With economic development, air pollution is becoming increasingly serious, which affects the sustainable development of the global economy. In order to explore policy measures to curb air pollution, this paper selects data from 30 regions in China and explores their impact studies on air pollution from the perspectives of environmental regulation and foreign direct investment using a systematic GMM model. Then, the threshold effect model is selected to verify their nonlinear relationship. The conclusions are as follows: (1) Environmental regulation does not pass the significance test. There is no significant “U-shaped” or “inverted U-shaped” relationship between environmental regulation and air pollution. In the eastern region, there is an inverted U-shaped relationship, which is consistent with the environmental Kuznets curve (EKC) hypothesis, and the effect in the central and western regions is higher than in the eastern region of China. (2) The entry of foreign direct investment (FDI) aggravates the environmental pollution problem in China, and the overall status quo is consistent with the pollution haven hypothesis, which shows an inverted U-shaped curve between FDI and air pollution. The eastern region does not have any U-shaped relationships. The other two regions show an inverted U-shaped curve between foreign direct investment and air pollution; these two regions are still in the left half of the curve, and the increase in foreign capital will lead to aggravation of the pollution status quo. (3) The industrial structure will aggravate air pollution in the whole country and the central and western regions; the eastern region shows a suppression effect, but this is not significant. Urbanization exacerbates air pollution in the central and western regions but has an insignificant effect in the eastern region. The level of economic development increases air pollution in all regions. The expansion of the population size brings a large amount of production and living pollution, which aggravates environmental pollution. The research in this paper can provide theoretical references for regional policies to control air pollution.

As an important factor of production, the use of energy will greatly improve production efficiency and is the material basis for China’s sustainable development. Environmental regulation plays an important role in energy efficiency (EE), while fiscal decentralization is an important institutional context for China’s economic development. In order to explore the role of environmental regulation and fiscal decentralization on EE, this paper measures the EE of 30 provincial regions in China from 2006 to 2020 by the super-efficient SBM method, and verifies the relationship between fiscal decentralization and environmental regulation on EE using a spatial econometric model, and conclusions as follows: (1) China’s overall energy efficiency averages 0.563, still at a low level, with the highest average efficiency value in the east and the lowest in the west. (2) An inverted U-shaped relationship exists between environmental regulation and EE, and its spatial spillover effect also shows an inverted U-shaped relationship. Fiscal decentralization promotes the regional EE, and its spatial effect also significantly positive. (3) When the level of environmental regulation increases, the EE level of the local and neighboring provinces will increase. The enhancement of fiscal decentralization system can promote local EE, but it has a negative effect on the energy efficiency level of neighboring provinces. Finally, based on the results of the empirical analysis, this paper proposes suggestions for improving regional EE, which are of great theoretical and practical value for improving climate change and achieving sustainable regional economic development in China.