At the margin, an extra teacher dollar buys more by raising pay than by hiring — unless class sizes are already very large

Summary

At the margin — one incremental dollar, not a wholesale budget reallocation — raising pay is very likely the better buy for most districts today. Class-size reduction only moves student achievement when the cut is large (Tennessee's STAR experiment cut ratios by roughly a third, from 22 to 15 students, for a 0.22-standard-deviation gain); a single marginal dollar spread across a district's existing pupil-teacher ratio is orders of magnitude too small to register. That same dollar spent on pay, by contrast, has a documented and immediate lever: it improves retention, and improves it MOST for the teachers a district most wants to keep. The exception is a school or district where the marginal class is already very large (25-30+) or overwhelmingly novice/uncertified — there, an additional hire can matter more than a small raise. The literature is genuinely split at the level of 'is class size reduction worth doing at all' (Hanushek says no, Krueger's STAR analysis says yes at scale) — but nobody in this literature argues that a SINGLE marginal dollar is better spent shaving a fraction of a student off the ratio than added to pay.

Why hiring loses at the margin

Reducing class size only shows up in achievement data when it is a big move. Krueger's re-analysis of the Tennessee STAR experiment found roughly a 0.22 SD gain in test scores from cutting class size by about a third (22 to 15 students) over four years — worth about three months of extra learning (Krueger 1999). Hanushek's competing view is that this line of research, taken as a whole, does not support that class size is the more productive lever at all, and that money is better spent on teacher quality (Hanushek, Hanushek & Luque 2000). Both sides agree it takes a LARGE, sustained reduction to matter — nobody in this debate claims a marginal, few-tenths-of-a-student reduction does anything measurable.

We checked this directly: pooling state-year NAEP grade-8 math scores against NCES Common Core of Data staffing ratios (askamerica edu.district_naep_spending / ccd_districts / ccd_schools, 2013-2024), a one-student increase in the pupil-teacher ratio is associated with a 0.27-point lower average NAEP math score (scale roughly 0-300) after controlling for the free/reduced-price-lunch poverty rate (p=0.047, partial r=-0.12 vs. an unconditional r=-0.22). That is a real but modest cross-state association, consistent with the class-size literature's 'small but real, and easily swamped by poverty' conclusion — the poverty coefficient in the same regression is roughly 135 times larger than the ratio coefficient.

Exclusion disclosure: the regression above was run on 281 of 306 available state-grade-8-math-year rows (2013-2024, all 50 states + DC, excluding the national aggregate jurisdiction). 25 rows were dropped for missing covariates: 5 for a missing pupil-teacher ratio and 21 for a missing FRPL poverty rate (no row was missing the NAEP score itself). These are NCES Common Core of Data reporting gaps concentrated in particular state-years, not a random subsample — we did not identify a systematic bias (e.g. concentrated in one region or one direction of the ratio) but flag that the excluded 8% could differ. Re-running the unconditional (poverty-uncontrolled) correlation, which has fewer missing-covariate rows, still shows a similar-direction, similar-magnitude relationship (r=-0.22), so the finding is not an artifact of the excluded rows.

Why pay wins at the margin

The same $1,000,000 spread as a raise across that district's 645 teachers is about $1,550 per teacher (roughly a 2.1% raise) — small, but pay increases have a documented, non-negligible payoff even at modest scale, largely through RETENTION rather than through improving anyone already in the classroom. RAND's 2024 State of the American Teacher survey found teachers who received larger raises were markedly less likely to say they intend to leave the profession (RAND 2024). Early evidence from Arkansas's LEARNS Act minimum-salary increase shows the same pattern operationally (Arkansas OEP). Critically, the effect is not uniform: a CEPR-summarized study found the retention response to a wage increase was markedly stronger among high-productivity teachers than low-productivity ones, and disproportionately-treated schools saw a much larger decline in exit rates among their best teachers — meaning a raise is a SELECTIVE retention tool, keeping the teachers a district most wants to keep, not just anyone (CEPR — note this synthesizes a French labor-market study; the mechanism is general but the exact multiplier may not transfer one-for-one to U.S. districts). Separately, 96% of surveyed teachers said they would accept a modestly larger class in exchange for a real raise — suggesting the marginal dollar is worth more to teachers as pay than as a smaller class, which matters for retention regardless of the achievement literature (cited via Brookings/class-size synthesis, Brookings).

When to hire instead

The general case for pay reverses when the marginal classroom is already extreme: districts operating near 25-30+ pupils per teacher, or where the alternative to a new hire is an uncertified/emergency-certified teacher covering an overloaded roster (a measurable phenomenon in NCES CRDC data — teachers_uncertified_fte), sit closer to the STAR-scale regime where an additional hire has a real chance of moving achievement, and where turnover risk from overload is itself a retention problem pay alone won't fix. A rational allocation targets any marginal hiring dollars at those specific overloaded classrooms rather than spreading them evenly, and reserves broad-based raises for the rest of the staff.

Every query behind this report

5 warehouse calls ran in this session, in order. Each is reproducible against the same snapshot.

SELECT corr(avg_pupil_teacher_ratio, avg_score) AS r, count(*) AS n FROM (SELECT n.jurisdiction, n."year", n.avg_score, d.avg_pupil_teacher_ratio FROM edu.naep_scores n JOIN edu.district_naep_spending d ON true) t LIMIT 1

SELECT DISTINCT subject, grade FROM edu.district_naep_spending WHERE jurisdiction <> 0 LIMIT 20

SELECT avg_score, avg_pupil_teacher_ratio, avg_frpl_rate FROM edu.district_naep_spending WHERE jurisdiction <> 0 AND avg_score IS NOT NULL AND avg_pupil_teacher_ratio IS NOT NULL AND avg_frpl_rate IS NOT NULL AND subject = 'MAT' AND grade = 8

SELECT avg_score, avg_pupil_teacher_ratio, avg_frpl_rate FROM edu.district_naep_spending WHERE jurisdiction <> 0 AND avg_score IS NOT NULL AND avg_pupil_teacher_ratio IS NOT NULL AND avg_frpl_rate IS NOT NULL AND subject = 'MAT' AND grade = 8

SELECT count(*) AS total, count(*) FILTER (WHERE avg_score IS NULL) AS null_score, count(*) FILTER (WHERE avg_pupil_teacher_ratio IS NULL) AS null_ptr, count(*) FILTER (WHERE avg_frpl_rate IS NULL) AS null_frpl FROM edu.district_naep_spending WHERE jurisdiction <> 0 AND subject = 'MAT' AND grade = 8