By extending the classical Overlapping Generations model, this study examines the effects of population ageing, public transfer payments, and social pension insurance on household savings rate, using data from the 2015~2019 China Household Finance Survey (CHFS). The findings suggest: First, household savings rate declines with population ageing, whereas limited public transfer payments and low levels of social pension insurance significantly increase household savings rate. Second, the effect of social pension insurance on household savings rate depends on residents' risk preferences: among non-agricultural households, higher risk preferences weaken its saving-promoting effect, while agricultural households consistently exhibit a positive effect. Third, heterogeneity analysis reveals that the negative effect of population ageing on household savings rate is more pronounced in rural and central-western regions, where public transfer payments and social pension insurance exert stronger positive effects. The study enriches the understanding of China's high household savings rate and offers important policy implications for addressing population ageing.