“More female leadership will lead to fairer treatment for all women.” This is a core argument in Sheryl Sandberg's controversial new book "Lean In: Women, Work, and the Will to Lead." But is it true?

Sheryl Sandberg (Laurent Gillieron/AP)

One criticism that's been levied at the book is that more elite women at the top will just make it easier for additional elite women at the top, diversifying the Davos crowd but making little difference for rank-and-file women. Having a female boss over a male boss still means having a boss. And a woman boss can’t overcome the demands of the bottom line, shareholder expectations, and the profit motive to benefit other female workers.

According to the latest empirical research, this critique is backwards. Female bosses do seem to make life better for rank-and-file female workers -- but they might make it harder for other female executives.

In their recent paper “Female Leadership and Gender Equity,” Geoffrey Tate and Liu Yang of UCLA follow men and women as they start new jobs after losing their jobs at recently closed plants, in order to best control for randomness. They find that women experience larger immediate wage losses than men, but that this wage gap is smaller when women move to firms that have a higher share of women as bosses. The authors conclude that having women in leadership positions “improve[s] the prospects of other women inside their firms.”

But the story is different on the elite level. In “Why Are There So Few Women Top Managers?,” Cristian L. Dezso of the University of Maryland and David Gaddis Ross and Jose Uribe of Columbia Business School look at the number of women in top management positions at Standard & Poor's 1,500 firms over twenty years. They find that the presence of a woman in a top management position reduces, rather than increases, the probability that a woman will occupy another top position. This is particularly true when a woman is chief executive.

“Top positions” here are usually defined as the top three to seven positions reported in corporate filings. You may normally think that the first woman in a top position like this will encounter the highest barriers and then it will get easier for the next one, and even easier for the woman after that. However one woman at the top will reduce the probability of another at top management.

Why is this? The paper can’t directly observe these dynamics, although the authors think two explanations can help. The first is that women themselves may discourage other women at elite levels, whether because of cultural norms or lack of general solidarity. The second is that if firms only want a woman in a senior position to satisfy cultural norms, perhaps to deflect questions of gender bias, it might bring resistance beyond the initial senior hire. In addition, the majority -- that is, men -- will react more strongly once they see their status positions as being threatened.

(Research from David Matsa and Amalia Miller finds that female board members are positively associated with a higher share of female senior managers. However, since boards are usually outsider-dominated, they are less focused on the two issues above, either the internal competition or issues of senior-level control.)

It’s worth clarifying what this research doesn’t tell us. It doesn’t tell us whether more women in elite positions are better for the businesses themselves, which they likely are. It also doesn’t tell us whether individual focus is the best way of advancing gender egalitarianism, which it likely isn’t. Numerous women’s opportunities will be defined by the number of hours they can work, the overall state of the economy and the legal and bargaining protections they have, rather than their ability to be promoted. And it doesn’t evaluating the radical critique that any advancement within the system and outside revolution is counterproductive, which is outside the scope of Wonkblog. This is answering the narrow question of the impact of senior women on the prospects of other women inside the same firm.

There is a presumption that, with time, women climbing the corporate ladder will naturally make it easier for other women to advance. And once that happens and there are a few more female CEOs, special efforts to identify and tackle the barriers women face, both institutionally and in the personal behaviors of men and women, will become less important. However, if this research holds, the precise opposite may be true at the top levels. More female leadership can lead to less fair treatment for potential female leaders.

Mike Konczal is a fellow at the Roosevelt Institute , where he focuses on financial regulation, inequality, and unemployment. He writes a weekly column for Wonkblog. Follow him on twitter here .