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In the Difference-in-Differences estimator, one key assumption is the anticipation effect, meaning that the real event date maybe a couple of years before the real event year (yearly data). I am wondering what should we do if we test and find out that the data violated the anticipation effect?

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The no anticipation assumption requires an individual outcome to not depend on future treatments.

The best way you can do in the presence of anticipation effects is to use an disaggregated approach and model the anticipation directly (the behavior of the agents, individuals who is aware of the future treatment and how they are acting accordingly etc.).

With aggregated methods such as DiD this might be possible in a few special cases (e.g. if you know the share of the population who anticipates a future event in a given year for example) but in general it will be difficult to find plausible results based on aggregated data alone. For disaggregated data this of course will require further information about the change in behavior in response to the anticipation of the treatment.

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