After stagnating in the mid-1990s, progress toward closing the earnings gap between men and women in America basically stopped in the last decade. The most recent data show that women earn, on average, around 20 percent less than men. Some cite discrimination, the time off that women take to give birth or care for their families, or their reluctance to negotiate for higher pay. Others say that women self-select into lower-paying jobs, or are, for whatever reason, less productive or competitive in the workplace.

A new study by David Newton and Mikhail Simutin provides a fresh perspective on why the pay gap is so persistent. The paper argues that it’s not just the gender of the worker that matters, but also the gender and age of the person awarding the salary.

The study finds that the gender pay gap is by far the largest when men manage women. And men still dominate at the very top of corporations, where wage setting may matter the most.

Drawing on a pool of data on more than 23,000 chief executives and other corporate officers over a period of 16 years, the study showed that female corporate officers received $2,960 less on average in annual compensation than male officers did. But female officers who worked for a male CEO earned on average $46,500 less per year than male officers. Age also played a role: The older the male CEO was, the bigger the pay gap.

Interestingly, the study also found a reverse pay gap for men working under women, though the difference is less extreme. Male officers working for women earned $21,960 less than female officers did, on average.

Source: Newton and Simutin, 2014

The study builds on a large body of academic work on social identity theory – the idea that people tend to treat those who are similar to them better than those who are not. Studies have shown that, when playing competitive games, people are much more charitable toward those of their own gender (think of it as “hooray for our team”).

So having more women at the top of the corporate hierarchy could have a powerful trickle-down effect, helping to ensure that women further down in the company are better recognized and rewarded for their achievements.

“The tone has be set at the top of organizations and really permeate the organization,” Peter Grauer, the chairman of Bloomberg Inc., said at a Committee for Economic Development panel on women in corporate leadership in Washington, D.C. on Nov. 14.

The issue with this strategy is that it’s a chicken-and-egg problem. Women in corporate leadership could help their subordinates, to be sure. But how can women get to the top in the first place?

Speaking from the same event, Barbara Krumsiek, the president, CEO and chair of Calvert Investments, pointed out that for most corporations the pipeline for getting women into leadership is a very leaky one. Women represent 47 percent of the workforce, but only 14 percent of executives and 4 percent of CEOs, Krumsiek said. And half of the companies in the S&P top 100 have no women among their top five paid executives.

According to Krumsiek, companies need to closely examine their own corporate culture to figure out why women aren’t succeeding – just as Harvard Business School did in its multi-year self-examination of why fewer women than men were graduating at the top of their class.

Rather than teaching women how to “lean in” or negotiate better, we should focus on changing corporations to better fit women, Krumsiek stressed. “We don’t need another self-help book for women, thank you very much,” she said. “Companies need to look internally at how they operate. We need more self-help books for companies.”