Difference-in-Differences Estimators of Intertemporal Treatment Effects

Abstract

We study treatment-effect estimation using panel data. The treatment may be nonbinary, non-absorbing, and the outcome may be affected by the treatment lags. We make parallel-trends assumptions, but do not restrict treatment effect heterogeneity, unlike commonly-used two-way-fixed-effects regressions. We propose reduced-form event-study estimators of the effect of being exposed to a weakly higher treatment dose for l periods. We also propose normalized event-study estimators, that estimate a weighted average of the effects of the current treatment and its lags. Finally, we show that the reduced-form estimators can be combined into an economically interpretable cost-benefit ratio.