Flexible Machine Learning Estimation of Conditional Average Treatment Effects: a Blessing and a Curse

Causal inference from observational data requires untestable identification assumptions. If these assumptions apply, machine learning methods can be used to study complex forms of causal effect heterogeneity. Recently, several machine learning methods were developed to estimate the conditional average treatment effect (ATE). If the features at hand cannot explain all heterogeneity, the individual treatment effects can seriously deviate from the conditional ATE. In this work, we demonstrate how the distributions of the individual treatment effect and the conditional ATE can differ when a causal random forest is applied. We extend the causal random forest to estimate the difference in conditional variance between treated and controls. If the distribution of the individual treatment effect equals that of the conditional ATE, this estimated difference in variance should be small. If they differ, an additional causal assumption is necessary to quantify the heterogeneity not captured by the distribution of the conditional ATE. The conditional variance of the individual treatment effect can be identified when the individual effect is independent of the outcome under no treatment given the measured features. Then, in the cases where the individual treatment effect and conditional ATE distributions differ, the extended causal random forest can appropriately estimate the variance of the individual treatment effect distribution, whereas the causal random forest fails to do so.