There's some truth in the stereotype that Republican men have old-fashioned views about women. According to the General Social Survey, a majority of politically conservative men believe that a woman’s job is “to look after the home and family.” And conservative men are twice as likely to oppose the idea that employers “should make special efforts to hire and promote qualified women.”

Perhaps these views explain the results of an unsettling new study that analyzed promotion rates at the nation’s top 200 law firms between 2007 and 2012. The results show that women have a much harder time making partner when they work under male bosses who donate to Republicans.

Gender inequality is already a huge issue at large law practices. Women consistently earn less, are underrepresented among leadership, and they make partner at about two-thirds the rate of men.

This new report, from Seth Carnahan, an assistant professor at the University of Michigan Ann Arbor, and Brad Greenwood, an assistant professor at Temple University, finds that women face particular disadvantage in offices where their bosses make more political contributions to Republicans than Democrats.

“The gender gap in promotions is almost twice as large when your bosses are conservative, compared to when your bosses are predominately liberal,” Carnahan says.

Carnahan and Greenwood arrived at this conclusion by scouring years of legal directories, political donation records, and press clippings. They had information about where people worked, the  kind of law they practiced, and also their career histories and educational backgrounds.

One hitch was that the researchers didn’t know who reported to whom, exactly. Instead, they looked at the all the partners who practiced the same kind of law in the specific office where a junior lawyer worked.

Consider, for example, a junior lawyer doing intellectual property work at one firm's San Francisco office. Her likely bosses would be the partners in that firm's San Francisco office who also specialize in intellectual property law. She might work for one or several of them at any given time.

If  the men in that group of partners donated twice as much money to Republicans than Democrats over the past decade, they were considered conservative. If they donated twice as much money to Democrats, they were considered liberal.

Already, women are half as likely as men to get promoted to partner. But under conservative male bosses, this gender gap in promotion rates widens by 80 percent. The researchers also show that the more money that male bosses donate to Republicans, the less likely women are to make partner in that office.

It’s not only that women suffer fewer promotions, either. The study finds that women are also more likely to leave the law firm if their bosses are Republican donors. Furthermore, conservative male bosses are less likely to serve on diversity committees, and less likely to pick women for their client teams, compared to liberal male bosses.

“What’s really interesting is that these differences exist at such dramatically different stages in a woman’s career,” Greenwood says. “You see this every step along the way.”

It’s hard to say what is causing what here, but the researchers can rule out a couple of things. The “conservative boss effect” isn’t explained by differences in legal specialties or geographic patterns. The study controls for those factors, and it takes into account the gender and racial makeup of partners at a firm. Between two similar offices, in similar areas of the law, the place with the more conservative atmosphere has more gender inequality.

This is not enough evidence to prove that Republican bosses are overtly discriminatory toward women, but it does suggest that women should be careful in places with conservative attitudes. It might be that these offices in general offer women less support, less flexibility, and less encouragement than more liberal firms.

Recent surveys from the National Association of Women Lawyers show that among top law firms, attrition is cited as one of the top reasons that women don’t get promoted to partnership. But maybe the question should be why women are quitting — and why, as Carnahan and Greenwood have shown, women are more likely to quit under conservative bosses.

Firms also blame the gender gap in promotions on the fact that women tend to bring in less business. But again, perhaps women could develop more client relationships if they were picked more often for client teams.

Carnahan doesn’t think that young lawyers need to rush to look up their bosses’ contribution records. But he does think that it’s important for them to pay attention to whether a firm takes gender inequality seriously.

Most people probably have a sense of their office’s disposition. And it could be that the most talented female lawyers compete to work at firms where they feel they will be valued, while the less talented ones have to settle for places that aren’t as hospitable to women. So the results of this study could reflect some self-sorting.

Nevertheless, the fact remains that the female lawyers seem to wilt under conservative bosses, particularly conservative male bosses.