maximum likelihood estimation are displayed in Formulas 11 and 12:

$\displaystyle\Delta r_{it}=\delta\mathop{\sum}\nolimits_{j=1}^{N}w_{ij}\Delta r% _{jt}+\left({\gamma-1}\right)r_{j,t-1}+\left({\alpha+\delta}\right)\mathop{% \sum}\nolimits_{j=1}^{N}w_{ij}r_{j,t-1}+s_{it}\sigma+u_{i}+\varepsilon_{it}$ (11) $\displaystyle\Delta r_{t}=\delta W\Delta r_{t}+\left({\gamma-1}\right)r_{t-1}+% \left({\alpha+\delta}\right)Wr_{t-1}+s_{t}\sigma+u_{i}+\varepsilon_{it}$ (12)

At time $t$ , $\Delta r_{t}$ can calculate the partial derivatives of the $h$ explanatory variable from the first individual to the $N$ individual in $s_{t}$ , and obtain the following partial derivative matrix:

$\displaystyle\left[{\frac{\partial\Delta r}{\partial s_{1h}}\cdot\frac{% \partial\Delta r}{\partial s_{Nh}}}\right]_{t}=\left[{{\begin{array}[]{c}{% \frac{\partial\Delta r_{1}}{\partial s_{1h}}\cdot\frac{\partial\Delta r_{1}}{% \partial s_{Nh}}}\\ {\frac{\partial\Delta r_{N}}{\partial s_{1h}}\cdot\frac{\partial\Delta r_{N}}{% \partial s_{Nh}}}\\ \end{array}}}\right]_{t}=\left({I-\delta W}\right)^{-1}\sigma_{h}$ (13)

From the perspective of spatial effects, elements on the diagonal are direct influences, while elements on non-diagonal lines are indirect influences. Because a change in an explanatory variable inside a spatial individual has varied direct and indirect consequences on that individual or other spatial individuals. Therefore, the direct impact of spatial effects can be evaluated using average diagonal components, while the non-principal diagonal items in each row’s average can be used to calculate the indirect impact.

According to the formula:

$\displaystyle\frac{\partial E\left({\Delta r_{t}}\right)}{\partial r_{t-1}}=% \left({I-\delta W}\right)^{-1}\left[{\left({\gamma-1}\right)I+\left({\alpha+% \delta}\right)W}\right]$ (14)

The average value of the main diagonal elements reflects the spatial convergence effect of each element itself, while the average value of the total of each row’s minor diagonal elements reflects the convergence effect of each element with other spaces. If $\gamma+\alpha+\delta=1$ , then this situation can be referred to as spatial cointegration. On this basis, $\frac{\partial E\left({\Delta r_{t}}\right)}{\partial r_{t-1}}=\left({I-\delta W% }\right)^{-1}\left({\gamma-1}\right)\left({I-W}\right)$ represents long-term non convergence of spatial individuals.

From the perspective of formula algorithms, the spatial econometric model introduces the adjacency between spatial positions into the model by constructing a weight matrix, making the expression of the model more accurate. Through spatial autocorrelation analysis, the spatial agglomeration and dispersion characteristics of regional economic phenomena, as well as the transmission and spatial spillover effects of regional economic phenomena, can be revealed, thereby gaining a deeper understanding of the interaction mechanisms between different regions, Provide a foundation for further analysis of spatiotemporal data evolution.

3. Empirical analysis of the evolution of regional economic spatiotemporal data

3.1 Data collection

To analyze the evolution of economic spatiotemporal data in the BTH region, this article chooses 13 cities in the BTH region, including Beijing and Tianjin municipalities, as well as 11 prefecture-level cities in Hebei Province, including Baoding, Langfang, Tangshan, Shijiazhuang, Handan, Qinhuangdao, Zhangjiakou, Chengde, Cangzhou, Xingtai, and Hengshui. The sequence is displayed in Table 3. The specific inspection year is 2013–2022. When selecting indicators, this article selects the most representative per capita GDP in regional economic development as the indicator for analysis.

Table 3
BTH regional city sequence

Administration	Sequence	City
Municipality directly under the central government	1	Beijing
	2	Tianjin
Prefecture-level city	3	Baoding
	4	Langfang
	5	Tangshan
	6	Shijiazhuang
	7	Handan
	8	Qinhuangdao
	9	Zhangjiakou
	10	Chengde
	11	Cangzhou
	12	Xingtai
	13	Hengshui

3.2 Spatial weight matrix

This article constructs a spatial matrix based on the formula and determines whether there are adjacent boundaries between them according to the actual spatial layout of the BTH area, thereby obtaining the corresponding weight matrix, as displayed in Table 4.

Table 4
BTH regional spatial weight matrix

Sequence	1	2	3	4	5	6	7	8	9	10	11	12	13
1	1	0	1	0	0	0	1	0	0	1	0	0	1
2	0	0	1	0	1	1	0	1	0	0	0	0	0
3	0	0	0	1	0	0	1	0	1	0	0	0	0
4	0	1	1	1	0	1	0	1	0	0	1	0	0
5	1	1	0	0	1	0	1	0	0	1	0	1	0
6	0	0	1	0	0	0	0	0	0	0	0	1	0
7	0	0	0	0	0	0	0	0	1	0	1	0	0
8	0	1	1	0	0	1	0	0	1	0	0	0	0
9	1	0	0	0	0	0	1	0	0	1	1	1	1
10	1	0	0	1	0	0	0	0	0	0	0	0	0
11	0	0	0	0	1	0	0	0	0	1	1	0	0
12	0	1	0	1	0	1	0	0	0	0	0	0	0
13	0	0	0	0	1	0	0	1	0	0	0	0	0

3.3 Spatial correlation

In view of the spatial weight matrix and the per capita GDP data of 13 cities in the BTH region, this article uses the Moran’ I to conduct spatial correlation analysis on the per capita GDP data of 13 cities in the region. When the Moran’ I exceeds 0, it indicates a certain spatial positive correlation between the ED level of cities in the region and their neighboring cities. The larger the index value, the stronger the positive relationship; when the Moran’ I is less than 0, it indicates a certain spatial negative correlation between the ED level of cities in the region and their neighboring cities; The higher the absolute value of this index, the greater the degree of spatial exclusion of adjacent cities; When the Moran’ I is 0, the degree of ED in the region is randomly independent. This article uses the normal test method to conduct a significance test on the Moran’ I and calculates the $Z$ -value of the test statistic through the Moran’ I and its standard deviation. The $Z$ -value is used to determine the significance of the Moran’ I. When the $Z$ -value exceeds 1.96 or falls below $-$ 1.96, it indicates that the Moran’ I is significant, indicating the presence of spatial autocorrelation. When the $Z$ -value ranges from $-$ 1.96 to 1.96, it indicates that the Moran’ I is not significant, meaning there is no spatial autocorrelation. In addition, the $P$ -value related to the $Z$ -value can be calculated and compared with a specific significance level (usually 0.05). When the Moran index remains significant at a specific level of significance, it indicates that specific attribute values within the region have significant spatial correlation. Conversely, it does not have spatial correlation. The Global Moran’I analysis is displayed in Fig. 1.

Figure 1.

Global moran index.

From Fig. 1, the global Moran indices of the BTH region from 2013 to 2022 are 0.295, 0.296, 0.273, 0.265, 0.289, 0.276, 0.292, 0.284, 0.261, and 0.265, respectively; The Global Moran’I is all positive, indicating that the level of economic development in neighboring regions is spatially positively correlated. In terms of space, the economic development of the BTH region showed a trend of agglomeration from 2013 to 2022, and the ED levels between adjacent regions showed the same direction. From the $Z$ -value results, the $Z$ -value of the Moran’ I in the BTH region from 2013 to 2022 was greater than 1.96, indicating that the Moran’ I passed the significance test. The $P$ -value test results of the $Z$ -value are displayed in Table 5.

Table 5

$P$ -value test results

Sequence	Particular year	$P$ value
1	2013	0.036
2	2014	0.024
3	2015	0.003
4	2016	0.032
5	2017	0.017
6	2018	0.028
7	2019	0.036
8	2020	0.015
9	2021	0.023
10	2022	0.018

From Table 5, the per capita GDP of each city in the BTH region from 2013 to 2022 passed a significance test of 0.05, indicating that the economies of each city in the region have a certain spatial correlation.

Although the spatial correlation of the BTH regional economy has been reflected in the Global Moran’I analysis, the Global Moran’I cannot deeply explore the agglomeration trends and phenomena of the region. It cannot effectively observe the dynamic changes of the regional economy, while the local Moran’ I can better observe it. Therefore, this article further analyzed the data of the BTH region in 2013 and 2022 using the Moran scatter plot, as displayed in Figs 2 and 3.

Figure 2.

Moran scatter map of BTH region in 2013.

Figure 3.

Moran scatter map of BTH region in 2022.

In Fig. 2, the five cities of Beijing, Tianjin, Langfang, Shijiazhuang, and Tangshan in the BTH region are located in the first quadrant. This indicates that these five cities have strong spatial correlation, belong to high concentration areas, and their economic development speed is fast. From the overall data, the economic spatial distribution of BTH region is relatively uneven, with most areas falling in the first and third quadrants, accounting for approximately 61.54%. This further indicates that the BTH regional economy showed a spatial positive correlation in 2013.

In Fig. 3, Beijing, Tianjin, Baoding, and Langfang in the BTH region are located in the first quadrant and belong to the economic center cities of the BTH region; Shijiazhuang, Tangshan, Qinhuangdao, and Cangzhou are located in the second quadrant; Xingtai, Hengshui, and Chengde are located in the third quadrant; Zhangjiakou and Handan are located in the fourth quadrant. From the overall data, the proportion of cities in the first and third quadrants is about 53.85%. Although there are still differences in regional ED, the spatial distribution balance of BTH regional economy has improved in 2022. The ED gap between core cities such as Beijing and Tianjin and other cities is gradually decreasing, driving the coordinated development of other cities around the Bohai Sea.

3.4 Evolutionary characteristics

There are many factors that affect the regional economies, and each factor has both mutual influence and causal relationships. To understand the evolution characteristics of regional economy, this article uses a spatial econometric model to analyze the spatiotemporal data of BTH regional economy.

Although regional economy is a complex system and its development and evolution are composed of multiple factors, regression analysis is conducted based on its main influencing factors. It can also largely judge the mechanism of various factors in the spatial and temporal pattern of regional economy, and thus analyze the characteristics of the evolution of regional economic spatial patterns. From a social perspective, its influencing factors mainly include regional policies and labor resources; from an economic perspective, its influencing factors include the level of urbanization, the development of industrial structure, the total industrial output value, and the development of the total value of the tertiary industry; from an environmental perspective, its influencing factors include import and export trade, transportation factors, production technology level, and natural resource factors. The influencing factor system is displayed in Fig. 4.

To determine the impact of various factors on the evolution of the BTH regional economic spatial pattern, it is necessary to use them as variables for quantitative analysis in this article. From the analysis of spatial correlation, the economic development pattern of BTH region has obvious spatial correlation, so it does not meet the prerequisite of the general regression analysis assumption that the sample observations are independent of each other. Therefore, on the basis of general regression, this article incorporates spatial econometric regression models to analyze it. The model fitting results and discriminant test results are displayed in Table 6.

Table 6
Model fitting results and discriminant testing

Variable	Fitting coefficient	$t$ value	$P$ value
Regional policies	0.28106	26.14725	0.00558
Labor resources	0.15379	18.58071	0.00722
Urbanization level	0.18213	21.36242	0.01724
Industrial structure development	0.09725	6.81324	0.00293
Gross industrial production value	0.21032	20.53891	0.00314
Total value of the tertiary industry	0.12856	15.06275	0.00527
Import and export trade	0.07391	4.19656	0.00361
Transportation factors	0.07625	4.08191	0.00001
Production technology level	0.05817	3.58762	0.00145
Natural resource factors	0.05301	3.40937	0.00072
Goodness of fit	0.63510	Correction of goodness of fit	0.63430
Maximum likelihood value of spatial lag	1953.80^*	Spatial lag robustness estimator	2184.30^*
Maximum likelihood value of spatial error	1243.60^*	Spatial error robustness estimator	1479.90^*

Note: “^*” indicates significant at the 0.05 level.

Figure 4.

System of influencing factors.

From Table 6, the spatial error model and spatial lag model are still significant at the specified 0.05 significance level. However, from the specific maximum likelihood value and robustness estimates, compared with the results of the spatial error model, the advantages of the spatial lag model are more significant. Therefore, this article uses a spatial lag model to analyze variables (represented by serial numbers 1–10), as displayed in Fig. 5.

Figure 5.

Model fitting results.

From the fitting results in Fig. 5, all influencing factors have a positive impact on the ED of the BTH region. Among them, regional policies, labor resources, and gross industrial product have a significant positive impact on the evolution of regional economic spatiotemporal data. Under the guidance of regional policies and industrial production, labor resources in the BTH region are becoming increasingly concentrated, and the gross industrial product is also continuously increasing. This not only drives the ED of its own city, but also has a positive impact on other regions. Although the level of urbanization and the impact of natural resources have a positive impact, their impact is relatively small. This is mainly due to the abnormal urbanization construction in the BTH region, which actually leads to the lagging economic development of some cities. The uneven spatial distribution and low utilization efficiency of BTH natural resources also constrain the coordinated ED of various cities.

4. Discussion

In the empirical analysis of the evolution of regional economic spatiotemporal data, this article studied the economic development data of 13 cities in the Beijing Tianjin Hebei region from 2013 to 2022 from the perspectives of spatial correlation analysis and evolution characteristics analysis

(1)
From the results of spatial correlation analysis, it can be seen that the global Moran index of the BTH region from 2013 to 2022 is positive, indicating that the economic development level of neighboring regions is spatially positively correlated. Among them, in 2013, Beijing, Tianjin, Langfang, Shijiazhuang, and Tangshan had strong spatial correlation; The spatial correlation between Beijing, Tianjin, Baoding, and Langfang in 2022 is strong. Overall, in the past decade of development, the economic spatial distribution balance of the Beijing Tianjin Hebei region has improved, and the economic development gap between core cities and other cities has gradually decreased.
(2)
From the analysis of evolution characteristics, it can be seen that BTH regional policies, labor resources, and industrial gross domestic product have a significant positive impact on the process of economic development. However, there are also problems of abnormal urbanization development and uneven spatial distribution of natural resources in the BTH regional economic development, which to some extent hinder the healthy and balanced development of the regional economy.

5. Conclusions

Regional economy plays an irreplaceable role in maintaining the stability of social and economic structure. Currently, issues such as uneven and unstable regional economic development have become a major obstacle to sustainable socio-economic development. In order to summarize the spatiotemporal evolution laws of regional economy and better promote the implementation of economic construction work, this article took the BTH region as an example and combined SEM to conduct in-depth research on the spatiotemporal data evolution of the economy in the region from 2013 to 2022. Regional policies, labor resources, and industrial GDP are important factors that lead to economic evolution. Deformed urbanization, uneven distribution of natural resources, and insufficient utilization have had a certain negative impact on the coordinated development of the regional economy.

In the actual development process, it is necessary for the BTH region to play the radiating role of core cities, improve location conditions, strengthen cooperation mechanisms, and drive the ED of other regions. In response to urbanization, construction and natural resource issues, scientific planning, adjustment of industrial structure, and improvement of natural resource prices and tax policies are adopted.

Although the spatiotemporal data evolution analysis of regional economy based on SEM in this article can provide some suggestions for regional ED, there are still some areas worth improving in this study. The spatiotemporal data evolution of regional economy in this article only selected a representative region for analysis, and the influencing factors of regional economy are relatively complex. The description in this article is still insufficient. In future research, further improvements would be made to address the limitations of the research scope and depth, in order to provide more objective suggestions for promoting the healthy development of the regional economy.

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Sequence	1	2	3	4	5	6	7	8	9	10	11	12	13
1	1	0	1	0	0	0	1	0	0	1	0	0	1
2	0	0	1	0	1	1	0	1	0	0	0	0	0
3	0	0	0	1	0	0	1	0	1	0	0	0	0
4	0	1	1	1	0	1	0	1	0	0	1	0	0
5	1	1	0	0	1	0	1	0	0	1	0	1	0
6	0	0	1	0	0	0	0	0	0	0	0	1	0
7	0	0	0	0	0	0	0	0	1	0	1	0	0
8	0	1	1	0	0	1	0	0	1	0	0	0	0
9	1	0	0	0	0	0	1	0	0	1	1	1	1
10	1	0	0	1	0	0	0	0	0	0	0	0	0
11	0	0	0	0	1	0	0	0	0	1	1	0	0
12	0	1	0	1	0	1	0	0	0	0	0	0	0
13	0	0	0	0	1	0	0	1	0	0	0	0	0

Sequence	1	2	3	4	5	6	7	8	9	10	11	12	13
1	1	0	1	0	0	0	1	0	0	1	0	0	1
2	0	0	1	0	1	1	0	1	0	0	0	0	0
3	0	0	0	1	0	0	1	0	1	0	0	0	0
4	0	1	1	1	0	1	0	1	0	0	1	0	0
5	1	1	0	0	1	0	1	0	0	1	0	1	0
6	0	0	1	0	0	0	0	0	0	0	0	1	0
7	0	0	0	0	0	0	0	0	1	0	1	0	0
8	0	1	1	0	0	1	0	0	1	0	0	0	0
9	1	0	0	0	0	0	1	0	0	1	1	1	1
10	1	0	0	1	0	0	0	0	0	0	0	0	0
11	0	0	0	0	1	0	0	0	0	1	1	0	0
12	0	1	0	1	0	1	0	0	0	0	0	0	0
13	0	0	0	0	1	0	0	1	0	0	0	0	0

Spatiotemporal data evolution of regional economy based on spatial econometric models

Abstract

Keywords

1. Introduction

2. The evolution of regional economic spatiotemporal data under SEM

2.1 BTH regional economy

2.1.1 Geographic location and natural environment

2.1.2 ED

Table 1 Current economic development status of BTH region in 2022

2.2 SEM

3.1 Data collection

Table 3 BTH regional city sequence

Table 4 BTH regional spatial weight matrix

Table 6 Model fitting results and discriminant testing

References

Table 1
Current economic development status of BTH region in 2022

Table 3
BTH regional city sequence

Table 4
BTH regional spatial weight matrix

Table 6
Model fitting results and discriminant testing

Sequence	1	2	3	4	5	6	7	8	9	10	11	12	13
1	1	0	1	0	0	0	1	0	0	1	0	0	1
2	0	0	1	0	1	1	0	1	0	0	0	0	0
3	0	0	0	1	0	0	1	0	1	0	0	0	0
4	0	1	1	1	0	1	0	1	0	0	1	0	0
5	1	1	0	0	1	0	1	0	0	1	0	1	0
6	0	0	1	0	0	0	0	0	0	0	0	1	0
7	0	0	0	0	0	0	0	0	1	0	1	0	0
8	0	1	1	0	0	1	0	0	1	0	0	0	0
9	1	0	0	0	0	0	1	0	0	1	1	1	1
10	1	0	0	1	0	0	0	0	0	0	0	0	0
11	0	0	0	0	1	0	0	0	0	1	1	0	0
12	0	1	0	1	0	1	0	0	0	0	0	0	0
13	0	0	0	0	1	0	0	1	0	0	0	0	0