The nonlinear relationship between pension insurance participation rate, replacement rate and saving rate, as well as the threshold effect of population aging are discussed through provincial panel data from 2000 to 2018 and Panel Smoothing Transition Regression Model (PSTR). According to the linear test results of PSTR, the impact of pension insurance on saving rate is nonlinear, and the effect of pension insurance participation rate and pension insurance replacement rate on saving rate are various in different old-age dependency ratio. When the old-age dependency ratio is higher than 0. 2002, the relationship between the pension insurance participation rate and the saving rate will change from a significant positive correlation to a negative correlation. Although there is always a negative correlation between the pension imsurance replacement rate and saving rate, when the old-age dependency ratio exceeds 0. 101, the negative impact of the pension insurance replacement rate on the saving rate will be greatly weakened. Therefore, it shows that with the acceleration of the aging process, the “cognitive effect” of pension insurance on savings changes to the “ substitution effect”, and this positive and negative transformation shows a nonlinear relationship between the two. In addition, driven by the differences in economic development and aging process in different regions, the relationship between pension insurance replacement rate and saving rate has regional alienation. There is a significant negative correlation between the pension insurance replacement rate and the saving rate in the central and western regions, while there is no significant negative correlation between the two in the eastern regions.
