With America on the precipice of electing its first female president, a great deal has been made of the considerable barriers to this moment: expectations of women that keep them from being able to even attempt such a run and sexist perceptions that could dissuade voters who might otherwise vote for them.

The truth of this is a bit knotty, and a few years ago two political scientists—Sarah Anzia, then a Ph.D. candidate at Stanford and now a professor at Berkeley, and the University of Chicago's Christopher Berry—tried to untangle cause and effect when it comes to the election of female politicians. What they found was fascinating: Female politicians are actually more effective, depending on how you measure these things. But what they found on the way to that conclusion is fascinating as well.

They started with a number of conclusions that are broadly accepted from the research. First, women of comparable qualifications to men are less likely to run for office. One likely reason is that 90 percent of them, specifically in the "candidate eligible" pool, believe there is "bias against women in elections." As do 75 percent of men.

Experimental studies back this up, as do large-scale surveys from NORC, Pew, and Gallup.

But! "One of the most well-known findings in the literature on women in politics is that female candidates win general elections at the same rate as male candidates … women raise as much money as during their campaigns as men."

One way of interpreting this is to conclude that, as they note, "many scholars have concluded that discrimination against women in politics is a phenomenon of the past." But another is to conclude that the women who run and win have to be twice as good to get half as much, or at least considerably more skilled.

So Anzia and Berry set up a couple clever tests to figure this out. The first is how much federal cash legislators bring home to their districts. (Granted, this may not fit everyone's idea of what makes a good politician.) They also looked at bill sponsorships to broaden the metrics.

And the women bring home the bacon. "In summary, the unambiguous result is that female legislators succeed in directing more discretionary spending to their home districts than male representatives. A spending advantage of 9% amounts to approximately an $88 per capita per year for districts represented by women," they write. "Given that the average district has 563,732 residents, the aggregate spending increase for the district is roughly $49 million when it sends a woman to Capitol Hill." In moderately conservative districts, the effect is even greater—13 percent.

The effect on bill sponsorship is even higher: 17 percent, or about 21 bills sponsored per congress versus 18. They also have more co-sponsors, suggesting to the authors that "women have stronger networks of collaboration with their colleagues." Perhaps as a result, those bills are more likely to advance farther through the legislative process.

This doesn't mean that women are more effective legislators by dint of their gender alone. To examine this, they devised an imperfect but clever test, looking at the records of women who took over from their husbands after being widowed. (It's a small sample, just eight legislators with a combined 57 years in the legislature.) They returned a smaller but not statistically significant amount of money to their districts as compared to male legislators.

In other words, when male and female legislators finally reach parity in their paths to elected office, they may reach parity when it comes to effectiveness as well. Until then, districts that look past gender will continue to reap the benefits.