Binary treatments in empirical practice are often (i) ex-post aggregates of multiple treatments or (ii) can be disaggregated into multiple treatment versions after assignment. In such cases it is unclear whether estimated heterogeneous effects are driven by effect heterogeneity or by treatment heterogeneity. This paper provides estimands to decompose canonical effect heterogeneity into the effect heterogeneity driven by different responses to underlying multiple treatments and the different compositions of these underlying effective treatments. This allows to avoid spurious discovery of heterogeneous effects, to detect potentially masked heterogeneity, and to evaluate the underlying assignment mechanism of treatment versions.
A nonparametric method for estimation and statistical inference of the decomposition parameters is proposed. The framework allows for the use of modern machine learning techniques to adjust for high-dimensional confounding of the effective treatments. It can be used to conduct simple joint hypothesis tests for effect heterogeneity that consider all effective treatments simultaneously and circumvent multiple testing procedures. It requires weaker overlap assumptions compared to conventional multi-valued treatment effect analysis.
The method is applied to a reevaluation of heterogeneous effects of smoking on birth weight. We find that parts of the differences between ethnic and age groups can be explained by different smoking intensities. We further reassess the gender gap in the effectiveness of the Job Corps training program and find that it is largely explained by gender differences in the type of vocational training received.