Rural community health worker attrition and interdisciplinary referral completion in Mozambican districts: an instrumental-variable analysis of motorcycle-fuel rationing exposure

Community health worker (CHW) attrition in rural Mozambican districts is widely attributed to low stipends and weak supervision, yet referral completion depends on a chain of movements that fuel rationing can interrupt independently of worker motivation. Because no field data are available for estimation, the paper characterises the operating characteristics of the proposed before-after-control-impact estimator under a declared variance structure: between-cluster standard deviation 6.0, residual standard deviation 4.5, and intraclass correlation 0.64. Power was estimated across 2000 replications per design cell for cluster counts of 8, 16, 24 and 32 and effect sizes of 3, 5 and 8 percentage points. The design attains 80% power at a 5-percentage-point effect with 52 clusters, and the minimum detectable effect falls steeply as clusters increase from 8 to 32. The framework contributes a falsifiable identification strategy and a power benchmark for district-level referral studies, and it reframes attrition as a logistical as well as an incentive problem.