Urban development-induced relocation of informal metalwork clusters and neighborhood noise-complaint mediation in Nairobi: a difference-in-differences estimation of workshop-density thresholds

Municipal relocation of informal metalwork clusters is frequently justified by nuisance abatement, yet the empirical basis for claiming that relocation reduces neighbourhood noise complaints rests on weak designs. No observational data are used. The analysis specifies a BACI estimator for a density-threshold model in which complaint mediation is a function of surviving workshop density after relocation, and evaluates its power 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. The variance structure assumes a between-cluster standard deviation of 6.0, a residual standard deviation of 4.5 and an intraclass correlation of 0.64. Power was estimated for each cell, and the minimum detectable effect at 80% power was derived. The design requires 54 clusters to detect a 5 percentage point effect at 80% power. The results indicate that the intraclass correlation of 0.64 dominates the design's sensitivity, that cluster counts below 24 cannot reliably distinguish a 3 percentage point threshold from zero, and that the density-threshold parameter is only weakly identified when relocation is partial. The credibility of relocation-as-nuisance-abatement claims depends less on the number of complaints recorded than on the density contrast the design can actually resolve, and it sets out the design conditions under which a BACI evaluation of workshop-density thresholds would be informative.