By Gretchen Morgenson, New York Times

Appointing more women to corporate boards has long been viewed as a good thing for a company’s performance and for society as a whole.

But gender diversity among directors carries another benefit, 2015 proxy filings show: a bigger paycheck for the company’s chief executive.

An analysis of CEO pay at 100 large companies last year by Equilar, a compensation research firm in Redwood City, California, found that companies with greater gender diversity on their boards paid their chief executives about 15 percent more than the compensation dispensed by companies with less diverse boards. In dollars, this translated to approximately $2 million more in median pay last year among these companies.

This data, which comes from a smaller set than Equilar’s broader study of pay at the top 200 companies, doesn’t necessarily prove cause and effect, of course. There could be other reasons for the disparity, too. The more diverse companies could be bigger or more profitable than average, for example.

Still, it stumped me. For some reason, I had expected female directors to stand tougher on pay issues.

But Nell Minow, a longtime expert on corporate governance, was unsurprised by the findings.

“It’s very difficult for women to get on boards, and I think they are under even more pressure to go along and get along,” said Minow, a vice chairwoman at ValueEdge Advisors, a consulting firm that works with shareholder groups on compensation and other issues. “The culture of the boardroom is to vote yes. You want to stay on the board, don’t you?”

Today, roughly one in five directors at a wide array of public companies is a woman, Equilar said. That’s up 31 percent over the last five years.

If Minow is right about board culture, anyone arguing for more women on boards should recognize that gender alone may not be enough to generate a new approach to pay.

Among the 100 largest companies Equilar studied, 57 percent have boards where women make up more than a fifth of the members, which is the average share of female directors among Standard & Poor’s 500 corporations.

The median pay among the chief executives overseeing the companies whose boards had more gender diversity was $15.7 million last year, Equilar found. This compares with $13.6 million received by heads of companies whose boards had 20 percent or fewer women.

Chief executive compensation at companies with more diverse boards also exceeded by 8 percent the $14.5 million median pay received by CEOs employed at the top 100 companies.

At the 10 large U.S. company boards with the greatest gender diversity, 46 of the 124 directors were women. That’s more than a third.

Macy’s, the giant retailer, ranked atop this list with six female directors out of 13. Wells Fargo came second with 40 percent of its board consisting of women. Procter & Gamble and Hewlett-Packard each had boards made up of 38.5 percent women.

At Abbott Laboratories and Cardinal Health, female directors accounted for 36.4 percent of the boards. At the remaining companies — Accenture, AT&T, ManpowerGroup and Tenet Healthcare — one-third of the board members were women.

Who’s at the bottom of the list? Twenty-First Century Fox, with 7.7 percent of its board made up of women; Express Scripts and Qualcomm did a little better with 8.3 percent; Emerson Electric had 9.1 percent, and Humana Inc. came in at 10 percent.

Most of the top 10 companies paid their chiefs more than the $14.5 million median at the top 100 companies, Equilar said. But four did not. Among these were ManpowerGroup, whose chief executive, Jonas Prising, received $9.1 million last year, and Terry Lundgren, Macy’s chief executive, who received $11.6 million.

Just being a director, of course, does not mean that you can have a direct impact on a company’s pay practices. That is the domain of the compensation committee, the board group that oversees the methodology used to determine top executives’ pay.

Women are not that common on these crucial committees. Even among the 10 most diverse boards, just under a third of the directors who are women — 14 of 46 — belong to compensation committees.

Still less likely, the analysis showed, is that a woman will serve as chairwoman of a board’s compensation committee. Women performed that function at just two of the 10 most diverse boards last year.

The chief executives at both of those companies — Accenture and AT&T — made more than the median pay at the top 100 companies analyzed by Equilar.

Marjorie Magner, a partner at Brysam Global Partners, a private equity firm, heads Accenture’s compensation committee and is its lead director. Pierre Nanterme, Accenture’s chief executive, received $15.8 million last year, or $1.3 million more than the median pay at the top 100 companies.

Magner declined to comment.

The other compensation committee chairwoman was Joyce Roché, former president and chief executive of Girls Inc., a nonprofit organization that tries to build confidence in girls. Under Roché's stewardship at AT&T, Randall L. Stephenson, its chief executive, received $22.4 million. That’s almost $8 million more than the median pay for the 100 top companies in 2015.

Roché declined to respond to questions about the pay situation at AT&T.

She was also AT&T’s compensation committee chairwoman in 2014 when Stephenson received almost $24 million. Company shareholders expressed displeasure with that pay package at AT&T’s annual meeting last year, where 23 percent of votes cast were against its compensation practices. That’s far above the 5 percent of nays cast on pay at the companies in the Standard & Poor’s 500-stock index during the same year.

Another notable detail about the highly diverse boards: There’s a lot of overlap among the directors. At the 20 companies with the most gender diversity, four directors who are women sit on two of their boards.

These multiple directorships aren’t unusual. Nearly one-quarter of female directors at S&P 500 companies sat on one or more corporate boards last year, Equilar found. Among directors who are men, only 19 percent held multiple board seats.

Does this indicate the existence of an “old girls’ network,” a small and relatively elite group of women who are sought after for board seats? Minow said it did.

“When you talk to executives, they always tell you: ‘We are looking for a consensus builder in a director,'” she said. “What that means is someone who doesn’t rock the boat.”

It’s not as if the pool of qualified women executives — those with so-called C-suite experience — isn’t growing. It is.

But it remains a relatively untapped pool. A study this year by Equilar and the U.S. 30 Percent Club, a group formed by business leaders seeking greater gender balance at public companies, found that four of five female executives currently working had never served on a board.

It is certainly good news that women have made headway as corporate directors in recent years. But for those who had hoped women who are directors would rein in runaway executive pay, the data indicates that gender diversity in the boardroom just doesn’t translate into meaningful change.

To Learn More:

Female CEOs Earn more than Males, but Make Up Only 5% of Executive Leaders (by Sarah Skidmore, Associated Press)

U.S. Trails Allies in Percentage of Women on Corporate Boards (by Noel Brinkerhoff, AllGov)

Companies with Women CEOs Outperform those Led by Men (by Noel Brinkerhoff, AllGov)

Little Progress for Women Execs in California’s Top Corporations (by Ken Broder, AllGov California)