Most of the childcare in the US (and probably every country) is done by women. As I walked past a men’s bathroom that had a baby changing table inside, I realized that this is a pretty rare occasion. Most of the baby changing tables are inside women’s rooms. Of course, this cannot explain the gender differences in caring for children, but it raises an interesting question: how much of the differences in child rearing is explained by institutions? If jobs offer maternal leave but not paternal leave, this tilts the incentives toward the woman taking time off. If men’s bathrooms don’t have changing tables, women will have to be the ones changing diapers when the family’s out and about.
Of course, there is also the question of whether this is driven by preferences. If 99% of women prefer to be the ones taking care of the children and 99% of men prefer not to, then putting changing tables in both bathrooms is probably inefficient. If most men use paternal leave to get ahead in their careers (as some have alleged), maybe paternal leave is not a great idea. However, my guess is that preferences co-evolve with infrastructure = if you put a baby station in the men’s bathroom, it will eventually be used.