Double machine learning for sample selection models

This paper considers treatment evaluation when outcomes are only observed for a subpopulation due to sample selection or outcome attrition/non-response. For identification, we combine a selection-on-observables assumption for treatment assignment with either selection-on-observables or instrumental variable assumptions concerning the outcome attrition/sample selection process. To control in a data-driven way for potentially high dimensional pre-treatment covariates that motivate the selection-on-observables assumptions, we adapt the double machine learning framework to sample selection problems. That is, we make use of (a) Neyman-orthogonal and doubly robust score functions, which imply the robustness of treatment effect estimation to moderate regularization biases in the machine learning-based estimation of the outcome, treatment, or sample selection models and (b) sample splitting (or cross-fitting) to prevent overfitting bias. We demonstrate that the proposed estimators are asymptotically normal and root-n consistent under specific regularity conditions concerning the machine learners. The estimator is available in the causalweight package for the statistical software R.

Evaluating (weighted) dynamic treatment effects by double machine learning

We consider evaluating the causal effects of dynamic treatments, i.e. of multiple treatment sequences in various periods, based on double machine learning to control for observed, time-varying covariates in a data-driven way under a selection-on-observables assumption. To this end, we make use of so-called Neyman-orthogonal score functions, which imply the robustness of treatment effect estimation to moderate (local) misspecifications of the dynamic outcome and treatment models. This robustness property permits approximating outcome and treatment models by double machine learning even under high dimensional covariates and is combined with data splitting to prevent overfitting. In addition to effect estimation for the total population, we consider weighted estimation that permits assessing dynamic treatment effects in specific subgroups, e.g. among those treated in the first treatment period. We demonstrate that the estimators are asymptotically normal and $\sqrt{n}$-consistent under specific regularity conditions and investigate their finite sample properties in a simulation study. Finally, we apply the methods to the Job Corps study in order to assess different sequences of training programs under a large set of covariates.