How many parents does it take? Parental time allocation and the effectiveness of fertility subsidies

There has long been an apparent consensus in the literature on intra-household allocation and fertility that greater paternal involvement in childcare relaxes maternal time constraints, enabling mothers to increase their labor supply or leisure. Recent evidence, particularly from South Korea, challenges this view: increases in fathers' childcare time have coincided with a further increase in mothers' time dedicated to child-rearing. This paper develops an Overlapping Generations (OLG) growth model to address such a puzzle. The central mechanism and our main innovation hinge on the functional form of the childcare technology. When maternal and paternal time are substitutes, the conventional result holds. However, when they are complements, greater paternal involvement necessarily raises maternal childcare time, depressing fertility and redirecting household resources toward child quality. We further argue that the elasticity of substitution should not be interpreted as a pure preference parameter, as it also reflects the social and institutional norms, the skills each parent brings to child-rearing and their intergenerational transmission. The model is extended to study the effectiveness of pro-natalist subsidies, suggesting that such policies may generate an unintended anti-fertility bias. Numerical simulations calibrated loosely to South Korean data confirm that the model is consistent with the observed quantity-quality trade-off and the persistence of low fertility despite active pro-natalist policy.