Median-based Splitting Rules for Causal Trees and Forests

Heavy-tailed and skewed outcomes are common in the randomized experiments and observational studies used to estimate heterogeneous treatment effects, yet the mean-squared-error criterion that guides splitting in honest causal trees is sensitive to the extreme values they generate. Building on the causal forest framework (Athey and Imbens, 2016; Wager and Athey, 2018), we introduce the Median Squared Deviation (MSD) criterion, which replaces the leafwise difference in means in the honest splitting objective with the Hodges–Lehmann location estimator while leaving honest leaf estimation and forest inference unchanged. Two further median-based rules, the Median Absolute Deviation (MAD) and the Least Median of Squares (LMS), serve as robust baselines. We evaluate the criteria in a simulation study covering precision, bias, and confidence interval coverage. MSD restricts its robustness to split selection and lowers the error of conditional average treatment effect estimates under heavy-tailed and skewed outcomes. Further, we re-visit two empirical applications: the first analyzes the electoral effects of a Mexican conditional cash transfer program on precinct-level observations, while the second application studies antiretroviral treatments in HIV-positive adults.