Dynamic covariate balancing: estimating treatment effects over time with potential local projections

Abstract This article concerns the estimation and inference of treatment effects in panel data settings when treatments change dynamically over time. We propose a balancing method that allows for (i) treatments to be assigned dynamically over time based on high-dimensional covariates, past outcomes and treatments; (ii) outcomes and time-varying covariates to depend on the trajectory of all past treatments; and (iii) heterogeneity of treatment effects. Our approach recursively projects potential outcomes’ expectations on past histories. It then controls the bias arising from the nonexperimental and sequential nature of this setting by balancing dynamically observable characteristics over time. We establish inferential guarantees for the proposed method even in cases where the number of observable characteristics greatly exceeds the sample size. We study numerical properties of the estimator and illustrate the advantages of the procedure in an empirical application.