Preliminary Study on Economic Convergence
The standard deviation of per-capita GDP is used to reflect the
-convergence of urban economy in different regions of Guangdong. From 2005 to 2020, the standard deviation coefficient (SD) of per-capita GDP continued to shrink, indicating that there is σ-convergence in Guangdong (
Figure 2). In terms of regions, the convergence trend in the PRD and the edge area is similar to that of Guangdong. From 2005 to 2020, the SD values of the PRD and the edge area decreased by 30.45% and 35.02%, respectively. The SD of the PRD is larger, but the decline is smaller, while the edge area is the opposite. It can be seen that the urban disparities in the PRD are larger but the convergence speed is smaller, and the urban disparities in the edge area is smaller, but the convergence speed is faster.
Geoda 1.18 software was used to test the spatial autocorrelation of urban per-capita GDP in Guangdong from 2006 to 2020. The results show that the global Moran’s
I of per-capita GDP in Guangdong’s cities is greater than 0.47, and the statistical
value is greater than 3.6, and all pass the 1% significance level test (
Table 3). It shows that the urban economy of Guangdong presents the distribution characteristics of spatial positive correlation, and there is spatial agglomeration between cities with similar per-capita GDP levels. The Moran’s
I values of
and
showed a decreasing trend, indicating that the spatial agglomeration characteristics of the urban economy in Guangdong continued to weaken.
The urban economy in Guangdong presents a spatial positive correlation distribution feature, and if spatial factors are not taken into account when conducting convergence analysis, it may lead to bias in the results. Drawing on previous research [
38] to select the model, we note the following: On the one hand, the LM and robust LM statistics of SAR and SEM were both significant at the 1% level (
Table 4), indicating that SDM has the best fitting effect. In addition, combining Hausman, it was found that the Walds statistics of SAR and SEM also passed the 10% significance test (
Table 4), rejecting the hypothesis that the model can simplify. This means that the two spatial transmission mechanisms included in SDM cannot be ignored in terms of their impact on economic growth. The Hausman test results rejected random effects (
Table 4), so we selected the SDM fixed effects model.
- 2.
Robustness testing
Using the time distance weight matrix (
) for spatial econometric analysis, the geographic distance weight matrix (
) was used in robustness tests for comparison. The results show that although there were some disparities in the size of the variable estimation coefficients, the direction and significance did not change fundamentally, in particular
and
, which are always strongly significant (
Table 5 and
Table 6). These indicate that the model design of this study is feasible and the results are robust.
When using SDM for analysis, Wald statistic testing is required to demonstrate the applicability of the model. The Wald spatial lag and Wald spatial error statistics corresponding to the
and
both passed the significance test (
Table 4), indicating that using SDM is appropriate.
- 3.
Space β-Convergence analysis
The test results of the absolute space β-convergence model are shown in
Table 4. The
corresponding to the two spatial weight matrices is significantly positive, which indicates that there is a significant positive spatial effect in Guangdong’s urban economy. The
of
is greater than
, indicating that economic spillovers between cities with close temporal distance is stronger than that of geographical distance.
The convergence coefficients of
and
are both significantly negative, indicating that there is absolute β-convergence in the per-capita GDP of Guangdong’s cities. The economically backward cities show a catch-up trend with the leading cities. According to Formula (14), the
and
can be calculated (
Table 5). The convergence rate of
and
is between 0.29% and 0.41%, and the half-life year is between 167.21 and 238.51 years. This shows that the absolute convergence rate of per-capita GDP in Guangdong’s cities is relatively low, the half-life year is long, and the economic disparities will exist for a long time. A regional comparison shows that the absolute value of convergence coefficient and convergence speed in the edge area is larger than that in the PRD, and the half-life year is shorter. Therefore, the convergence trend in urban economic development disparities in the edge area is stronger than that in the PRD.
Overall, the per-capita GDP of Guangdong’s cities has an absolute convergence trend, but the convergence cycle is relatively long, and the current situation of unbalanced economic development will not change in a short period of time. There are disparities in the convergence of different regions, and the convergence trend in the edge area is stronger than that of the PRD.
Considering the influence of industrial agglomeration (
), industrial proximity (
), investment (
),
,
, and fiscal, the conditional space β-convergence model was used to test the spatial convergence of per-capita GDP in Guangdong. The results are shown in
Table 5. The
of
and
is significantly negative, and the absolute values are greater than the absolute space convergence (
Table 5 and
Table 6). It shows that when setting variables, the urban economy of Guangdong still has convergence, and the convergence intensity is greater. This once again proves the convergence of the urban economy in Guangdong. The convergence speeds (
) of
and
are 0.96% and 1.53%, respectively, and the half-life (
) is between 45.4 and 72.36 years (
Table 6). The conditional convergence trend is stronger than the absolute convergence. Barro et al. (1991) considered a convergence rate of 2% and half-life year of 35 years to be typical features of cross-regional economic convergence research [
42]. Wenqing P. (2010) calculated that the economic convergence rate of Eastern, Central and Western China is only 1.15%, and the catch-up cycle is 60.4 years [
43]. The speed and period of conditional convergence in our study are close to the above research results, which indicates that the estimation results of the conditional β-convergence model are more robust and reliable. A regional comparison shows that the absolute values of
and
in the edge area are greater than those in the PRD, and the
is shorter, which again shows that the conditional convergence trend in the edge area is stronger.
In
, the regression coefficients of industrial agglomeration (
) are significantly positive, indicating that industrial agglomeration has positive externalities.Convenient transportation between cities can contribute to economic spillover. Hypothesis (H1a) is validated. The regression coefficient (
) and spatial lag coefficient (
) of industrial proximity are significantly negative, indicating that industrial proximity has a negative impact on the local economy and the economic development of neighboring regions. Hypothesis (H3b) is validated. The regression coefficients of
,
, and
in Guangdong are all positive. Among them, the coefficient of
is the largest. It shows that investment, R&D and fiscal have a positive effect on urban economic convergence, and fiscal has the greatest effect. The coefficients of lnFDI are all negative, indicating that the growth of FDI is not conducive to Guangdong’s economic convergence. FDI is more profit-driven and often gathers in areas with superior geographical conditions and fast investment returns, resulting in higher spatial differentiation. Yang et al. (2015) demonstrated the positive impact of fiscal expenditure on economic development [
37]. As an important means of government intervention in the economy, fiscal plays an important role in optimizing resource allocation and strengthening macro-control. The coefficients of lnInves and lnfiscal are larger in the PRD than in the edge area, indicating that investment and fiscal have a more positive impact on the economic convergence of the PRD. The coefficient of lnFDI is significantly negative in the edge area, but not significant in the PRD, indicating that FDI has a greater negative impact in the edge area. As shown in
Figure 1, there is a gradient difference in the economic level between the PRD and edge area, and the urban economic levels within the two regions are relatively similar. The coefficient of industrial agglomeration in the PRD and edge area is not significant, but it is significantly positive throughout Guangdong Province. This indicates that the “squeezing effect” generated by industrial agglomeration occurs between the PRD and edge area. The economic spillovers brought about by industrial agglomeration occur between regions with significant economic gradients, and hypothesis (H2) is validated.