School leaders regularly make decisions on how to deploy their finite resources—staff, money, time—in ways they believe will best serve their students. While distribution is likely intended to be both efficient (providing the maximum benefit possible) and egalitarian (not benefiting one group of students over another), reality dictates that tradeoffs between these two goals must regularly be made, per the “leaky bucket” theory propounded by Arthur Okun in 1975.[1] Can such tradeoffs be measured? A new study from the American Educational Research Journal gives it a try.
Researchers Paul Yoo of Stanford and Paul Hanselman of the University of California, Irvine, use data on elementary school students from one unnamed western state—specifically, 375,000 unique students who entered fourth and fifth grades between 2005–06 and 2013–14 at 700 unique public schools. This represents almost 95 percent of the state’s fourth and fifth graders during those school years. According to the researchers, per-pupil spending was within 10 percent of the national average, and funding policy was less progressive than the median state in providing compensatory support for high-poverty districts. Average third-grade achievement in math and reading ranked below the national median on a nationally normed metric, and the achievement gaps between lower- and higher-income students were wider than the median state. Student data include demographic characteristics (gender, race/ethnicity, special education status, gifted status, and economic disadvantage status), attendance, and academic outcomes for each year in reading and math. They standardize test scores within each year, grade, and subject to have a mean of 0 and a standard deviation of 1.
Yoo and Hanselman create value-added models of student achievement to generate annual estimates of schools’ (a) overall effectiveness in promoting learning and (b) differential effectiveness in promoting more learning for low-income students relative to higher-income peers.
What they find is that the schools in their study are, overall, minimally effective at promoting learning compared to the average expected value-add of schools in the state, with sample schools adding approximately 1 month of learning in math and reading for students in grades four and five, as compared to 2 to 3 months for the average school serving those grades. They also find that the most effective schools achieve that result by adding more learning to their higher-income students than to their lower-income students. The difference is small but significant, with higher-income students coming closer to the average (2–3 months of learning), while lower-income students fall just short of a month of learning. This doesn’t mean that the schools are ineffective for low-income students, just that there is a difference between high- and low-income kids, which they say is proof of a tradeoff made between equity and efficiency in provision of education.
Or, more accurately, a set of tradeoffs. The researchers tested a number of variables that impacted the outcomes of students, including prior academic achievement levels, racial/ethnic diversity in schools, and concentrations of low- and high-income students, among others. Most of them had small and modestly-significant impacts on student learning. Some were positive and some were negative, but no obvious patterns were discernable among schools. They conclude that “many important aspects of tradeoffs are rooted in organizational practices” from building to building, but do not have enough evidence at the school level to speculate about mechanisms. Even in districts where financial allocations are made centrally, school- and even classroom-level use of funds will have a differential impact on students.
Yoo and Hanselman are convinced from their findings that their resource buckets are leaking (per Arthur Okun) in these schools, but cannot generalize beyond them—or, likely, even beyond the specific grade levels they study. However, they seem equally convinced that the mechanisms are knowable and would be useful to know, especially for school leaders charged with allocating resources. They suggest several avenues of deeper research that could get closer to isolating specific allocation decisions, and their effects on students, including case studies comparing similar schools with differing outcomes.
SOURCE: Paul Y. Yoo and Paul Hanselman, “Efficiency-Equity Tradeoffs in Schools: Evidence from Elementary School Learning,” American Educational Research Journal (May 2026).
[1] The researchers offer this example of such a tradeoff: “Consider a school administrator deciding how to allocate limited staff. Assigning all staff as classroom teachers would minimize average class sizes, potentially providing the richest learning environments overall, but this allocation would preclude targeted, compensatory use of resources, such as for tutoring, that could support more equitable outcomes.”
