Finance chiefs and their bosses who don’t help their employers avoid enough tax are more likely to be forced out.

Because CFOs are often held accountable for the corporate tax function, they’re more likely to be fired when the company’s tax rate is significantly higher than those of their peers, according to a new study of the relationship between corporate tax rates and their job risks for chief executive officers and CFOs.

Scholars have long theorized that C-suite turnover is more likely to happen when company tax rates are comparatively too low – indicating the possibility that tax avoidance schemes are in play. In that case, regulators and investors might end up calling for the heads of CEOs and CFOs.

While the authors of the paper find evidence for that assumption, the link between low tax rates and top-executive firings tends to hold up only during periods when regulators are on the prowl for corporate tax cheats – periods like that following the enactment of the Sarbanes-Oxley Act of 2002. Their data “suggests that the relation between paying relatively too little tax and CEO turnover obtains only in periods with high regulatory scrutiny on tax aggressiveness,” they write.

On the other hand, they find ongoing evidence that over the long haul, boards tend to reward CFOs and CEOs who deliver lower tax rates. Perhaps that’s because efficient tax management is a sign that the company’s doing a good job of producing cash flow and managing its finances overall. Even though “paying too little tax potentially increases reputational costs and scrutiny from regulators and taxing authorities, after-tax cash flows for these firms are likely to be higher relative to firms paying too much tax,” according to the paper.

In summing up their argument, professors James A. Chyz of the University of Tennessee and Fabio B. Gaertner of the University of Wisconsin-Madison, write: “Specifically CEOs who do not avoid enough tax are more likely to be forced out. Unlike the effect of avoiding too much tax, the … result of avoiding too little tax holds throughout our sample period.”

The authors base their findings on a sample of about 5,000 companies that had “CEO turnover events” and compares it with effective corporate tax rates for the sample group. They also looked at a much smaller sample of CFO turnover data, and found the results for the finance chiefs “somewhat consistent with our CEO results.”