Education researchers often express test score differences in standard deviations, which allows for a consistent measure of gaps across different tests, populations and contexts. Measured using that conventional approach, the gap in math scores between disadvantaged eighth graders and their classmates in Michigan is 0.69 standard deviations. This places disadvantaged children roughly two grades behind their classmates. By contrast, the gap based on persistent disadvantage is much wider: 0.94 standard deviations, or nearly three grades of learning.

In fact, there is a nearly linear, negative relationship between the number of years of economic disadvantage and math scores in eighth grade. These lower scores do not appear to be caused by more years of disadvantage, however. When we look at third-grade scores, nearly all of the eighth-grade score deficit is already in place. By third grade, those children who will end up spending all of primary school eligible for subsidized meals have already fallen far behind their classmates.

What is the explanation? It appears that years spent eligible for subsidized school meals serves as a good proxy for the depth of disadvantage. When we look back on the early childhood of persistently disadvantaged eighth graders, we see that by kindergarten they were already far poorer than their classmates.

We can see this with national data. The Early Childhood Longitudinal Study, run by the Department of Education, tracks a sample of children who started kindergarten in 1998. Among children who were eligible for subsidized meals through eighth grade, household income during kindergarten was just $20,000. For those who were only occasionally eligible, it was closer to $47,000, and for those never eligible, $80,000.

These data also show that persistently disadvantaged children are far less likely than other students to live with two parents or have a college-educated mother or father. Just 2 percent of persistently disadvantaged children have a parent with a college degree, compared with 24 percent of the occasionally disadvantaged (and 57 percent of those who were never disadvantaged).

No one ever actively decided that eligibility for subsidized meals was the best way to measure students’ economic disadvantage. The metric was widely available and became by default the standard way to distinguish between poorer and richer children. But it was always an imprecise measure, and we can do better at little cost.

Many states now use administrative data on eligibility for means-tested programs such as welfare benefits and food stamps to automatically qualify children for subsidized meals in school. Since these programs have a range of income cutoffs, their eligibility flags can be used to distinguish between children who are extremely poor and those who are nearly middle class. The children whose families persistently receive benefits will be the neediest of all.

Why does all this matter? Many federal, state and local programs distribute money based on the share of a district’s students who are eligible for subsidized meals. But schools that have identical shares of students eligible for subsidized meals may differ vastly in the share of students who are deeply poor. The schools with the most disadvantaged children have greater challenges and arguably need more resources.