Fertility-related pensions and cyclical instability

Using an overlapping generations Cobb-Douglas economy with endogenous fertility,

we show that the introduction of a fertility related component in unfunded public pensions may

destabilise the economy and cause chaotic fluctuations when individuals are short-sighted. In

particular, the risk of cyclical instability increases with both the individual degree of thriftiness and

the relative weight of individual fertility in the pension system, while being reduced by a higher

preference for having children. It is illustrated for realistic economies that if PAYG pensions are

linked to individual fertility, then even a small-sized pension system brings the economy into the

unstable region with chaotic fluctuations. Our results identify a novel possible factor responsible for

the trigger of persistent deterministic cycles in an overlapping generations context, and also

represent a policy warning about the dramatic destabilising effects of fertility-related pension

reforms, which are currently high in the theoretical debate as well as in the political agenda in

several developed countries.