Companies with “insider” chairpersons pay their chief executives a lot more than those with “outsider” chairpersons, according to a report released Wednesday by Institutional Shareholder Services, or ISS.

The Rockville, Md.-based firm analyzed data from S&P 500 companies and found that compensation over a three-year period was 42% higher on average for CEOs that had an insider chairperson (excluding those in a combined role), than for CEOs of companies whose board was chaired by an independent outsider.

CEOs who were also chairperson of the board of their companies were paid 29% more on average than CEOs of companies chaired by an independent outsider. In 2015, about 51% of S&P 500 companies combined the chair and CEO roles, down from about 54% in 2014.

Company revenue played a part in average CEO pay, but there was not a significant correlation with other potential factors, such as indexed shareholder return performance or CEO tenure, according to the ISS report.

“While many studies have examined the impact of financial, economic, and operational measures on CEO pay, the effect of board leadership structures has to date not been a significant part of the body of analysis,” ISS’ head of Americas research Carol Bowie said in a press release. “These findings suggest that companies with a greater level of independent oversight are able to provide a more effective check on CEO compensation.”

The ISS report supports calls by shareholder advocacy groups for companies to separate the jobs of chair and CEO, reasoning that a company’s top manager shouldn’t also lead the board that oversees his or her performance and compensation, according to The Wall Street Journal.

However, shareholders have proven largely comfortable with the combined role: They have voted on 372 proposals to separate the roles at S&P 500 companies over the past decade, but approved only about 6% of them, according to ISS.

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