Study on the Driving Mechanism and Mathematical Model of Domestic and Foreign Capital Flows in Free Trade Zones on Regional Economic Development

China’s economy has made tremendous development since the reform and opening up, however, the economic development of the east, middle and west is very unbalanced and the gap is obvious. There are many ways to measure the gap between regions, such as Sill entropy, extreme difference rate, Gini coefficient, Lorenz curve, and structural entropy. In this paper, Theil’s index is chosen to measure the economic gap between east, middle and west China.

Theil entropy (Theil and Henri), also known as Theil index, has the following expression: (1)T=∑i=1NPilog(PiYi)

Where i indicates a certain region, in this case the three regions of East, Center and West, Y_i indicates the proportion of GDP of region i to the whole country, and P_i is the proportion of population of region i to the whole country.

The larger the value of Sierre entropy, the larger the gap between the levels of economic development of each region, and conversely, the smaller the value of Sierre entropy, the smaller the gap between the levels of economic development of each region. The Sill entropy value of China’s regional economic disparity is shown in Fig. 1. The change of Sill entropy value before 1998 is not large, which indicates that China’s regional economies are relatively stable. However, after 1998, the value of Sierre entropy continued to rise and reached a peak in 2009, and after 2009, the value of Sierre entropy fluctuated at a high level of consolidation, indicating that China’s regional economies stabilized at a high point, forming a pattern of strong in the east and weak in the west.

Figure 1.

The Theil and Henri of the economic gap in China

The overall measurement of internal and external capital flows in the FTZ is a very complex issue, and the correlation between regional investment and savings is measured to indirectly project the internal and external capital flows in the FTZ by constructing the intertemporal savings-investment model (F-H model) [26], which examines the average savings and investment rates of 21 OECD countries from 1960 to 1974, and measures the correlation between regional investment and savings. The model assumes that if capital cannot flow between FTZs, local savings can only be invested in the FTZ, and investment in the FTZ can only rely on local savings, at which time the savings of the FTZ and its investment are highly correlated. On the contrary, if capital can flow freely between FTZs, the correlation between savings and investment in the FTZ is no longer significant. The model has been widely utilized to measure the flow of both internal and external capital in FTZs.

According to the F − H model, the relationship between the β value, the investment rate and the savings rate, which measure the degree of internal and external capital flows in the FTZ, is: (2)(I/Y)i=a+β(S/Y)i+εi

Where: (I/Y)i denotes the investment rate for a given region, which is the ratio of the amount of investment in that region to the GDP of that region, i.e., the investment rate. a is the intercept term. (S/Y)_i denotes the ratio of the amount of new savings in a region to the GDP of this region, i.e., the savings rate. β is the ratio that indicates the conversion of savings into investment in this region. ε_i is the random perturbation term.

Model F − H can also be used to test the FTA internal and external flows between regions within a large country, as evidenced by the following: two regions of the country are chosen and set as region A and region B. Assuming that there are no FTA internal and external flows between regions A and B at the beginning of the period, and that, according to macroeconomics theory, the savings of region A are equal to its investment, i.e., S = I, there is: (3)(I/Y)=β(S/Y)

So the β value is 1 at this time.

Now assume that all other factors remain constant and that there is an outflow of capital I* from region A in the time t period: (4)Iz=I−I*≺St

So: (5)(I/Y)t=β(S/Y)t (6)It=I+I*≻St (7)(I/Y)t=β(S/Y)t

From (6) and (7) formula can be seen, region B of the β value at this time will certainly be greater than 1.

Therefore, from the relative size of the β value of the two regions, we can know a country’s interregional FTZ internal and external investment flows, so we use the F − H model to test the internal and external investment flows in China’s FTZ.

As the current investment is affected by the previous period’s investment, there is a big gap between the investment level of Chinese provinces, in order to eliminate this effect of internal and external capital flow in FTZ, according to the previous theory, we establish the following autoregressive model: (8)(I/Y)t=a+a1(I/Y)t−1+β(S/Y)t+εt

where t represents the time of each period, (I/Y)_t−1 is the investment rate lagged by one period, a₁ is the autoregressive coefficient of the investment rate lagged by one period, and other letters have the same meaning as above.

A uniform parameter β is estimated as the regional β value for the whole country in that year using cross-sectional data for each Chinese province in each year and substituting it into equation (8). The savings of each province is the difference between its GDP and its final consumption (the sum of consumption of residents and government consumption). The total investment in each province is determined by the gross capital formation, which is mainly due to fixed capital formation and inventory additions. The ratio of the amount of investment and savings in each province to the GDP of that province is taken as the investment and savings rate of each province [27]. All original data are from the China Statistical Yearbook and the CECN statistical database.

The β values of internal and external capital flows in China’s FTZs are shown in Figure 2. After the reform and opening up, the internal and external capital flows in China’s FTZs are very active, consistent with the reality, which is manifested in the rapid flow of capital from the central and western parts of the country to the developed and open regions in the eastern part of the country, until the internal and external flows in the FTZs began to flatten out around 2009, and reached a high-stage flow stabilization, and the internal and external flows in the FTZs were even slower after 2019, which indicates that the capital in the eastern part of the country is beginning to gradually tend to be saturated.

Figure 2.

China free trade zone capital flows of β values

1)

Selection of explanatory variables

Gross domestic product GDP, as an important indicator of the economic situation of a country or region, can reflect the sum of the value of all final products and services produced by the country or region in a specific time period. Therefore, GDP is selected as an explanatory variable.

The paper mainly studies what effects the internal and external capital flows in the FTZ have on the regional economic development. Due to the large differences in the amount of data of each indicator, in order to make the data change more smoothly, the indicators are firstly logarithmically processed and the multiple regression model is established, see formula (9), where ε denotes the error term: (9)ln(GDP)t =β1×ln(COB)t+β2×ln(FAS)t +β3×ln(TFT)t+β4×ln(FDI)t +β5×ln(ISR)t+β6×ln(URB)t+ε

Due to the missing data of some provinces, the data of 29 provinces from 2014-2023 will be selected as data samples, and the 29 sets of data will be divided into 3 parts according to the geography, in which Beijing, Tianjin, Shanghai, Hebei, Liaoning, Jiangsu, Zhejiang, Fujian, Shandong, Guangdong, and Hainan are the eastern part. Shanxi, Jilin, Anhui, Jiangxi, Henan, Hubei, and Shanxi are the central regions. Chongqing, Sichuan, Guizhou, Yunnan, Shaanxi, Gansu, Qinghai, Inner Mongolia, Guangxi, Ningxia and Xinjiang are the West. For the convenience of the study, it is assumed that there is no lag in capital and that all capital is fully invested in the current year. The data used are from the China Financial Yearbook, provincial statistical yearbooks, and authoritative survey reports issued by the National Bureau of Statistics.

With the help of STATA15 software, the descriptive statistics of the indicators for the eastern, central and western regions are shown in Tables 1, 2 and 3, respectively. The eastern region has a higher GDP, which is 4.393 trillion yuan. The central region is second, which is 14539.38 billion yuan. The western region is the lowest at 906,592.6 billion yuan. Among the explanatory variables, the 2 indicators of capital of banks (COB) and foreign capital (FDI) are the highest in the eastern region and the lowest in the western region. The annual investment in central financial infrastructure (FAS) and central financial transfer (TFT) is the highest in the central region, the second in the western region, and the lowest in the eastern region. Among the control variables, industrial structure situation (ISR) is highest in the central region, second in the eastern region, and lowest in the western region. The urbanization process (URB) is highest in the eastern region, second in the central region, and lowest in the western region.

The explanatory variable selected in this paper for how internal and external capital flows in the FTZ affect regional economic growth is Gross Domestic Product (GDP). The selected explanatory variables are: central government transfer payments (TFT), fixed asset investment (FAS), foreign direct investment (FDI), bank funds (the difference between bank deposit and loan balances COB). Moreover, in order to better study the relationship between internal and external capital flows and regional economic growth in the FTZ, two control variables are selected, namely, the level of industrial structure heightening (ISR) and the level of urbanization (URB). After regression with Stata software, the empirical analysis results of the model are shown in Table 4.

To analyze the eastern region of China, from the regression results of the model of the impact of internal and external capital flows of the FTZ on the economic growth of the eastern region, it can be seen that the value of R² is 0.933, and this value indicates that the fitting degree of this model is relatively high, and the specific results of the analysis are as follows: 1)

In eastern China, bank capital and fixed asset investment have a positive impact on economic growth, and promote economic growth.

The regression of central China shows that the value of R² is 0.915, which indicates that the fit of the model is very high, and the specific analysis is as follows: 1)

The influence of bank capital on the economic growth of central China is positive, the economy grows when the bank capital grows, that is to say, the economic growth needs to be driven by the increase of bank capital.

The R² value obtained after the regression of the model in the western region is 0.963, which indicates that the model has a high degree of fit, and the analysis results are as follows: 1)

The impact of bank funds in western China on the region’s economic growth is positive, and the reason why this indicator has a positive and positive impact on the growth of the region’s economy is because the opening up of bank loans provides financing channels for local enterprises and individuals who have difficulty in financing, and enables them to satisfy their needs for funds.

Investment in fixed assets is an important driver of economic growth. In view of the current situation of fixed-asset investment, the following aspects must be emphasized: first, to grasp the focus of fixed-asset investment and maintain the scale of investment to meet the requirements of regional economic growth. The focus of investment in fixed assets should be placed on optimizing the investment structure, improving the quality of investment, and enhancing the efficiency of investment, while focusing on the stability and coordination of investment growth, and controlling the scale of investment in the region within an acceptable and reasonable range, to promote the healthy development of the regional economy. Second, oriented to the weak links, focus on key projects. To guide fixed asset investment to infrastructure construction, environmental protection and water conservancy and other weak links to increase investment, optimize the direction and structure of investment, enhance the efficiency of the allocation, to provide direction for the transformation of the economic structure, in which the government should be dedicated to play an important role in leading. Third, the process of investment-led economic growth can not be sustained, so the factors of production to form a synergy to reduce resource allocation failure and hollowing out phenomenon, to maintain the stability of the economic system. At the same time, it is necessary to increase investment in science and technology education, accelerate technological innovation, and promote sustainable economic development by fostering innovation.

Establishing a perfect technological innovation system, accelerating the transformation of scientific and technological achievements, encouraging industries to leap up the high-value chain, realizing the adjustment of the regional industrial structure, and bringing into play the benefits of upgrading the industrial structure. First, strengthen the cultivation of core competence and improve the competitive advantage of enterprises. The FTZ government should establish a technological innovation system that is enterprise-oriented, market-oriented, and combines industry, academia and research, and should actively guide enterprises to utilize their products and capabilities to form core competencies and reduce cost consumption. Secondly, a clear industrial orientation, investment attraction, and project construction around leading industries. At the macro level, the government should guide the industrial strategy, conform to the trend of the times of industrial change and integration and development, accelerate the development of modern service industry, focus on improving the efficiency and quality of services, and build a new service industry system. Finally, it is crucial to address shortcomings in the social sector and support high-quality economic development. With the support of artificial intelligence, industrial internet, and other new infrastructures, the short boards in the social welfare field should be solved through scientific and technological means. Efforts should be made to promote the improvement and upgrading of education, culture, healthcare, sports and entertainment, ecological protection, and environmental governance, so that the promotion of industrial structure upgrading to the regional economy can be expanded to a wider scope.

As a link in the strategic layout of continuous deepening reform in the new era, the free trade zone is an important helper for economic growth and upgrading of economic structure, while consumption plays a role in the whole economic operation [28]. How to leverage the consumption effect, maximize the reform dividend, and promote rapid growth in the regional economy can be further developed and enhanced through the following points. First, give the FTZ greater reform autonomy, strengthen the top-level design and system construction, further implement the negative list system, prompt industries to strengthen cooperation, improve the exclusive industrial chain of the FTZ, and lay a solid foundation for the long-term development of the FTZ. Second, improve the legal system of the FTZ, introduce development-related legislation in a timely manner, create a safe and stable operating environment, and provide effective measures to deal with possible disputes. Third, promote the construction of the consumer market system in the FTZ, and take institutional reform as a point of presence to promote the enhancement of supply chain technology content, so as to better connect the various circulation links and improve the trade facilitation level of the FTZ.