The policy has achieved many of the hoped-for long-term outcomes, chief among them more fluidity in who does what around the house. Previous studies found that fathers who take paternity leave are more likely, a year or so down the road, to change diapers, bathe their children, read them bedtime stories, and get up at night to tend to them. Patnaik’s study confirmed this; looking at time-use diaries, she found that men who were eligible for the new leave—whether or not they took it—ended up spending more time later on routine chores like shopping and cooking.

If these changes sound minor, they aren’t. As men have taken on more domestic work over the past 20 or so years, they have gravitated toward the fun stuff, like hanging out with the kids, rather than the boring but inescapable duties, like boiling the ravioli or vacuuming Cheerios out of the family-room carpet. The University of Oregon sociologist Scott Coltrane has noted that when men share “routine repetitive chores,” women feel they are being treated fairly and are less likely to become depressed.

In Quebec, women whose husbands were eligible for the new leave were more likely to return to their original employers and were more likely to work full-time, resulting in their spending “considerably” more hours on paid work. (When women work full-time, it alters the home division of labor more than when they work part-time.) And as women were spending more time working for pay, men were spending less: the Quebec paternity-leave policy resulted in a small but long-term decrease in fathers’ time at work.

This finding hints at the possibility that paternity leave could erode the fabled “fatherhood wage premium.” In the early 20th century, employers explicitly and even proudly paid married men more than they paid single men—and much more than they paid women—in recognition of the fact that husbands were the conduit by which families got fed. Even after employers dropped these formal policies, fathers have continued to enjoy a wage bonus, either because they are seen as being more motivated and reliable, or because they work longer hours, or both. But Patnaik’s study suggests that paternity leave might give men a new mind-set, prompting them to trade more money for more time at home, more flexibility, or both. In this way, it could make men behave more like women.

Which points to a core goal of many workplace-equity policies: spreading the parenthood stigma around. Widespread paternity-leave plans raise the possibility that bosses will stop looking askance at the résumé of a 20‑something female applicant, or at least apply the same scrutiny to a similar male applicant.

While it’s too soon to tell whether California’s, New Jersey’s, and Rhode Island’s paid-paternity-leave programs will be as transformative as Quebec’s, the early signs are positive. Since California instituted its program, the percentage of “bonding leaves” claimed by men has risen from 18.7 in 2005 and 2006 to 31.3 in 2012 and 2013. A study by the economist Eileen Appelbaum and the sociologist Ruth Milkman showed that initial concerns that the California law would be a “job killer” were unfounded, and that workplaces have figured out effective and creative ways to cover for leave-taking parents. The biggest hurdle seems to be getting the word out, particularly among lower-income families that could benefit enormously from the program. (Part of the beauty of the California policy is that it extends leave to men in non-white-collar jobs.)