We frequently cover the growing retirement crisis here in the U.S. on Money & Markets. Regular readers already know that lower- and middle-class earners generally struggle with saving enough money for retirement.

As it turns out, many so-called “top earners” are in the same boat, according to a study by economists at the Schwartz Center for Economic Policy Analysis at the New School for Social Research, highlighted in a recent CNBC article.

Per CNBC:

“We always knew the bottom and the top were different and that they were growing apart, ” said Teresa Ghilarducci, an economics professor at the New School for Social Research and a co-author of the report. “But we were surprised that our retirement system creates winners and losers even within the same class of workers.”

Researchers tracked the retirement savings of people ages 51 to 56, using the Health and Retirement Study and tax data from the IRS.

And the authors of the study found a large range of retirement readiness among people in the top fifth of earnings, which shows even a large number of top earners aren’t prepared and could struggle financially as they age.

The study showed about 30% of people ages 51 to 56 who earn more than $80,000 a year have less than $200,000 saved for retirement, while 15% have more than $700,000.

Only 3% have reached the magic $1 million savings goal suggested by most experts.

“Even the top earners don’t have as much as you’d expect them to have,” said Siavash Radpour, a research associate at the New School for Social Research and another author on the study.

Of course, lower-income Americans won’t exactly feel sorry for them. Half of retirement wealth in the U.S. is owned by workers making more than $80,000 a year. Those earning less than $25,000 a year hold just 1% percent of retirement savings, and that imbalance is only getting worse.

In 2010, about 51% of Americans who made less than $25,000 a year had no retirement savings, up from 45% in 1992.

Still, the research shows that income goes only so far in determining the health of a person’s retirement savings. That balance hangs on many other factors, including whether or not your job offers you a 401(k), which assets your employer selects and if you took breaks from the workforce. (More than 40% of millennials don’t have access to a retirement plan through their job, according to Pew Trusts).

“There’s so much arbitrary stuff involved,” Ghilarducci said. “It’s not just whether you’re high-income, low-income or middle-income.”

Back in the 1980s, she said, 401(k) plans were framed as a comprehensive solution to the shortcomings of Social Security.

However, the researchers found that median retirement wealth falls 84% short of what people would accumulate if they saved 6% of every paycheck with a 50% employer match.

The authors recommend that lawmakers bolster Social Security and consider “guaranteed retirement accounts, ” in which people save in low-fee accounts with modest returns and then are later paid out in regular installments.

“We’ve run the experiment for 40 years,” Ghilarducci said. “We pronounce it a failure.”