  Causal inference from observational data requires untestable identification
assumptions. If these assumptions apply, machine learning (ML) methods can be
used to study complex forms of causal effect heterogeneity. Recently, several
ML methods were developed to estimate the conditional average treatment effect
(CATE). If the features at hand cannot explain all heterogeneity, the
individual treatment effects (ITEs) can seriously deviate from the CATE. In
this work, we demonstrate how the distributions of the ITE and the CATE can
differ when a causal random forest (CRF) is applied. We extend the CRF to
estimate the difference in conditional variance between treated and controls.
If the ITE distribution equals the CATE distribution, 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 CATE distribution.
The conditional variance of the ITE 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 ITE and CATE distributions differ, the
extended CRF can appropriately estimate the variance of the ITE distribution
while the CRF fails to do so.
