Fertility decline and a pay-as-you-go pension system in a two-sector model

We investigate how fertility decline affects the benefit of a pay-as-you-go pension using a two-sector overlapping generations model. We show that whether fertility decline reduces pension benefits is determined by the capital intensity ranking between the two sectors. When the consumption-goods sector is capital-intensive, fertility decline decreases pension benefits. Contrastingly, when the investment-goods sector is capital-intensive, the size of the price elasticity determines whether fertility decline reduces pension benefits. When elasticity is sensitive, fertility declines increase pension benefits. We also present numerical simulations. Our results suggest that, although it remains theoretically possible that fertility decline increases pension benefits, such a paradoxical result is unlikely to occur.