Studying how to achieve mutual promotion between financial development and foreign direct investment inflow contributes to the Chinese government’s work of formulating rational financial policy and FDI policy from a holistic point of view and promoting the healthy and ordered growth of the entire economy in China. Based on the provincial panel data from 2007 to 2018, this paper constructs comprehensive evaluation indexes for financial development and introduces functional data analysis (FDA) methods, extracts functional β-convergence from functional linear regression to analyze the two-way time-varying relationship and convergence and divergence between financial development and FDI in the country and the eastern, central, and western regions. The empirical results show that the mutual influence of FDI and financial development presents regional differences. In general, FDI has a promoting effect on financial development, while financial development has an inhibitory effect on FDI, and there is basically no convergence effect. Based on these conclusions, if the governments of various regions in China want to reduce the differences in financial development, promote coordinated financial development, and promote sustainable financial development, they should actively implement financial development policies, optimize the financial environment, and implement differentiated foreign investment policies to promote regional financial development.
Essentially, financial development is a continuous and time-varying process. This paper explicitly accounts for this by introducing functional data analysis to convert discrete observations into a smooth curve in order to represent the continuous process of financial development at the regional level. Regional disparities in financial development in China are reexamined from three dimensions: financial scale enlargement, financial structure adjustment, and financial intermediary efficiency. Disparities are then decomposed using an extended functional Theil index. It is necessary to introduce functional data into the research of financial development level. Through the functional research of China’s financial development level index of three different dimensions, the financial development level can be studied at the level of speed and acceleration, which fills up the research gap. The results imply that (1) the disparity in the level of financial scale enlargement and disparity in velocity and acceleration of financial intermediary efficiency are both statistically significant across regions, while the regional disparity in financial structure adjustment is insignificant, and (2) the downward trends of the total disparity in three dimensions are all dominated by the declining intraregional disparities. Since all 31 provinces have broken the traditional regional division, China does not need to implement region-specific protective policies in strengthening its deepening financial reforms.
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