Shrinkage Bayesian Causal Forest with Instrumental Variable

We propose Shrinkage Bayesian Causal Forest with Instrumental Variable (SBCF-IV), a method for discovering and estimating subgroups with heterogeneous Complier Average Causal Effects (CACE) in sparse high-dimensional settings with imperfect compliance. SBCF-IV places a sparsity-inducing Dirichlet prior on splitting probabilities within Bayesian Additive Regression Trees used to estimate the conditional intention-to-treat and the complier share, concentrating posterior mass on the few covariates that genuinely moderate the complier effect. The resulting split frequencies then enter a downstream CART as variable-level costs, directing it toward the relevant moderator variables and yielding an interpretable partition of the covariate space. The Bayesian feature-selection mechanism thus regularizes effect estimation and simultaneously steers subgroup discovery. Monte Carlo experiments show that, as the share of irrelevant covariates grows, SBCF-IV recovers the true partition more reliably than BCF-IV at both the tree and unit level, and retains nominal coverage in regimes where BCF-IV’s intervals deteriorate. We apply the method to the Oregon Health Insurance Experiment and the 401(k) eligibility data.

Submitted (under review)