Causal-Attribution Evaluation for Artificial Intelligence Agriculture Subsidy Targeting Under Endogenous Cooperative Enrollment: A Computer Instrumental-Variable Bound for Equity Audits

Artificial intelligence systems that rank farmers for agricultural input subsidies are increasingly evaluated by comparing enrolled cooperative members with non-members, a design that conflates programme effect with the self-selection of farmers into cooperatives. The design is characterised analytically and by replication: between-cluster standard deviation 6.0, residual standard deviation 4.5, intraclass correlation 0.64, with 2000 replications per design cell across 8, 16, 24 and 32 clusters and effects of 3, 5 and 8 percentage points. The bound identifies the conditions under which an audit can separate algorithmic misranking from enrollment-driven selection, and it specifies the cluster count at which the equity contrast becomes estimable. Fifty-four clusters are required for 80 per cent power at a 5 percentage point effect. The contribution is a design-level audit instrument rather than a new estimator: it tells evaluators what a targeting audit can and cannot attribute, and it converts an unverifiable causal claim into a bounded, reportable quantity.