Shrinkage Bayesian Causal Forest with Instrumental Variable

This paper proposes a novel framework for estimating heterogeneous treatment effects using Instrumental Variables (IV) in observational studies with sparse data and imperfect compliance. To address these limitations, we build upon the Bayesian Instrumental Variable Causal Forest (BCF-IV) framework that has been developed to estimate the conditional Complier Average Causal Effect (CACE) non-parametrically while retaining interpretability. BCF-IV uses Bayesian Additive Regression Trees (BART) to identify treatment effect heterogeneity and to estimate the conditional CACE based on the conditional Intention-To-Treat (ITT) effects and the proportion of compliers. Our approach extends BCF-IV by proposing a Shrinkage Bayesian Instrumental Variable Causal Forest (SBCF-IV) algorithm. SBCF-IV adopts the SoftBART algorithm and makes two major contributions. First, SBCF-IV implicitly discriminates between relevant and irrelevant covariates when estimating conditional ITT effects and proportions of compliers. Secondly, our approach implements varying posterior splitting probabilities from SoftBART into the discovery of heterogeneous subgroups. These modifications enhance SBCF-IV’s ability to handle sparse data and to detect variables that drive the heterogeneity of treatment effects. A simulation study suggests that a more precise estimation of conditional CACE can be achieved while maintaining interpretability, particularly in scenarios with sparsity, confounding, and nonlinearity. In an empirical application, we revisit the Oregon Health Insurance Experiment to demonstrate the use of SBCF-IV in comparison to BCF-IV and discuss the differences in the estimates for the conditional CACE.