We consider the estimation of the effect of a policy or treatment, using panel data where different groups of units are exposed to the treatment at different times. We focus on parameters aggregating instantaneous and dynamic treatment effects, with a clear welfare interpretation. We show that under parallel trends conditions, these parameters can be unbiasedly estimated by a weighted average of differences-in-differences, provided that at least one group is always untreated, and another group is always treated. Our estimators are valid if the treatment effect is heterogeneous, contrary to the commonly-used event-study regression. 
We consider the estimation of the effect of a policy or treatment, using panel data where different groups of units are exposed to the treatment at different times. We focus on parameters aggregating instantaneous and dynamic treatment effects, with a clear welfare interpretation. We show that under common trends conditions, these parameters can be unbiasedly estimated by weighted sums of differences-in-differences, provided that at least one group is always untreated, and another group is always treated. Our estimators are valid if the treatment effect is heterogeneous, contrary to the commonly-used event-study regression. We also propose placebo estimators to test our identifying assumptions
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parallel
common
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a weighted average
weighted sums
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We also propose placebo estimators to test our identifying assumptions