A complete framework for model-free difference-in-differences estimation

We propose a complete framework for model-free difference-in-differences analysis with covariates, where model-free means data-driven, in particular nonparametric estimation and testing, variable and scale choice. We start with searching for the preferred data setup by simultaneously choosing confounders and a scale of the outcome variable along identification conditions. The treatment effects themselves are estimated in two steps: first, the heterogeneous effects stratified along the covariates, then the average treatment effect(s) for the population(s) of interest. We provide the asymptotic statistics as well as the finite sample behavior of our methods, and suggest bootstrap procedures to calculate standard errors and p-values of significance tests. The pertinence of our methods is shown with a study of the impact of the Deferred Action for Childhood Arrivals program on human capital responses of non-citizen immigrants. We show that past results underestimated the positive impact on school attendance for individuals aged 14-18, and the positive impact on high school completion. Moreover, we find that the parametric methods fail to identify the negative impact on school attendance of college aged individuals. Practical issues including bandwidth selection, sample weights, and implementation are given in the supplement.