Rural Interdisciplinary Sociology of Village Agricultural Extension Agent Caseload Caps and Technology Adoption Spillovers in Zambian Farming Blocks: A Boundary-Discontinuity Analysis of Assignment Thresholds

The central problem is that caseload caps are assignment rules, not treatments: they generate discontinuities in agent-to-farmer ratios that are confounded with the very sorting processes sociologists of rural extension seek to explain. The paper specifies a before-after-control-impact design with a regression-discontinuity assignment rule, characterises its operating characteristics under a declared variance structure (between-cluster SD = 6.0, residual SD = 4.5, intraclass correlation = 0.64), and reports power and minimum detectable effect estimates 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 requires 54 clusters to detect a 5-percentage-point effect at 80% power. The contribution is a sociological reframing of caseload caps as boundary institutions whose discontinuity is analytically productive rather than a nuisance, together with a design-based protocol for estimating spillovers at assignment thresholds. Adoption spillovers are best understood as network-mediated boundary effects whose identification depends on treating the cap as a rule that sorts farmers into differently structured extension networks.