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 .
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, as a way to evaluate the welfare effects of the policies that occurred over the duration of the panel . 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 estimators of a dynamic linear model, with group-specific but time-invariant effects of the current and lagged treatments, which may be used to evaluate ex-ante the effect of future policies .
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with a clear welfare interpretation
as a way to evaluate the welfare effects of the policies that occurred over the duration of the panel
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placebo estimators to test our identifying assumptions
estimators of a dynamic linear model, with group-specific but time-invariant effects of the current and lagged treatments, which may be used to evaluate ex-ante the effect of future policies