Descriptive statistics of variables.

The study of spatio-temporal evolution characteristics and factors affecting the coordinated development of population and green economy (CD_PGE) in Shandong province, China, has significant decision-making implications for promoting high-quality and sustainable regional development. Based on 2001 to 2020 panel data for each city and economic zone in Shandong province, this paper constructs an evaluation model for the CD_PGE systems. Using growth elasticity models, geographic concentration models, kernel density estimation models, spatial autocorrelation, analysis of population and regional green economy development in Shandong Province from the perspective of spatial agglomeration coupling, spatial and temporal coupling coordination patterns, and evolutionary characteristics. In addition, we use the fixed effect models and panel quantile models to empirically test the effects of coordinated demographic and green economy development. The results show that: (1) In terms of demo-graphic and economic development characteristics, Shandong’s demographic and green economy development trends are good, but there are still many challenges. (2) According to the time series evolution and spatial distribution characteristics, the degree of CD_PGE in Shandong Province is on the rise, and the level of spatial distribution is distinct. (3) From the spatio-temporal dynamical grid evolution of the degree of CD_PGE, the CD_PGE is characterized by significant spatial clustering, but with large regional differences. (4) From an impact factor perspective, both market mechanisms and government intervention have a significant impact on the degree of CD_PGE, but the direction and extent of the impact vary.