Estimation of the treatment effect variance in a difference-in-differences framework

We compare two regression-based estimators of treatment/policy effects in a standard difference-in-differences setting without additional covariates. These two estimators, deriving from what we term the piled and unpiled regression models, produce identical finite-sample estimates, thus sharing the same theoretical variance. However, they are not equivalent with regard to the estimation of such a variance. We show that under the assumed model the piled approach should be preferred since it results in a more efficient variance estimator, thereby returning more reliable standard errors for the treatment effect. We further show that this result holds even when the normality assumption for the regression error terms is violated.