Robust Nonparametric Difference-in-Differences Estimation

We consider the problem of treatment effect estimation in difference-in-differences designs where parallel trends hold only after conditioning on covariates. Existing methods for this problem rely on strong additional assumptions, e.g., that any covariates may only have linear effects on the outcome of interest, or that there is no covariate shift between different cross sections taken in the same state. Here, we develop a suite of new methods for nonparametric difference-in-differences estimation that require essentially no assumptions beyond conditional parallel trends and a relevant form of overlap. Our proposals show promising empirical performance across a variety of simulation setups, and are more robust than the standard methods based on either linear regression or propensity weighting.