Group Average Treatment Effects for Observational Studies

Abstract

The paper proposes an estimator to make inference of heterogeneous treatment effects sorted by impact groups (GATES) for non-randomised experiments. The groups can be understood as a broader aggregation of the conditional average treatment effect (CATE) where the number of groups is set in advance. In economics, this approach is similar to pre-analysis plans. Observational studies are standard in policy evaluation from labour markets, educational surveys and other empirical studies. To control for a potential selection-bias, we implement a doubly-robust estimator in the first stage. We use machine learning methods to learn the conditional mean functions as well as the propensity score. The group average treatment effect is then estimated via a linear projection model. The linear model is easy to interpret, provides p-values and confidence intervals, and limits the danger of finding spurious heterogeneity due to small subgroups in the CATE. To control for confounding in the linear model, we use Neyman-orthogonal moments to partial out the effect that covariates have on both, the treatment assignment and the outcome. The result is a best linear predictor for effect heterogeneity based on impact groups. We find that our proposed method has lower absolute errors as well as smaller bias than the benchmark doubly-robust estimator. We further introduce a bagging type averaging for the CATE function for each observation to avoid biases through sample splitting. The advantage of the proposed method is a robust linear estimation of heterogeneous group treatment effects in observational studies.