It’s often said that Americans are living “longer, healthier lives,” and while that’s true overall, white wealthy people are still far more likely to enjoy good health than other demographics in old age. A new research letter published in JAMA Internal Medicine Monday revealed clear racial, income, and educational disparities in the number of senior citizens who experience good health—and the gaps have only widened over time.

For this report, researchers from the University of Michigan looked at adults older than 65 who reported their health as “excellent” or “very good” at least twice within one calendar year, between 2000 and 2014. As a whole, seniors were feeling healthier by the end of that time period. However, white people and wealthy people were most likely to consider themselves very healthy. The most highly educated seniors consistently felt healthier than those with less education, and as the study went on, the health of that group only improved. In 2000, 57.4 percent of highly educated seniors considered themselves in very good or excellent health, and by 2014, that number had risen to 63 percent.

JAMA Internal Medicine

Meanwhile, the poorest adults, those who never married, those with a high-school degree or less, blacks, and Hispanics all saw declines in the number who reported themselves as being in “excellent” or “very good” health. The finding that older Hispanics are in relatively poor health, and saw declines in health over time, bucks a popular theory in public health known as the “Hispanic paradox,” in which Hispanics have been found to have generally good health and long life expectancies despite their often-difficult life circumstances.

The poor health of high-school graduates in this study mirrors earlier studies by Princeton’s Angus Deaton and Anne Case, who found an increase in mortality rates among white middle-aged people without high-school diplomas. Although the people in Case and Deaton’s studies were slightly younger— 50 to 54—this study shows what happens to those individuals if they do survive into their 60s.

The surprising disparities that emerge in this study underscore the fact that health insurance does not always guarantee good health. People over 65 are eligible for Medicare, yet some groups are clearly healthier than others. Access to a doctor is essential, but overall health, it seems, is the sum of what happens in a lifetime.