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We study the benign overfitting theory in the prediction of the conditionalaverage treatment effect (CATE), with linear regression models. As thedevelopment of machine learning for causal inference, a wide range oflarge-scale models for causality are gaining attention. One problem is thatsuspicions have been raised that the large-scale models are prone tooverfitting to observations with sample selection, hence the large models maynot be suitable for causal prediction. In this study, to resolve thesuspicious, we investigate on the validity of causal inference methods foroverparameterized models, by applying the recent theory of benign overfitting(Bartlett et al., 2020). Specifically, we consider samples whose distributionswitches depending on an assignment rule, and study the prediction of CATE withlinear models whose dimension diverges to infinity. We focus on two methods:the T-learner, which based on a difference between separately constructedestimators with each treatment group, and the inverse probability weight(IPW)-learner, which solves another regression problem approximated by apropensity score. In both methods, the estimator consists of interpolators thatfit the samples perfectly. As a result, we show that the T-learner fails toachieve the consistency except the random assignment, while the IPW-learnerconverges the risk to zero if the propensity score is known. This differencestems from that the T-learner is unable to preserve eigenspaces of thecovariances, which is necessary for benign overfitting in the overparameterizedsetting. Our result provides new insights into the usage of causal inferencemethods in the overparameterizated setting, in particular, doubly robustestimators.

Benign-Overfitting in Conditional Average Treatment Effect Prediction with Linear Regression