Causal Inference for Computer Agriculture Irrigation Advisory Effects Under Farmer Self-Selection: An Artificial Intelligence Instrumental-Variable Bound Evaluation

Computer agriculture irrigation advisories are typically evaluated by comparing farmers who adopt them with farmers who do not, yet adoption is self-selected and the resulting contrast conflates advisory effects with the characteristics that lead farmers to seek advice. The design is formalised as a linear model with cluster-level random effects, and the interaction between treatment and post-period is identified under an exclusion restriction on the instrument. A replication-based evaluation was conducted across 2000 design cells for cluster counts of 8, 16, 24 and 32 and effect sizes of 3, 5 and 8 percentage points, with a between-cluster standard deviation of 6.0, a residual standard deviation of 4.5 and an intraclass correlation of 0.64. The results indicate that 54 clusters are required to detect a 5 percentage point effect at 80% power under the declared variance structure. The framework provides a defensible basis for bounding advisory effects when random assignment is infeasible and farmer self-selection is unavoidable.