  This paper develops a sparsity-inducing version of Bayesian Causal Forests, a
recently proposed nonparametric causal regression model that employs Bayesian
Additive Regression Trees and is specifically designed to estimate
heterogeneous treatment effects using observational data. The sparsity-inducing
component we introduce is motivated by empirical studies where not all the
available covariates are relevant, leading to different degrees of sparsity
underlying the surfaces of interest in the estimation of individual treatment
effects. The extended version presented in this work, which we name Shrinkage
Bayesian Causal Forest, is equipped with an additional pair of priors allowing
the model to adjust the weight of each covariate through the corresponding
number of splits in the tree ensemble. These priors improve the model's
adaptability to sparse data generating processes and allow to perform fully
Bayesian feature shrinkage in a framework for treatment effects estimation, and
thus to uncover the moderating factors driving heterogeneity. In addition, the
method allows prior knowledge about the relevant confounding covariates and the
relative magnitude of their impact on the outcome to be incorporated in the
model. We illustrate the performance of our method in simulated studies, in
comparison to Bayesian Causal Forest and other state-of-the-art models, to
demonstrate how it scales up with an increasing number of covariates and how it
handles strongly confounded scenarios. Finally, we also provide an example of
application using real-world data.
