Adaptive Orthogonalization for Stable Estimation of the Effects of Time-Varying Treatments

Abstract: Inferring the causal effects of time-varying treatments is often hindered by highly variable inverse propensity weights, particularly in settings with limited covariate overlap. Building on the key framework of Imai and Ratkovic (2015), we establish sufficient balancing conditions for identification in longitudinal studies of treatment effects and propose a novel estimator that directly targets features of counterfactual or potential covariates. Instead of balancing observed covariates, our method balances the components of covariates that are orthogonal to their history, thereby isolating the new information at each time point. This strategy directly targets the joint distribution of potential covariates and prioritizes features that are most relevant to the outcome. We prove that the resulting estimator for the mean potential outcome is consistent and asymptotically normal, even in settings where standard inverse propensity weighting fails. Extensive simulations show that our estimator attains efficiency comparable to that of g-computation while providing superior robustness to model misspecification. We apply our method to a longitudinal study of private versus public schooling in Chile, demonstrating its stability and interpretability in estimating their effects on university admission scores.