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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.

Research on the Two-Way Time-Varying Relationship between Foreign Direct Investment and Financial Development Based on Functional Data Analysis