Marginal Treatment Effects in Difference-in-Differences

Difference-in-Differences (DiD) is a popular method used to evaluate the effect of a treatment. In its most simple version a control group remains untreated at two periods, whereas the treatment group becomes fully treated at the second period. However, it is not uncommon in applications of the method that the treatment rate only increases more in the treatment group. This article presents identification results for the marginal treatment effect (MTE) in such fuzzy designs. We show that we can modify the standard identifying assumptions in DiD designs with covariates to identify the MTE in models with essential heterogeneity. We propose two different procedures for the estimation of the MTE that rely on different assumptions regarding the potential outcomes model and prove their asymptotical normality. Furthermore, we derive a doubly-robust estimator for the local average treatment effect (LATE) which augments the two-way fixed effects regression model with a control function and unit-specific weights that rise from the propensity score. We assert the desirable finite-sample properties through simulation studies of a linear MTE model. Finally, we use our results to investigate heterogeneity on the returns to primary school attendance in Indonesia