Two report authors, Isabel Sawhill and Richard Reeves, both of Brookings, found that:

among children born of normal birth weight to married mothers who were not poor and had at least a high school education at the time of their child’s birth (advantaged-at-birth), 66 percent can be expected to be ready to start kindergarten, versus only 46 percent otherwise. This gap never narrows.

Citing the work of Sean Reardon of Stanford, Duncan and Murnane point to a substantial increase in the test score gap between low and high income students taking the SAT:

In the late 1960s, test scores in reading of low-income children lagged behind those of their better-off peers by four-fifths of a standard deviation — about 80 points on an SAT-type test. Forty years later, this gap was 50 percent larger, amounting to nearly 125 SAT-type points.

Bradbury and Triest, the Boston Federal Reserve economists, follow up by drawing attention to the inexorable disadvantages accruing to already disadvantaged kids:

A 40 percentage-point gap in college enrollment of students born in the early 1960s between poorest-quartile and richest-quartile students expanded to a 51 point gap for the later cohort; similarly, the earlier cohort’s 31 point gap in college completion between rich and poor grew to a 45 point gap for the later cohort.

Bradbury and Triest put forward a bleak assessment of the options available to young people born into the poorest families, even children who possess considerable native gifts:

A key question is whether primary schools, once children come under their care, level the playing field and reduce these disparities. Most research findings suggest that they do not.

Not only do “children of affluent parents graduate from college at substantially higher rates than children of low-income parents,” according to Bradbury and Triest, “the gap persists even when controlling for ability in the form of test scores.”

They cite data showing that

a child’s earnings in adulthood reflect parental investments in his/her human capital (education) as well as his/her endowment of earnings capacity and market luck. That endowment, in turn, is determined by the reputation and “connections” of their families, the contribution to the ability, race, and other characteristics of children from the genetic constitutions of their families, and the learning, skills, goals, and other “family commodities” acquired through belonging to a particular family culture.

Four key factors or mechanisms of intergenerational earnings persistence “that are related to family incomes and that have a return” in the labor market play an outsize role in determining the fate of American children, according to studies cited by Bradbury and Triest: “noncognitive skills, cognitive ability, early labor market experiences, and educational attainment.”

Smeeding notes that

low incomes have a well-established negative impact on brain development, social-emotional development, and lifelong outcomes.

But, he continues,

a little more money makes a big difference to children on the bottom rungs of the ladder.

The benefits of the Earned-income tax credit, the Child Tax Credit and the Supplemental Nutritional Assistance Program (food stamps), Smeeding writes,

lead to better outcomes for children and parents, especially positive longer-term developmental effects on low-income children.

These resources are distributed — increased, diminished and otherwise tweaked — through political processes, over which by definition children are powerless.

Sawhill and Reeves cite impressive gains from a five-stage program of intensive and sustained intervention with poor children and adolescents. These range from “biweekly home visits and group meetings to instruct and equip parents to be effective teachers for their children” during infancy to a “comprehensive high school reform initiative aimed at reducing student dropout rates.” Children whose parents are positioned, materially and psychologically, to take advantage of such interventions are fortunate, but the children themselves have no control over access to these resources.

Sawhill and Reeves write that the benefits of these interventions exceed the costs:

The baseline 20 percentage point gap in the share of low-income and high-income children reaching middle class by middle age shrinks to 6 percentage points after the multi-stage intervention.

In their essay, Duncan and Murnane cite three “innovative, quite durable programs” — the Boston pre-K program, the campuses of the University of Chicago charter school and New York City’s small high schools of choice — that provide “proofs that it is possible to improve the education of substantial numbers of low-income children.” But these successful programs are available to a vanishingly small proportion of the poorest children nationwide.

The Russell Sage report, despite presenting some good news, highlights an unresolved dilemma: Are there economic forces at work that are inexorably worsening equality of opportunity regardless of government intervention?

Bradbury and Triest implicitly raise this issue when they point out that

Nations or eras with greater disparities in pay levels according to educational attainment will, other things equal, have higher intergenerational earnings elasticities, hence, lower mobility, because any level of intergenerational correlation in education translates into greater differences in earnings and, hence, higher correlation of parent and child earnings.

This is precisely what has happened in the United States. From 1979 to 2012, the earnings gap in inflation-adjusted annual pay between high school and college graduates has grown from $17,411 to $34,969 for men and from $12,887 to $23,280 for women, according to data compiled by David Autor, an economist at M.I.T.