Teacher Margarita Hernandez, second left, leads a group of preschoolers with an outdoor art project at a Head Start Program in Hillsboro, Ore.

Many studies of the long-term effects of pre-kindergarten programs in the United States find that they improve outcomes for those pre-K kids later in life, yet the effects on educational outcomes seem to fade out over the course of the next 13 years.  A child might get a boost to their academic outcomes early in their kindergarten and elementary school career, but the benefits dissipate as they go through high school.

What might be behind this fade-out effect? A potential answer comes from a new paper that also offers some insight into a key tradeoff in economics between equity and efficiency.

The new paper, released today as part of the Equitable Growth Working Paper series, is from economists Rucker C. Johnson of the University of California-Berkeley and C. Kirabo Jackson of Northwestern University. The two researchers seek an answer to a seemingly important question: Are educational investments made at different points in a child’s life complementary? To put this another way: Does education spending during kindergarten through grade 12 build on the returns from education spending earlier in life?

Johnson and Jackson look at the interaction between increases in Head Start funding and increases in K-through-12 education spending and examine how that spending affects outcomes later in life for low-income children. Because they are looking at what they believe are exogenous changes to spending for both programs, the economist interpret their results as showing a causal impact.

Johnson and Jackson find that there are complementarities between these two kinds of educational spending. When an area has higher levels of spending on Head Start, higher levels of K-through-12 spending will have more of an impact on outcomes than a similar increase when spending on Head Start is lower. And it works the other direction as well—increases in Head Start spending will improve outcomes more in areas where K-through-12 spending is already high. This complementarity result may partially explain some of the fade-out for pre-kindergarten programs. It’s hard to maintain the gains from Head Start if the primary and secondary schools the child attends next aren’t well funded.

But beyond the specific policy result, the paper also offers an illustration where the trade-off between equity and efficiency doesn’t seem to exist, at least when it comes to some aspects of education spending. Because spending on Head Start programs has more power when subsequent spending on primary and secondary schools is high, the redistribution of funds when K-12 spending is already high will not only improve equity but efficiency as well. According to Johnson and Jackson, “for a district that spent $5,000 per-pupil (about 20 percent above the average [national] spending level)” on primary and secondary schools, “the marginal dollar spent on Head Start led to between 2 and 4 times the improvement in adult outcomes as that spent on K-through-12 education.” In short, money could be taken from these programs, given to spending on Head Start and the result would be higher average adult outcomes and a more equitable distribution as well.

We aren’t sure how strong the tradeoff between equity and efficiency is throughout the U.S. economy. In fact, that’s a question that Equitable Growth is quite interested in. But if the research by Johnson and Jackson holds up, then we may have found a very powerful example where the tradeoff doesn’t exist at all. A better understanding of this relationship is something policymakers and researchers should be very interested in.