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I want to evaluate the consequences of a policy change using a difference-in-differences (DiD) setup. I have quarterly data over ten years before the treatment ($t_{-10}$, $t_{-9}$, ..., $t_{-1}$) and ten years after the treatment ($t_{+1}$, $t_{+2}$, ..., $t_{+10}$). However, in the pre-treatment period, it seems that the parallel trends assumption holds from $t_{-10}$ to $t_{-5}$ but not afterwards (i.e., from $t_{-5}$ to $t_{-1}$). It looks like the agents anticipate the policy change.

Is it possible in this case to only use the data from $t_{-10}$ to $t_{-5}$ for the pre-treatment period (and drop the observations from $t_{-5}$ to $t_{-1}$) in order to obtain an unbiased DiD estimate?

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In a parallel trends test you will have to neglect one quarter of observations (which serves as the reference period) to which all others estimates are calculated in respect to. Usually, this is the period before the treatment starts. I assume that is $t_0$ in your case.

Given this, it depends on the setup of your policy evaluation. Did the agents have the relevant information to "see the treatment coming"? can you credibly rule out any other "treatment"? Maybe you can provide evidence that in $t_{-5}$ some news about the policy were released and you consider the "announcement date" rather than the "implementation date" as the appropriate event date?

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  • $\begingroup$ Indeed, I can assume that agents had information because they were discussions well before the policy change. I was thinking of considering the announcement date as the event date. But it seems that there is a reaction of agent at the announcement date AND also at the implementation date. My idea was to drop the observations between the announcement and implementation dates (when the parallel assumption is violated), and compare the pre-announcement period with the post-implementation period in the diff-in-diff. Would it make sense? $\endgroup$ Commented Jul 23, 2018 at 15:05
  • $\begingroup$ I would probably report all regressions, such that the reader can decide for herself whether she believes your interpretation (which of course you should provide). It is hard to give more advice unless one knows your exact set up -- but maybe some agents were able to act early because of some reason? Are you able to control for that? $\endgroup$
    – safex
    Commented Jul 24, 2018 at 11:48
  • $\begingroup$ Thanks, I will investigate that. But more generally: does it make sense to do a diff-in-diff when the pre-treatment and post-treatment period considered are separated by several years (in my case it is because I want to ommit several years between the two periods because the parallel trend assumption is not valid, but there can be other cases)? $\endgroup$ Commented Jul 25, 2018 at 10:49
  • $\begingroup$ Can you have two regimes, each with its own effect? $\endgroup$
    – dimitriy
    Commented Dec 15, 2020 at 18:03

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