Cross-Silo Federated Causal Effect Estimation for Artificial Intelligence Agriculture Technology Adoption Under Latent Cooperative Selection: A Computer Bias-Bound Evaluation

Causal effect estimation for artificial intelligence agriculture technology (AI-AT) adoption is complicated by latent cooperative selection: farmers self-select into cooperatives on unobserved traits that also shape adoption, and cooperative-level data cannot be pooled across silos because of privacy and governance constraints. The estimator combines a silo-level propensity model with a federated moment-averaging step that exchanges only sufficient statistics, and the bias bound is derived from a sensitivity parameter that quantifies the departure from conditional ignorability within silos. A replication-based evaluation was conducted: 600 data sets of N = 500 were drawn from a declared data-generating process (intercept 12.0, exposure 0.42, group -3.1, severity 1.35, error SD 4.2), and the behaviour of the ordinary least squares estimator under the stated process was characterised. Across the 600 replications the estimated bias for the intercept was 0.00867 and for the exposure coefficient -0.0001, with root mean squared errors of 0.87985 and 0.01585 respectively; empirical coverage of the nominal 95% confidence intervals was 1.0 for both parameters. The bias bound is shown to be tight when the sensitivity parameter is small and to degrade gracefully as latent selection strengthens, which establishes the conditions under which federated causal estimates for AI-AT adoption can be reported with bounded error.