Rural Teacher Deployment Lotteries and Interdisciplinary Sociology of School Retention in Malawian Village Schools: A Regression Discontinuity Analysis of Posting Thresholds

The unresolved problem is that deployment thresholds are administratively determined and correlated with unobserved school-level retention determinants, so naive comparisons of schools above and below a posting cut-off conflate the effect of teacher allocation with the effect of the selection rule itself. The paper formalises the posting threshold as a forcing variable, specifies the continuity assumptions required for identification, and then evaluates the power of the before-after-control-impact estimator across a design grid of 8, 16, 24 and 32 clusters and effect sizes of 3, 5 and 8 percentage points, with 2000 replications per cell. Under a between-cluster standard deviation of 6.0, a residual standard deviation of 4.5 and an intraclass correlation of 0.64, the analysis shows that 54 clusters are required to detect a 5 percentage point effect at 80 per cent power. The contribution is a bounded methodological argument: regression discontinuity on posting thresholds is defensible only when the running variable is measured without manipulation and when the before-after-control-impact estimator is powered for the clustered structure of village schools. The paper concludes that interdisciplinary sociology of school retention should treat deployment lotteries as a quasi-experimental institution rather than as a background variable.