Urban Sociology of Metropolitan Development Permit Moratorium Boundary Maps and Informal Construction Timing in Nairobi's Peri-Urban Wards: A Spatial Regression Discontinuity Analysis of Freeze Lines

Metropolitan development permit moratoria in Nairobi's peri-urban wards are drawn as boundary maps, and the freeze line is routinely treated as a sharp discontinuity in the regulatory environment that should produce a matching discontinuity in informal construction timing. Because no observational data on Nairobi permit records or construction starts are used, the study is a design-based evaluation: it characterises the operating characteristics of a before-after-control-impact estimator applied to a spatial running variable under a declared variance structure with an intraclass correlation of 0.64, a between-cluster standard deviation of 6.0 and a residual standard deviation of 4.5. 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 analysis indicates that 54 clusters are required to detect a 5 percentage point discontinuity at 80 per cent power, a requirement that exceeds the 32-cluster maximum examined and that most ward-level moratorium evaluations cannot meet. The freeze line is better understood as a bundled institutional treatment than as a unidimensional regulatory cut, and it specifies the design conditions under which spatial regression discontinuity at moratorium boundaries can support causal claims about informal construction timing.