Abstract: Pension fund balance reflects the change and stability of pension income and expenditure. Taking the average replacement rate as the core explanatory variable, this paper constructs a PSTR model to analyzes the non-linear characteristics, time trend and regional differences that affect the change of cumulative balance rate in the context of aging. When the population aging level exceeds 10.63%, increasing the average replacement rate will accelerate the consumption of the accumulated surplus of pension funds; the negative effect of the average replacement rate on the cumulative surplus rate is positively related to the aging level of population in each region; the speed of economic development, the system support rate and CPI have non-linear effects on the cumulative surplus rate. Therefore, it is an inevitable choice to maintain the current average replacement rate in the short term and gradually reduce the regional differences in the changes of pension fund income and expenditure in the long term.

Keywords: population aging; pension fund; cumulative surplus rate; average replacement rate; PSTR model