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This article analyzes the relationship between family policies focused on childcare for children under the age of three and fertility levels. In the current context of very low European fertility, it is important to understand whether public support for families can help increase fertility or if, on the contrary, existing fertility levels are the exact reflection of the reproductive desires of families, regardless of the family-support of the policies that may exist in each country. This analysis was carried out through a stochastic dynamic mathematical model that incorporates both demographic variables and family policy variables. A sensitivity analysis was carried out on Spain and Norway, two countries that have very different models of family policies. This sensitivity analysis allows establishing a relationship between the existing family policies and the total fertility rate and also the expected evolution of fertility rates in the future, if the current family policies remain constant. The results showed that the models which lead to an increase in fertility are those which are most generous and which also incorporate a gender perspective, so they allow the identification of good practices and maximum levels of policy efficiency in regards to different objectives such as increase fertility and advances towards gender equality. By contrast, models with erratic and insufficient support clearly contribute to maintaining fertility at very low levels and perpetuate unequal gender relationships. There is, therefore, space for state agency to develop more effective public policies in both dimensions.