We construct a simple exchange economy overlapping generations model in which there are along with a public social security various private insurance schemes to explore fertility and the effects of various variables on it. In the private system parents can invest in children and benefit from their support (care and income support) in the old age. An introduction of the public system will lower the incentive to have children, i.e. the fertility will be lower. This is an important negative externality of public pension system. We test some of the model's basic implications using long historical panel data from 11 countries for the period 1750-1995. In addition, two other data sets, the WDI (World Bank) and MZES (Manheim University) are used to reinforce the empirical results that are obtained with historical data. These analyses show that, opposite to common beliefs, there is a positive relationship between ageing and fertility if we control for the key determinants of fertility (size of the public sector, level of income, education and infant mortality). By contrast there is a strong negative relationship between the size of the public sector and fertility. The same is true in terms of income and education while the fertility effect of infant mortality is clearly positive.