Pension Rules, Fertility Feedback and Indexation in an Aging Economy

This paper investigates how the rules of a points-based pay-as-you-go pension system shape the feedback from fertility to the dependency ratio. The accounting parameters of the system are a convention, whereas the rule that closes its budget is a policy that sets the slope of that feedback. The paper compares the steady states and the local stability of these closures in a continuous-age overlapping generations economy with endogenous fertility. When forgone earnings cost pension rights, letting the point value absorb aging scales the defined-benefit feedback by the ratio of the discounted pension to the dependency ratio, a factor below one exactly when the Aaron condition fails; with an endogenous interest rate, a goods cost of children and wage-indexed pensions, the same ordering holds whenever pensions crowd out capital. In a closed-economy illustration with logarithmic utility the feedback is 0.35 under defined benefits and 0.04 under the points closure at the reference return, and at a fixed return of 1.5% the ordering reverses if parental time costs no pension rights and accounts for more than 0.16 of the net price of a child. After a fall in fertility that alone would raise the dependency ratio from 0.50 to 0.80, the long-run ratio is 0.81 under the points closure and 0.97 under defined benefits at an elasticity of fertility of one half, and in the transition of the age-structured population the closures separate after about sixty years when fertility responds to the realized dependency ratio, and within two generations when it responds to the stationary ratio. Two appendices extend the analysis to the indexation of pensions when relative prices move. Working paper, not peer reviewed. First version: July 2024. This version: November 8, 2026. JEL classification: E21, E62, H55, J11, J13, C61.