This paper develops an overlapping generations model with intergenerational transfer of time in the form of grandparenting and pay-as-you-go (PAYG) pension system. The introduction of time transfer allows taking into account child care responsibilities. Under the situation of population ageing, a fall in the fertility rate leads to not only a reduction in contributions to the pension system but also lower childcare responsibilities that increase life-cycle income. Hence, the impacts of demographic changes on old labour decisions and pensions need to be re-examined. I find that in countries with low fertility rates and small pension systems, a fall in fertility rate reduces working time in old age. Consequently, population ageing due to a lower fertility rate always decreases pensions. On the other hand, for countries with high fertility rates and countries with low fertility rates but large pension systems, a decrease in fertility rate reduces retirement age. In these countries, pensions will increase if retirement is elastic to changes in fertility. In all cases, longer life expectancy increases pensions if retirement is relatively inelastic to changes in longevity.

中文翻译：

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代际时间转移、退休和公共养老金

本文提出了一种代际重叠模型，以祖父母和现收现付（PAYG）养老金制度的形式进行代际时间转移。时间转移的引入允许考虑儿童保育责任。在人口老龄化的情况下，生育率下降不仅会导致养老金制度缴款减少，还会降低育儿责任，从而增加生命周期收入。因此，需要重新审视人口变化对旧劳动力决策和养老金的影响。我发现，在生育率低且养老金体系规模较小的国家，生育率下降会减少老年工作时间。因此，由于生育率较低而导致的人口老龄化总是会减少养老金。另一方面，对于生育率高的国家和生育率低但养老金体系庞大的国家来说，生育率的下降会降低退休年龄。在这些国家，如果退休对生育率的变化具有弹性，养老金就会增加。在所有情况下，如果退休对寿命变化相对缺乏弹性，则预期寿命的延长会增加养老金。