Efficient Estimation of Treatment Effects Using Neural Networks with a Diverging Number of Confounders

The estimation of causal effects is a primary goal of behavioral, social, economic and biomedical sciences. Under the unconfounded treatment assignment condition, adjustment for confounders requires estimating the nuisance functions relating outcome and/or treatment to confounders. The conventional approaches rely on either a parametric or a nonparametric modeling strategy to approximate the nuisance functions. Parametric methods can introduce serious bias into casual effect estimation due to possible mis-specification, while nonparametric estimation suffers from the ''curse of dimensionality". This paper proposes a new unified approach for efficient estimation of treatment effects using feedforward artificial neural networks (ANN) when the number of covariates is allowed to increase with the sample size. We consider a general optimization framework that includes the average, quantile and asymmetric least squares treatment effects as special cases. Under this unified setup, we develop a generalized optimization estimator for the treatment effect with the nuisance function estimated by ANNs. We further establish the consistency and asymptotic normality of the proposed estimator and show that it attains the semiparametric efficiency bound. The proposed methods are illustrated via simulation studies and a real data application