Study on the spatial and temporal correlation and allometric growth mechanism between population aging and carbon emissions in China

Population aging and carbon emissions are critical issues for China’s development. As an enormous complex system, the population and the carbon emission development process have non-negligible differences in time, space, and speed. Therefore, this paper first demonstrates the spatial and temporal correlation between population aging and carbon emissions from 1995 to 2020, then uses the allometric growth analysis model to make a cross-sectional temporal comparison and a vertical spatial comparison of the relationship and development rate of the two, and finally uses the ridge regression model to determine the forces and interaction mechanisms of the factors influencing the relationship between population aging and carbon emissions at allometric rates. The results show that (1) China has a long-term positive temporal correlation effect relationship between population aging and carbon emissions from 1995 to 2020, and the overall correlation is high. The spatial correlation intensity between population aging and carbon emissions varies significantly across Chinese provinces, with a general spatial distribution trend of high in the south, low in the north, and prominent in the center. (2) China’s population aging and carbon emissions mainly show a negative allometric growth type of relationship, i.e., a strong trend of population aging expansion and a strengthening trend of carbon emission system shrinking. The number of provinces with negative allometric growth is gradually increasing, mainly in North, East, Central, and Southwest China. (3) From 1995–2010 period to the 2011–2020 period, the influence of the factors of the population, production, and economic dimensions on the population aging index and the carbon emission allometric scalar index gradually weakened, and the influence of the consumption and technology dimensions increased significantly. The factors on the population and consumption side of the dimension mainly contribute to the expansion of carbon emissions and drive positive allometric growth. The production side, the economic structure, and technology dimension factors drive negative allometric growth. The paper fully explores the bidirectional correlation, differential development trend, and interaction mechanism between the two systems of population and carbon emissions and effectively compensates for the lack of research content in terms of elemental correlation, spatial and temporal connection, and speed synergy.