Advocates focus on the stunning success of two tiny programs in the 1960s and 1970s, Perry Preschool and Abecedarian. Children from low-income families who participated in them were more likely to graduate from high school and get a job and less likely to end up on welfare.

Yet critics correctly note that programs often work when small but don’t scale up. It’s an open question whether those two programs would have an impact as great today if they were rolled out nationwide.

Republican critics focus on (and misunderstand) a major, well-designed project called the Head Start Impact Study. It found that Head Start produces educational gains that fade away. By third grade, when the research ended, there was little detectable difference between those assigned to Head Start and those in control groups.

That’s disappointing. And that’s why critics denounce Head Start as a waste of money.

Yet early education has always had an impact not through cognitive gains but through long-term improvements in life outcomes. With Perry, Abecedarian and other programs, educational gains fade, yet, mysteriously, there are often long-term improvements on things that matter even more, such as arrest rates and high school graduation rates. The Head Start Impact Study couldn’t examine those outcomes.

Other researchers have, and their findings are almost unanimous. One rigorous study led by Eliana Garces, then of U.C.L.A., found that Head Start graduates were more likely to graduate from high school and attend college than their peers. David Deming of Harvard found that children who attended Head Start were more likely to graduate from high school and less likely as young adults to be “idle” — out of a job and out of school.