A Robust Estimation Approach for Conditional Marginal Effects with Binary Treatments

This paper proposes a nonparametric approach to estimate conditional marginal effects based on a class of orthogonal estimators (OEs) that can handle high-dimensional data and require no assumption for model specification. In addition to introducing the existing OE built on Augmented Inverse Propensity Weighting (OE-AIPW), we create another OE built on Conditional Average Treatment Effect (OE-CATE) that shares alike statistical properties and can improve estimation performance under certain data generating processes. Our approach involves a two-stage procedure in which the first-stage yields an orthogonal signal with machine learning algorithms being used to handle high-dimensional confounders, and the second-stage proceeds with a nonparametric regression of the orthogonal signal on the moderators. We establish theoretical properties including consistency, asymptotic normality, and efficiency, for OE-CATE. Monte Carlo simulations demonstrate the theoretical insights and guide the practical application of our approach. We replicate two empirical studies to illustrate the application of OEs in two important scenarios: discontinuous propensity scores and randomized experiments.