Analysis of the Strength of China’s Inter-Provincial Economic Linkage Intensity and Its Influencing Factors

: The construction of the intensity of China's inter-provincial economic ties is of great significance to the spatial carrier of China's inter-provincial modern industrialization system . We uses entropy method, modified gravity model and grey correlation model to measure inter-provincial economic linkage intensity in 2019 and its influencing factors. The research shows that: (1) The strength of China’s inter-provincial economic connection network is different, and the economic connection is not balanced. It is mainly concentrated in Beijing-Tianjin-Hebei region and Jiangsu-Zhejiang-Shanghai region. There is a certain coincidence between the economic connection network and the total economic connection intensity in space, and the economic development of each province is closely related to the connection between provinces. (2) The relationship between the China’s inter-provincial economic linkage intensity and the gray correlation degree of each subsystem is infrastructure > social development > economic development > ecological environment protection > population and labor development. Among them, 6 subsystems have a correlation degree of 0.79 or more for the strength of interprovincial economic linkage, and the strongest correlation is 0.823 for infrastructure.


Introduction
Regional economic linkages is an important content of economic geography and other disciplines.Foreign scholars' earliest research on regional economic linkages can be traced back to Thünen's agricultural location theory.Weber 's industrial location theory, Perroux's growth pole theory, Myrdal's circular cumulative causality theory, Hirschman's unbalanced growth theory, and Friedman's "core-periphery" theory, which are used to explain the reasons for the partial agglomeration of spatial economy, regional economic development and mutual transmission [1].Then, [2] proposed a "core-periphery" structure model based on the monopolistic competition model and explained the prevalence of production factors in theory, and proved the rationality of the economic geography structure in terms of economic efficiency.Importantly, [3] further found that when the population size and land scale continue to expand to a certain threshold, the "core-periphery" structure will consist of multiple core regions to form a higher level of economic geography.Since then, [4] have tested the spatial connection of economic development between regions through the analysis of spatial panel data.[5,6] have studied the spatial accessibility, spatial flow and spatial structure in the study of regional economic linkages.In the early stage of domestic scholars, [7] systematically summarized, expounded and established the concept, system and basic mode of attraction scope, and put forward the division method to classify the attraction scop.[8] used the modified gravity model and grey correlation model to analyze the strength of geo-economic linkages between Hainan and its neighboring countries and its influencing factors.[9] used the annual average daily round-trip flow data between cities at the national and provincial highway observation stations, and used the Arc-GIS spatial analysis method to describe the city.On the basis of constructing economic linkages between cities, [10] introduced social network analysis to study the structural evolution and driving mechanism of economic networks in the Yangtze River Economic Belt.
Based on the modified gravity model, we calculated the economic linkage intensity of China's provinces (not included in the study due to the lack of data in Hong Kong, Macao and Taiwan, Xinjiang and Tibet) in 2019.Then we used the grey correlation model to analyze the inter-provincial economy of China, so as to obtain the structural characteristics of the spatial economic linkages between Hainan Province and other provinces and cities in China.It provides some theories and data for further optimizing the economic development policy and its path optimization with domestic and foreign economic linkages, it provides support for Hainan Free Trade Port to promote the formation of a new development pattern of domestic and international dual circulation and mutual promotion.

Data Sources
Our research is based on the "China Urban Statistical Yearbook", "China Urban Construction Statistical Yearbook" issued by the National Bureau of Statistics, as well as the statistical yearbooks of various provinces and cities.Part of the completed data are extracted from the statistical bulletins of national economic and social development and government work reports of various provinces and cities.A small amount of missing data in individual provinces are interpolated by mean substitution method.In the above national data, due to the lack of data in Hong Kong, Macao and Taiwan, Xinjiang and Tibet, or incomplete statistics, it is not included in the study.

Construction of Index System
Previous scholars usually use a single indicator to represent the quality of the city when using the gravity model to calculate the degree of connection.A single indicator can only measure a single aspect of the level of urban economic development, and cannot comprehensively and scientifically measure the comprehensive strength of a province.Therefore, based on the principles of comprehensiveness, pertinence, comparability and operability, construct Table 1 Urban Comprehensive Strength Index Calculation Index System.The indicators constructed include 5 aspects: population and labor development, economic development, social development, infrastructure, ecological environment and protection.Among them, three representative indicators are selected for population and labor development, seven indicators that can reflect the level of urban economic development are selected for economic development.9 indicators are selected for social development from 5 aspects of residents' income and consumption level, education, science, culture and health services, information attention ability and social security.4 indicators are selected for infrastructure, and 3 indicators closely related to ecology are selected for ecological environment and protection.The 26 indicators can objectively reflect the comprehensive level of cities in various provinces and cities.

Modified Gravity Model Construction
The gravity model in economic geography is gradually evolved based on Newton's universal gravity model, which is mainly used to predict the flow of human, information and goods between cities, regions and even countries [11].This model is widely used in the field of economic geography, and has been continuously improved and revised to form a rich theoretical system of economic gravity model.In the economic field of provinces and cities, the gravity model can measure the economic links between provinces and cities.The formula is: Among them: F  is the gravitational value between provinces and cities;   and   represent the economic development level of i and j respectively;   denotes the distance between provinces and cities.
For getting a more objective inter-provincial contact distance, we use the time cost of transportation, the monetary cost of transportation, and the linear spatial distance between provincial capitals.The formula is as follows: )   (2 is the distance between province i and province j,   represents the weight value of the kth transportation mode,   represents the monetary cost of the kth transportation mode from province i to province j,   is the time cost of the kth transportation mode from province i to province j,   represents the linear spatial distance from province i to province j, and b represents the distance attenuation index.After referring to the relevant research results, the gravitational coefficient K and the distance attenuation coefficient b are both taken as 1.

Grey Correlation Model
In the geographical system, the relationship between many factors is grey.The time series data is dynamic, so it is hard to distinguish the primary and secondary influencing factors.The grey correlation model can effectively solve the above problems.It can quantitatively analyze the dynamic development process of the system, and reveal the dominant factors and secondary factors affecting the development status of the system through the consistency of the similarity of the changes between the system factors.This model is widely used in geography research.The calculation formula is as follows: In the formula: | 0 () −   ()| is the absolute difference between the mother sequence of the kth province and the influencing factor i;  is the resolution coefficient, the value range is between 0-1, and the experience is generally considered to take 0.5; N is the number of provinces and cities.

Measurement of Urban Comprehensive Strength Level
The original data in the index system established above are standardized by range, and the relevant weights of each economic index in the index system are calculated by entropy method.The weights are shown in Table 2  The economic connection intensity network between provinces in China is different and the economic linkage is not balanced (Fig. 1).It is mainly concentrated in Beijing-Tianjin-Hebei region and Jiangsu-Zhejiang-Shanghai region.In the Beijing-Tianjin-Hebei region, Beijing, Tianjin, Hebei and Shandong have strong economic linkages, showing gradient distribution characteristics.The economic linkages between Beijing and Tianjin are in the first echelon.Beijing and Tianjin account for 85.42 the total inter-regional economic linkages.The coordinated development of Beijing, Tianjin and Hebei is a major national strategy in China.The 3 sides actively promote the economic development of the three parties by virtue of their geographical advantages and industrial cooperation.The inland hinterland of Shandong is adjacent to Hebei, the coastal north is connected with Beijing and Tianjin channels.The south is connected with Anhui, Jiangsu, Zhejiang and Shanghai, connecting the 2 major economic zones of the north and the south.However, the connection between Shandong and the Beijing-Tianjin-Hebei region is closer than that between Jiangsu, Zhejiang and Shanghai.In Jiangsu, Zhejiang and Shanghai, the economic linkages between Anhui, Shanghai, Zhejiang and Jiangsu are closer, while the economic linkages with other provinces are smaller.

Analysis on the Inter-Provincial Economic Linkage Intensity
The total intensity of economic linkage reflects the communication between the province and the outside world, and the gap in the total economic linkages between provinces reflects the imbalance of economic linkages between provinces in China (Fig. 2).Based on the modified gravity model, the total economic linkage of Tianjin is as high as 9716.51,while the minimum economic connection strength of Hainan Province is only 38.56, which is 251 times different.There is a certain overlap between the economic connection network and the total economic connection intensity in space.The total economic connection of several major urban agglomerations in China, Beijing-Tianjin-Hebei, Jiangsu-Zhejiang-Shanghai, Anhui-Jiangnan and Chengdu-Chongqing regions is significantly higher than that of other regions, and these regions are also economically developed regions, so the economic development of each province is closely related to the inter-provincial linkage.The influence mechanism of inter-provincial economic linkage intensity is complex and affected by many factors.This paper uses the grey correlation model to quantitatively analyze the influencing factors of China's inter-provincial economic linkage intensity.Taking inter-provincial economic linkage intensity as the mother sequence, this paper constructs 26 influencing factors of 6 subsystems of population and labor development, economic development, social development, infrastructure, ecological environment and protection, and analyzes the relationship between the mother sequence and the subsequence.

Analysis of the Influencing Factors of China's Inter-Provincial Economic Linkage Intensity
The results from table 3 show that the relationship between the intensity of China's inter-provincial economic linkages and the grey correlation of each subsystem is infrastructure > social development > economic development > ecological environment and protection > population and labor development.
Infrastructure is an important support for economic development and plays a leading role in the real economy.It is the basis for the unified economic development, social and ecological benefits.The better the infrastructure development of a province, the better the annual electricity consumption, the total post and telecommunications business, and the number of Internet broadband access users can intuitively reflect the ability of the region to communicate with the outside world, so its grey correlation degree reaches 0.823.Social development has promoted the economic development of various provinces and cities in terms of per capita household savings deposits, regional Internet attention, and per capita consumption expenditures.Social development and economic development complement each other.The better the economic development of a region, the stronger the ability to radiate outward, and the better it can drive the development of surrounding provinces and cities and its own.Coordinating the development relationship among economy, ecological environment and social welfare is the focus of sustainable development, and it is also the inherent requirement of practicing the concept of high-quality development.Therefore, although the explanatory ability of ecological environment and protection is weaker than that of other subsystems, its correlation with economic connection degree still reaches 0.799.

Conclusions
We use the entropy method and the modified gravity model, as well as the grey correlation model, to measure the intensity of China's inter-provincial economic linkages in 2019 and its influencing factors.Based on the analysis and research results, the following conclusions are drawn.
(1) China's inter-provincial economic linkages network strength is different, economic linkages are not balanced.It is mainly concentrated in Beijing-Tianjin-Hebei region and Jiangsu-Zhejiang-Shanghai region.There is a certain coincidence between the economic connection network and the total amount of economic connection intensity in space.The economic development of each province is closely related to the connection between provinces.
(2) The results from Table 3 show that the relationship between the intensity of China's interprovincial economic linkage and the grey correlation of each subsystem is infrastructure > social development > economic development > ecological environment and protection > population and labor development.Among them, the correlation degree of six subsystems to the inter-provincial economic linkage intensity is above 0.79, and the strongest correlation is that the infrastructure is 0.823.

Discussion
Due to the availability of data and the complexity of interprovincial economic linkage activities, there are still some areas for improvement and improvement in this study, which need to be further studied in the future.In the future, it is necessary to deeply explore the new pattern and new dynamics of inter-provincial economic relations under the new situation.Since the reform and opening up, under the background of the increasingly full role of the market, the inter-provincial economic ties have been continuously strengthened, the trend of factors flowing to a better environment has become stronger and stronger, and the traditional pattern of inter-city economic ties based on administrative boundaries "drawing land as a prison" has been constantly changing, which requires clarification of the new structure and new pattern of the inter-city economic connection network in the new period.

Table 1 :
Urban Comprehensive Strength Index Calculation Index System

Table 2 :
: Index Weight Table of Urban Comprehensive Strength Level

Table 3 :
Grey Correlation Statistical Table