Flexible machine learning estimation of conditional average treatment effects: a blessing and a curse
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Causal inference from observational data requires untestable assumptions. If these assumptions apply, machine learning (ML) methods can be used to study complex forms of causal-effect heterogeneity. Several ML methods were developed recently 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 estimated 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 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 characteristics of the ITE distribution while the CRF fails to do so.
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