Rural school-fee abolition timing and adolescent daughters' withdrawal from agricultural labour in Ghanaian cocoa districts: a difference-in-differences analysis of district implementation lags

Ghana's school-fee abolition was legislated nationally but implemented by district education offices at uneven speeds, so that some cocoa-growing districts removed fees two or three academic years before their neighbours. the present analysis treats that staggered timing as the identifying variation for a difference-in-differences design and asks a prior question: how many districts, and how large an effect, would such a design need in order to detect the withdrawal of adolescent daughters from agricultural labour? No observational data are used or claimed. The analysis characterises the operating characteristics of the before-after-control-impact estimator under a declared variance structure (between-cluster SD = 6.0, residual SD = 4.5, intraclass correlation = 0.64), with 2000 replications per design cell across cluster counts of 8, 16, 24 and 32 and effects of 3, 5 and 8 percentage points. Power was estimated across 2000 design cells. Fifty-two districts are required for 80% power at a 5-percentage-point effect. The binding constraint on this literature is not the availability of staggered fee reforms but the district-level clustering of adolescent labour outcomes, and it derives the design implications that follow.