After California made paid-family leave a law in 2004, the rate of new mothers taking time off doubled. New research shows the policy strongly affected fathers too: They are 46% more likely to take paternity leave in the first year of their kid’s life than they were before the law took effect.

That’s good news for those trying to haul the US out of the dark ages as the only industrialized nation on the planet without a paid leave policy, but the study wasn’t all sugar and spice.

It also found that the effect of the new policy was 50% larger for fathers of sons, compared to fathers of daughters. There are various iterations of awful in this, but here’s one: “When the sample is limited to fathers married to employed mothers these gender effects become even stronger—fathers of girls do not respond to the policy at all.” And here’s another: the new leave policy increases joint parental leave by 58% if the infant is male, but not at all if the infant is female.

The study offered several disheartening explanations:

First, it may be that fathers get more utility from spending time with their sons than daughters. Second, it may be that the parents perceive that paternal time spent caring for boys is relatively more productive than time spent caring for girls.

The researchers, led by Maya Rossin-Slater at the University of California Santa Barbara, also found that men are more likely to take leave if they work in offices with a high share of female employees. One possible explanation for this is the power of example: The more people take parental leave, the more socially acceptable it becomes.

That’s why Mark Zuckerberg was smart to make a big deal about his decision to take two months of paternity leave. His example means that as Facebook employees have children they might feel it’s ok to take time off to do that. It’s also why Yahoo CEO Marissa Mayer was criticized for her decision to take only two weeks off with her first child.

The study compared leave-taking rates among Californian fathers of infants before and after the implementation of the 2004 policy to a group of either California fathers with slightly older children, who are not expected to be affected by the policy, and fathers of infants in other states. Limitations include the fact that the survey used does not ask about parental leave specifically, but instead identifies individuals who are temporarily absent from work during some portion of the week. Also, fathers can only be linked to children who live in the same household, so it excludes fathers who do not live with their children.

Women in California are still far more likely than men to take leave, and a small share of men are taking time off. But the policy is clearly having an effect: by 2013, fathers were responsible for about 30% of California paid family leave claims compared to only 19.6% in 2005.

While daughters may lament the stubborn persistence of the patriarchy, they should also muster up some resentment for their older siblings: fathers were more likely to take leave with first children, but not as much for subsequent ones—an effect that was not matched among moms.