  Causal random forests provide efficient estimates of heterogeneous treatment
effects. However, forest algorithms are also well-known for their black-box
nature, and therefore, do not characterize how input variables are involved in
treatment effect heterogeneity, which is a strong practical limitation. In this
article, we develop a new importance variable algorithm for causal forests, to
quantify the impact of each input on the heterogeneity of treatment effects.
The proposed approach is inspired from the drop and relearn principle, widely
used for regression problems. Importantly, we show how to handle the forest
retrain without a confounding variable. If the confounder is not involved in
the treatment effect heterogeneity, the local centering step enforces
consistency of the importance measure. Otherwise, when a confounder also
impacts heterogeneity, we introduce a corrective term in the retrained causal
forest to recover consistency. Additionally, experiments on simulated,
semi-synthetic, and real data show the good performance of our importance
measure, which outperforms competitors on several test cases. Experiments also
show that our approach can be efficiently extended to groups of variables,
providing key insights in practice.
