Fig. 3

Kernel density estimation of digital finance, 2011–2022. Note: 1. Unimodal Distribution and Concentration: Throughout the study period, the digital finance kernel density curve consistently exhibited a unimodal distribution with a high peak, indicating that most prefecture-level cities in China share a similar level of digital finance development without significant polarization. 2. Rightward Shift and Leapfrog Development: 2016 marked a pivotal turning point, with the curve shifting markedly to the right each subsequent year. This corresponds to the implementation of China’s “Broadband China” policy and the expansion of mobile payments into rural areas after 2016, accelerating the improvement of digital financial infrastructure and enabling prefecture-level cities to achieve leapfrog development in digital finance. 3. Right Tail and Regional Leadership: The curve exhibits a pronounced right tail that lengthens over time, indicating that prefecture-level cities in the eastern coastal regions, leveraging their economic foundations and technological advantages, have achieved significantly higher levels of digital finance development compared to other areas. This has fostered a development pattern characterized by “leading cities driving progress while the broader region follows suit.”