The overwhelming majority of Americans still make more money than their parents, but upward mobility is elusive for many, particularly for African Americans and those without a college degree, according to a new study released Monday.

While 84 percent of Americans earn more than their parents, about a third moved up between income classes during the past four decades, according to a new study from the Economic Mobility Project at the nonpartisan Pew Charitable Trusts. Sixteen percent of all families surveyed dropped from the income levels of their parents, and blacks were more likely to be downwardly mobile than whites.

“While most Americans have more income earnings or wealth than their parents, it may not be enough to move them to a higher rung of the economic ladder,” said Diana Elliott, the project’s research manager.

Among the most striking findings: The chances of moving from the bottom of the income spectrum to the very top is only 4 percent, a figure that suggests the American “rags-to-riches” story is “more often found in Hollywood than in reality,” the survey noted.

Researchers parsed data from about 2,200 families participating in the University of Michigan’s Panel Study of Income Dynamics, which has tracked the family income and wealth accumulated by a group of parents and their children from 1968 to 2009.

The study looked at mobility in two ways — “absolute” and “relative.” In terms of “absolute” mobility — whether families make more money in inflation-adjusted dollars than their parents — Americans are doing just fine. In all, 84 percent are earning more than their parents and half of them are accumulating greater wealth than their parents did at the same age, roughly in their 40s.

But the study showed that Americans in the past 40 years have had a harder time moving up and down between income classes — what the researchers called “relative mobility.” Forty-three percent of those raised by the bottom level of income earners were likely to be stuck there as adults, while 40 percent of the children from the highest-earning families were likely to remain high earners themselves.

Africans Americans and those without a college degree have the most difficulty climbing the rungs, according to the study, “Pursuing the American Dream: Economic Mobility Across Generations.”

African Americans have a harder time earning more than their parents than whites, and, among the middle class, only 23 percent accumulate more wealth than their parents, compared with 56 percent of whites. Half were likely to fall out of the middle income ranges and into the ranks of the lower class. This study does not include data on Latino families because only a handful were part of the original study group group from 1968.

Erin Currier, the manager of the Economic Mobility Project, said there are a host of factors that can affect whether someone moves up or down the income ladder, including education and how much a family has in savings.

Those with college degrees are three times more likely to rise from the bottom of the family income ladder to the top, the study showed, while those without secondary degrees are more likely to stay mired in the bottom.

Even geography can play a role. Those who grow up in high poverty neighborhoods are likely to become downwardly mobile, regardless of how much money their parents make, Currier said. A previous study released by Pew earlier this year showed that those living in some states in the Northeast and Mid-Atlantic — including Maryland — have higher upward mobility than the national average, while several states in the South were below the national average.