Female job applicants are more likely to ask for more money when employers explicitly give them the option, a new paper finds.

The wage gap between men and women is notoriously tricky to account for. Over the course of a lifetime, women make, on average, 72 percent of what men earn—but it's not clear why. Some point to the fact that many women take extended amounts of time off from work when they have children. Others say women pick jobs in fields that aren't as highly paid as jobs men are drawn to. Others blame sexism, whether implicit or explicit.

A recent working paper from the National Bureau of Economic Research focuses on another factor: whether women are as willing to negotiate their salaries as men. The idea that women are less likely to negotiate has gained traction over the past few years, inspiring several books and websites devoted to helping women ask for more money at work.

The paper, called "Do Women Avoid Salary Negotiations?" is based on an experiment by Andreas Leibbrandt of Australia's Monash University and John A. List from the University of Chicago that involved 2,500 job seekers in nine American cities. The study explored how men and women responded to job advertisements for an administrative assistant position, and how they behaved in interviews after applying. The paper concludes that there is no statistically significant difference between men's and women's willingness to negotiate their salaries. However, there are differences between men and women in terms of the conditions under which they're most comfortable negotiating:

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Women are more likely to negotiate when an employer explicitly says that wages are negotiable. Men, on the other hand, are more likely to negotiate when the employer does not directly state that they can negotiate.

In the study, men negotiated more often when they were told only this: "The position pays $17.6 an hour." Whereas women were more likely to negotiate when they were told this: "The position pays $17.6 per hour. But the applicant can negotiate a higher wage," OR "The position pays $17.6 per hour/ negotiable." So, just a few words made a noticeable difference in whether or not women would negotiate: "the applicant can negotiate," or even more simply, "negotiable."

This gender difference also extends to job preference: Men are more likely to apply for a job where the wages are not explicitly negotiable.

Women are less likely to negotiate face to face. When negotiations happen in an impersonal environment (over email), gender differences in negotiations are smaller. In other words, women are more likely to negotiate over email than in person.

Gender differences in negotiating vary from city to city. Of the nine cities where the study took place, men were more likely to negotiate in four of them (Washington, DC; Denver; Los Angeles, and Portland), while women were more likely to negotiate in five (Atlanta, Dallas, Houston, San Francisco, and San Diego).

According to the paper's authors, these findings have possible policy implications. They write:

We find that simple manipulations of the contract environment can significantly shift the gender composition of the applicant pool. More precisely, by merely adding the information that the wage is 'negotiable' we successfully reduced the gender gap in job applications by approximately 45%. Thus, details of the contract environment have important effects on the gender gap, and with such knowledge public officials can design laws to take advantage of such effects.

The paper does not, of course, examine negotiating patterns after the applicant gets the job. How do men and women negotiate differently as they advance in their careers, after a year, or two, or ten of experience at a given company? Does women's preference for impersonal negotiations negatively affect their willingness to ask for a raise from a boss whom they know well?

Also left unanswered: What's going on in D.C., LA, Portland, and Denver? (Or Atlanta, Dallas, Houston, San Francisco, and San Diego, for that matter.) What makes a city's culture more or less hospitable to women's (or men's) negotiations?

Download the full report at the NBER website ($5 charge).