“We cannot be satisfied as long as the colored person's basic mobility is from a smaller ghetto to a larger one.” Martin Luther King Jr., August 26, 1963.

The idea that everyone—no matter how humble their beginnings—can move up the ladder and succeed is core to the American dream. Americans of all races and ethnicities dream that with hard work and initiative, they can do better for themselves and see their children prosper. But while many African-Americans shared that dream in 1963, they also feared that in reality they were trapped in a ghetto, whether physical or economic. Fifty years later, we have a good sense of how the children of those marching on Washington have fared.

To analyze economic mobility for black and white children, I looked at individuals who were under 18 years in 1968 and compared their average adult income with their parents’ average income when they were around the same age.

What I found for black children born into the bottom fifth of the economic distribution (some of whom may have been living in actual neighborhood “ghettos”) may not be surprising, given the many reports describing the challenges facing poor black families.

• The black-white gap in upward mobility is large when you’re starting from poverty. Over half (54 percent) of black children born into the bottom of the economic distribution were still in the bottom as adults. Only 13 percent rise to middle class and only 4 percent reach the wealthiest fifth of the income distribution.

• The odds of moving up are somewhat better for poor white children: while 31 percent were stuck at the bottom, 25 percent moved to middle class, and 8 percent to the top fifth of the income distribution.

What was more startling, (and generated considerable discussion when the findings were first released in 2007), was what tended to happen to black children born into the middle class.

A disturbingly high 45 percent of black children whose parents were solidly middle class (with incomes in the middle fifth, or of about $49,000 to $65,000 in 2006 dollars) ended up falling to the bottom fifth. For comparison, only 16 percent of white children born to middle-class parents with similar incomes suffered the same economic descent.

One likely explanation is that almost half (49 percent) of middle-class black children (family income in the middle quintile or higher) lived in poor neighborhoods, compared to only 1 percent of white children, according to research by Patrick Sharkey.

In short, Dr. King was justified in his pessimism about black mobility, broadly defined, in 1963.  Even growing up in a family with middle-class income did not protect black children from future poverty in the same way it protected white children.

Children leave Tapley School at Springfield, Mass., January 12, 1965 during recess. A Federal judge in Boston ruled that segregation existed in Springfield schools and ordered a plan by April 30 to end it. This is one of the oldest schools in the city, built in 1887 and is 90% Black according to the National Association for the Advancement of Colored People. Photo by AP