To further promote rural revitalization strategies and achieve common prosperity, it is necessary to clarify the relationships among public expenditure for agriculture, agricultural green total factor productivity (AGTFP), and the urban–rural income gap (URIG). On the basis of panel data for 30 provincial regions in China from 2012 to 2022, this study constructs a panel vector autoregression (PVAR) model and explores their mutual interaction and influence from both dynamic and static perspectives through the Granger causality test, impulse response analysis, and variance decomposition methods. The research results show that public expenditure on agriculture, AGTFP, and URIG exhibit significant self-reinforcing trends. There is a significant two-way interaction effect between public expenditure on agriculture and URIG, indicating that these factors promote and complement each other. In addition, both improving AGTFP and increasing public expenditure on agriculture can help narrow URIG, but the positive impact of AGTFP exhibits greater magnitude and sustainability. In conclusion, from a long-term perspective, to develop the rural economy and promote rural revitalization, it is necessary not only to increase public expenditure on agriculture continuously, but also to focus on enhancing AGTFP.

The integration of financial technology expenditures and green total factor productivity (GTFP) constitutes a critical impetus for sustainable economic advancement. This study employs provincial panel data from China (2012–2020) and uses the SBM model with undesirable outputs, the PVAR model, moderation effect analysis, and threshold regression to investigate the underlying mechanisms and threshold effects of financial technology expenditure on GTFP. The results show that (1) financial technology expenditure has a significant promoting effect on the growth of GTFP, with a coefficient of 0.614 (p < 0.05), indicating the need for further increases in fiscal investment in science and technology; (2) the effect of financial technology expenditure on GTFP varies across the eastern, central, and western regions of China, with stronger effects observed in the eastern region, suggesting that the government should formulate differentiated financial technology expenditure policies on the basis of local conditions; and (3) that educational investment and industrial upgrading play strong moderating roles in the impact of financial technology expenditure on GTFP, with interaction term coefficients of 0.059 (p < 0.05) and 0.206 (p < 0.1), respectively. Threshold analysis further reveals that the positive effect strengthens significantly once educational investment surpasses a log value of 9.3674 and industrial upgrading exceeds a ratio of 0.0814. However, currently, China’s education investment and industrial structure upgrading are still insufficient, necessitating further increases in education investment and promoting the transformation and upgrading of the industrial structure.