A difference-in-differences estimator by high-dimensional covariate balancing propensity score

We develop a high-dimensional covariate balancing propensity score (HCBPS) approach for estimating the average treatment effect on the treated (ATT) within a difference-in-differences (DID) framework, accommodating settings where the number of potential covariates may far exceed the sample size and where either panel data or repeated cross-sectional data are available. This method refines the post-selection estimator obtained from the Lasso approach and is robust to covariate selection errors and model misspecification. We show that the proposed estimator is root-n consistent and asymptotically normal and provide a uniformly valid confidence interval when both the propensity score and outcome models are correctly specified, as well as when only one of them is correctly specified. More importantly, the proposed variance estimator is form-invariant whenever at least one of the two working models is correctly specified. Simulation studies demonstrate the desirable finite-sample performance of the proposed estimator, and an empirical application to tariff reductions in Mozambique indicates that tariff cuts are associated with lower customs bribe payments, with the negative estimated effect persisting after conditioning on a richer set of institutionally motivated pretreatment covariates.