Debiased Semiparametric Efficient Changes-in-Changes Estimation

Abstract: We introduce a novel extension of the influential changes-in-changes (CiC) framework [Athey and Imbens, 2006] to estimate the average treatment effect on the treated (ATT) and distributional causal estimands in panel data settings with unmeasured confounding. While CiC relaxes the parallel trends assumption inherent in difference-in-differences (DiD), existing approaches typically accommodate only a single scalar unobserved confounder and rely on monotonicity assumptions between the confounder and the outcome. Moreover, current formulations lack inference procedures and theoretical guarantees that accommodate continuous covariates. Motivated by the intricate nature of confounding in empirical applications and the need to incorporate continuous covariates in a principled manner, we make two key contributions in this technical report. First, we establish nonparametric identification under a novel set of assumptions that permit high-dimensional unmeasured confounders and non-monotonic relationships between confounders and outcomes. Second, we construct efficient estimators that are Neyman orthogonal to infinite-dimensional nuisance parameters, facilitating valid inference even in the presence of high-dimensional continuous or discrete covariates and flexible machine learning-based nuisance estimation.