Within-School Elasticities of Inefficiency
Response of class-size reducibility to enrolment shocks
	Grade Mix (pp → pp)	Phase Mix (pp → pp)	Enrollment (% → pp)
Coefficient	-0.381	-0.256	-0.007
Std. Error	0.054	0.049	0.002
p-value	0.000	0.000	0.000
95% CI	[-0.486, -0.275]	[-0.351, -0.161]	[-0.010, -0.003]
Impact of 10 unit change	-3.81 pp	-2.56 pp	-0.07 pp
Mean change (sample)	7.38 pp	2.66 pp	14.89%
N (school-years)	32,352	38,700	32,352
Schools	9,512	9,512	9,512
Mean inefficiency (%)	24.60%	24.60%	24.60%
Notes: Dependent variable: ΔInefficiencyst = Inefficiencyst − Inefficiencys,t−1 (pp). Inefficiency ≡ percentage reduction in class size achievable by reallocating employed teachers across grades within school. Independent variables: • Grade Mix: 0.5 × Σg |sg,t − sg,t−1| where sg,t = Learnersg,t / ΣgLearnersg,t (pp). • Phase Mix: 0.5 × Σp |sp,t − sp,t−1| where phases are Foundation (R–3) vs Intermediate/Senior (4–7) and sp,t = Learnersp,t / ΣpLearnersp,t (pp). • Enrolment: 100 × (Enrolmentst − Enrolments,t−1) / Enrolments,t−1 (%). Specifications: ΔInefficiencyst = β1Mixst + β2ΔEnrolmentst + αs + γt + εst. School FE αs. Year FE γt. SE clustered at school level. Sample: 32,352 school-years from 9,512 schools (2018–2023). Balanced on consecutive year pairs with non-missing variables.