Can you change kids’ lives by sending them to preschool? It’s a question we’ve been trying to answer for at least half a century.

A few promising pilot programs in the 1960s and 1970s got the ball rolling by demonstrating eye-popping results: vastly improved educational outcomes for kids who attend preschool. The gap between poor and rich students looked like it could nearly vanish if we could figure out how to scale up and replicate those results.

Unfortunately, that’s been difficult. As subsequent studies have found, many programs don’t scale, and promising small-scale preschool programs seem particularly vulnerable to that shortcoming. The preschool programs offered nationwide through programs like Head Start probably have effects, even sizable ones, but they don’t get the results that we saw in the most promising pilot programs. Over the past couple decades, we’ve struggled to figure out what works at scale in early childhood education — and what doesn’t.

A new working paper from economists at the University of Michigan takes a new approach: It looks at census data from 2000 to 2013 to dig into the long-term outcomes of Head Start for its students.

Studies of the long-term effects of Head Start run into a lot of limitations because there’s limited data available. Using census results allows this study to analyze life outcomes for one-quarter of US adults, which can help identify effects that are hard to be confident of with a small sample size. The adults whose outcomes in 2000-2013 they examined would have been preschool age during the rollout of Head Start from 1965-1980.

Since Head Start was rolled out on a county-by-county basis and had age-eligibility guidelines, it’s possible to compare children who were just a year too old for the program to children who were eligible. Using this approach, the study finds that Head Start looks like a stunningly cost-effective program — since kids who attended preschool do better later in life, government revenue is actually increased by sending kids to preschool.

“Participating children,” the paper finds, “achieved 0.29 more years of education, were 2.1 percent more likely to complete high school, 8.7 percent more likely to enroll in college, and 19 percent more likely to complete college. In addition, Head Start increased economic self-sufficiency in adulthood by almost 4 percent of a standard deviation — gains driven largely by a 12-percent reduction in adult poverty and a 29-percent reduction in public assistance receipt.”

By reducing adult poverty and use of social services as an adult for the children who were enrolled in it, the paper suggests that Head Start pays for itself.

This goes against a recent narrative that has been building against Head Start. Most people have heard a different story: that the program doesn’t work at all. They may have heard about a recent massive study commissioned by the Department of Health and Human Services, which found “the benefits of access to Head Start at age four are largely absent by 1st grade for the program population as a whole.”

Or they may have heard about a natural experiment created in 2008 when Tennessee had to assign spots in its Head Start program by lottery. Researchers found the program had no or negative effects: “the control children caught up with the pre-k participants on [kindergarten and subsequent] tests and generally surpassed them.”

How should we interpret this new finding in light of that evidence? How can the benefits of Head Start fade away after a few years — and then crop up 10 years after that? When we take a deeper look at the Head Start literature, it looks like the new study is pointing at something real.

Does early childhood education work or not?

Hundreds of studies have now explored the effects of early-childhood interventions on everything from reading and writing ability to odds of going to prison later in life. The picture those studies paint is initially confusing.

On the one hand, the gains that children achieve as a result of participating in early childhood education programs tend to be short-lived. They do learn to read sooner than their counterparts, but after a few years of school, their test scores are comparable. This is often called the “fade-out,” and opponents of preschool programs point to it as proof the programs will do no long-term good — at least until we change the rest of the school system to sustain these gains.

On the other hand, there are high-quality studies that find dramatic life-long effects from early childhood education programs, including reductions in crime, extra years of education, and improved income as adults. The effects are often small in individual studies, but a fairly compelling pattern emerges in a meta-analysis of many of them.

How can that happen? How can an intervention have no significant medium-term effects but be life-changing decades later?

There are two plausible mechanisms. One is that preschool provides kids with intangible skills — emotional stability, problem-solving, confidence interacting with authorities — that persist even once the academic gains have faded.

The other is that preschool benefits families — increasing labor force participation by parents and household income by alleviating some of the burden of child care. That’s the “preschool works because it’s daycare” model, which I described in a previous piece.

Which model does the new research fit?

The true explanation of the effects of preschool will likely include effects from both of those sources, and maybe many others. But it’s still useful to know which explanation seems to be doing the most work.

One good place to look is in arrest rates, drug addiction, and other measures of impulsive behavior. Some studies have shown that Head Start reduces criminal convictions, obesity, and depression — which might be explained by Head Start increasing intangible skills. Others, though, don’t find any such effects.

The working paper from the University of Michigan, written by Martha J. Bailey, Shuqiao Sun, and Brenden Timpe, is in the latter category — it finds pronounced effects on educational attainment, adult poverty, and reliance on benefits as an adult, but it found “no evidence of reductions in incarceration.” (Their dataset didn’t enable looking at obesity or depression.)

Right now, the research on whether Head Start affects incarceration looks pretty mixed. Here’s why that matters: If Head Start’s long-term effects are a result of improving students’ emotional regulation, problem-solving, and impulse control — as has been hypothesized — we might expect to see that reflected in reduced rates of crime, drug addiction, teen pregnancy, and other life outcomes associated with impulsivity.

If, instead, there’s no change in those indicators, that might be some reason to suspect that Head Start’s long-term effects largely come from increasing household income and allowing Head Start attendees’ parents to work better jobs. If this is what’s going on, we’d instead expect to see higher household income growing up, and improvements for indicators tied to economic outcomes. (It’s still a bit surprising that we wouldn’t see effects on incarceration — but they might be small, and hard to detect in a sample like this one.)

This is an important difference. If most of the benefits of Head Start come through the stability it offers families, then we should favor the full-day rather than half-day Head Start programs because they’ll do more for family income. We probably shouldn’t worry about requiring teachers to have advanced degrees, which some proponents of Head Start reform have pushed for. And we should expect strong results from proposals like a basic income for children.

But if most of the benefits of Head Start come from the intangible skills it teaches, we should work on learning how to measure them, so we don’t have to squint at longitudinal studies to identify the effects and estimate the cost-effectiveness of the programs.

The most important takeaway from the new research, though, is that it’s past time for critics and advocates of Head Start to stop talking past each other. We should direct less energy toward research confirming that reading and math scores don’t see lasting improvement, which looks pretty well established at this point and which isn’t key to the case for preschool programs. Researchers should instead focus on digging into the long-term effects of Head Start and understanding what mechanisms might explain them — and whether there’s a more cost-effective way to get the same results.

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