5.1. Unit Root Test
Before the regression analysis of the empirical model, it was required to conduct a corresponding unit root test on the panel data to ensure the stability of the data, avoid the spurious regression of the panel data model, etc. To better carry out the unit root test on the empirical model of this paper that reflects the impact of inclusive finance and human capital on regional economic growth, the author selected LLC (Levin, Lin, Chu) test, IPS (Im, Pesaran, Shin) test, ADF (Augmented Dickey-Fuller)-Fisher test and PP (Philips-Perron)-Fisher test as the methods to test the unit root, and conducted the unit root test from two aspects, namely homogeneous unit root test and heterogeneous unit root test, to ensure the stability of the different data selected and avoid the spurious regression phenomenon of subsequent regression analysis results. First, the author conducted the unit root test on all sequence original values in the empirical analysis model of this paper, and the test results are displayed in
Table 3.
In view of the unit test results of the sequence original value in
Table 3, only two variables, namely
IFI and
CPI, passed the 1% significance level test using four test methods, while none of the other variables could pass the test. This indicated that these sequences have unit roots, and thus it was necessary to carry out first-order difference processing on sequences and further investigate the sequence stability.
Table 4 shows the results of the unit root test of sequence first-order difference, and it can be discovered that, except for INV sequence, which passed 5% of the significance level tests under the IPS test, the other sequences passed the LLC test, IPS test, ADF-Fisher test and PP-Fisher test at the significance level of 1%. This suggests that all the sequences do not have the unit root and maintain stable after receiving the processing of first-order difference. Although the original value of various variables could not pass the unit root test, the variables, after first-order difference processing, all passed the unit root test. Therefore, they can be regarded as the sequence of the first-order integration. Thus, it can be known that various variables constitute the sequence of integrated of order, which met the preconditions of the cointegration test, thus allowed conducting the co-integration analysis of the panel data model.
5.2. Cointegration Test
According to the results of the unit root test of sequences of the panel data model in this paper, it can be perceived that regional economic growth, inclusive finance and human capital, degree of government intervention, degree of regional opening, investment level of fixed assets and degree of inflation and other sequences were all sequences of integrated order, thus meeting the preconditions of the cointegration test. In the process of cointegration test, this study chose both Kao test and Pedroni test to conduct an in-depth analysis of the co-integration relationship between different sequences respectively.
Table 5 exhibits the cointegration test results, and it can be discovered that in the Kao test,
p value was smaller than 0.05, which illustrated that the original hypothesis of “there exists no co-integration relationship” can be rejected. In the Pedroni test, only the
p values of Panel PP statistic and Panel ADF statistic were smaller than 0.05, while, in the intergroup statistics, only the
p values of Group PP statistic and Group ADF statistic were smaller than 0.05, which illustrated that only the results of four statistics passed the cointegration test while the results of the other three statistics temporarily could not indicate the existence of a cointegration relationship in the sequence.
It is worth noting that, in the co-integration analysis and research of panel data of different time spans, Pedroni (2010) [
35] pointed out that, when T ≤ 20, among seven statistics, only the efficiency of Panel
ADF-Statistic and Group
ADF-Statistic were relatively high; hence, when T = 11, the cointegration test process just needs to observe the
p value of two statistics. It can be perceived that the
p values of both Panel
ADF-Statistic and Group
ADF-Statistic were smaller than 0.05, suggesting that the original hypothesis of “there exists no co-integration relationship” can be rejected. Therefore, the two test results prove that regional economic growth, inclusive finance and human capital, degree of government intervention, degree of regional opening, investment level of fixed assets and degree of inflation and other sequences have stable incidence relations in the long-term development and it is allowed to carry on the subsequent regression analysis of the empirical model.
5.3. Result Analysis
The author further employed F test and Hausman test to discriminate the type of panel data model, the null hypothesis of the F test is a true model and a mixed regression model. The alternative hypothesis is a true model and a fixed effects model. The null hypothesis of Hausman test is an individual random effects model, while the alternative hypothesis is a true model and an individual fixed effects model, and the results are as follows.
According to
Table 6 and type of panel data model, the model to verify influence of inclusive finance and human capital on regional economic growth should be a fixed effects model.
According to the discrimination results of types of the panel data model, it is suggested to build a double-fixed effect model of individuals and time that reflects the impact of inclusive finance and human capital on regional economic growth. This study first conducted a regression analysis of the panel data model of the overall national sample, and comprehensively analyzed the linear relationship and the nonlinear relationship among inclusive finance, human capital and regional economic growth. The regression results are shown below.
Table 7 exhibits the regression results of the panel data model of total samples around the country. In this table, Model 1 is the most basic model, while Models 2–6, respectively, analyze the possible nonlinear influence relationship between inclusive finance and human capital and regional economic growth.
Based on Formula (10), Model 1 carried out a regression analysis on the linear relationship between inclusive finance and human capital and regional economic growth, and the regression results reveals that both inclusive finance and human capital are significant at the level of 1%, and, moreover, all control variables are significant at the levels of 5% and 1%, which illustrates that there exists a significant linear influence relationship between inclusive finance and human capital and regional economic growth. The coefficients of these two indexes are positive numbers, proving that both inclusive finance and human capital produce a positive impact in promoting regional economic growth.
Based on Model 1, Model 2 added the square term of inclusive finance to explore whether there is a nonlinear relationship between inclusive finance and regional economic growth. While considering the linear influence relationship of human capital, the regression results reveal that the square term of inclusive finance is not significant. Inclusive finance and human capital are significant at the level of 1%, which illustrates that there still only exists a linear influence relationship between inclusive finance and regional economic growth, while the nonlinear influence relationship is not significant when considering the linear influence relationship of human capital.
Based on Model 1, Model 3 added the square term of human capital, and studied where there is a nonlinear influence relationship between human capital and regional economic growth while considering the linear influence relationship of inclusive finance. The regression results reveal that the square term of human capital and inclusive finance is significant at the level of 1%, while human capital is not significant, which illustrates that there is a nonlinear influence relationship between human capital and regional economic growth but the linear influence relationship is not significant when considering that inclusive finance generates the linear effect. This suggests the influence of human capital on regional economic growth weakens when the human capital is set to be in a fixed range of value. However, when the human capital exceeds the fixed range of value, the influence continues strengthening.
Based on Model 1, Model 4 simultaneously added the square term of inclusive finance as well as the square term of human capital to examine whether there are both a linear influence relationship and a nonlinear influence relationship between inclusive finance and human capital and regional economic growth. The regression results indicate that the square terms of inclusive finance and human capital are both significant at the level of 1%, while the square term of inclusive finance and human capital is not significant, which explains that there is a significant linear influence relationship between inclusive finance and regional economic growth and a significant nonlinear influence relationship between human capital and regional economic growth when considering the linear effect and the nonlinear effect generated by inclusive finance and human capital at the same time. This means that the promoting effect of inclusive finance on regional economic growth is relatively stable, while the nonlinear influence between human capital and regional economic growth is significant. Based on that, one can predict that the influence of human capital on regional economy would not change along with changes of human capital.
Based on Model 2, Model 5 made improvements, and mainly examined whether inclusive finance and regional economic growth have a nonlinear influence relationship or a linear influence relationship. The regression results reveal that inclusive finance and the square term of inclusive finance are significant, respectively, at the levels of 1% and 5%. Furthermore, the coefficient of the square term of inclusive finance is a negative number, demonstrating that there exists a significant linear influence relationship as well as an inverted U-shaped nonlinear influence relationship between inclusive finance and regional economic growth. When inclusive finance develops to certain stage, the influence of inclusive finance on regional economic growth reaches a peak. If the influence exceeds the peak, wasted financial resources would be caused.
Based on Model 3, Model 6 made corresponding adjustments. It mainly examined whether there exists a nonlinear influence relationship or a linear influence relationship between human capital and regional economic growth. The regression results show that the square term of human capital is significant at the level of 1%. Furthermore, the coefficient is a positive number, while human capital is not significant, which illustrates that there is a significant U-shaped nonlinear influence relationship between human capital and regional economic growth. This result is similar to the result of Model 3. It also suggests that the influence of human capital on regional economic growth gradually weakens and then strengthens.
By arranging the regression analysis results of total samples of the country, the conclusion can be drawn that, in different conditions, the forms of impact of inclusive finance and human capital on regional economic growth differ to a relatively extent, while the regression results of Models 1–5 all verify the significant positive promotion role between inclusive finance and regional economic growth, while the regression results of Model 3, Model 4 and Model 6 all verify that there exists a significant nonlinear influence relationship between human capital and regional economic growth.
To further explore the impact of inclusive finance and human capital in different Chinese regions, here, according to the division way of Chinese eastern region, central region and western region, this paper divides the total samples of the country into the sample of the eastern region, the sample of the central region and the sample of the western region, due to a small gap in inclusive finance and human capital of different regions. Equation (10) is used to conduct a regression analysis of sample data in different regions, a fixed effects model is built, and the regression results are shown as follows.
Table 8 exhibits the regression results of samples of different Chinese regions. Among them, Model 7 is the regression result of the sample of the eastern region, Model 8 is the regression result of the sample of the central region, and Model 9 is the regression result of the sample of the western region. As indicated in the regression result of Model 7, inclusive finance and human capital are significant, respectively, at the levels of 5% and 1%. Furthermore, both coefficients are positive numbers, proving that inclusive finance and human capital play a significant positive promotion role on regional economic growth in the eastern region. In the regression result of Model 8, both inclusive finance and human capital are significant at the level of 1%, but the coefficient of inclusive finance is a negative number while the coefficient of human capital is a positive number, which indicates that inclusive finance generates a significant inhibiting effect on regional economic growth in the central region, while human capital produces a significant positive effect in stimulating regional economic growth. According to the regression result of Model 9, both inclusive finance and human capital are significant at the level of 1%. Furthermore, both coefficients are positive numbers, suggesting that inclusive finance and human capital play a significant positive promotion role on regional economic growth in the western region.
By sorting the regression results of the samples of the eastern, central and western regions, it can be perceived that there are significant influence relationships among inclusive finance and human capital and regional economic growth, but their influencing mechanisms are largely different in different regions. This phenomenon may exert a serious impact on regional industrial structure and economic sustainable development, so it is supposed to develop different policies according to the economic environment of different regions to cope with the differences in the impact of inclusive finance and human capital.