Researchers reviewed federal government data on more than 55,000 older adults. They found that between 2000 and 2014, there was a 14 percent increase in the rate of those who reported good health.

However, those with graduate degrees had the most improvement -- 56 more healthy people per thousand -- while the rate remained flat among those with only a high school diploma.

Rich seniors had the best rate of good health throughout the study period, with the rate increasing from 490 per 1,000 to 603 per 1,000.

Overall, 52 percent of older adults with good health had high incomes. Just 31 percent of those with poor health had high incomes.

Whites were more likely than blacks or Hispanics to have good health. The rate of good health among whites rose from 442 per 1,000 to 533 per 1,000 during the study. The rate of good health among blacks and Hispanics remained flat, but the rate did increase among other racial/ethnic groups.

Study author Matthew Davis said he was "amazed" at the obvious health disparities based on race, income and education.

"The widening health disparities is particularly striking because older Americans have access to health care [through Medicare]," said Davis, an assistant professor at the University of Michigan's School of Nursing.

"Policies have to extend beyond just getting people access to health care to get at what's driving disparities. The lack of improvement in health among all groups could imply that public health initiatives are leaving some people behind," he added in a university news release.

The study was published online in the journal JAMA Internal Medicine.