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Normally, we test for anticipation effects as an assumption when using difference-in-differences. However, it seems that it is necessary for examining the impact of laws on firms' behaviour. For example, we want to test if anti-collusion laws affect firms' asset growth. Therefore, we expect that firms will know about the establishment of the laws (due to media, government discussion, insider information), leading to firms changing their asset growth before the actual event dates.

On the other hand, I am wondering if we need to test for anticipatory effects if the event date is a natural event (i.e., not a law, etc.), say for example, that the level/percentage of vaccinated people/population is 30% or a tsunami. In my opinion, I do not think a formal anticipation test is needed here. Is this correct?

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    $\begingroup$ In the case of a natural event/experiment which does some of the work of “randomization” for us, then yes we should suspect very little anticipation. However, it doesn’t mean the groups are guaranteed to be moving on a stable, parallel trajectory before the shock. $\endgroup$ Oct 19 '21 at 6:15
  • $\begingroup$ @ThomasBilach , do you mean that in this case, we should focus on parallel trend problem rather than "no anticipation assumption" ? $\endgroup$
    – Nguyen Lis
    Oct 19 '21 at 7:01
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    $\begingroup$ We should always be concerned with the pre-treatment trends. If you do find a deviation from a common trend close to the event, then this could be interpreted as selection bias, unless you have some strong theoretical basis to argue the case for anticipation. $\endgroup$ Oct 19 '21 at 19:02
  • $\begingroup$ Hi @Thomas, thank you, can I ask what is the "selection bias" here? I thought the deviation found should mean that there is difference between control and treatment group before event date ? $\endgroup$
    – Nguyen Lis
    Oct 19 '21 at 19:04
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    $\begingroup$ In keeping with my fictitious example involving mold, say we didn't choose households/islands because they were impacted by the disaster, but rather because they were already high in mold prevalence. In other words, the units selected to receive a treatment were the ones with a mold problem. Do you see how this could introduce bias? $\endgroup$ Oct 19 '21 at 19:14
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A natural event is merely 'mimicking' the features of random assignment. As in your example, a tsunami is a natural event and may impact some regions, but not others. Is anticipation not a concern in this context? Perhaps. But maybe it is. Was the event/shock instantaneous, or did the local population have time to prepare for the event? Say you're assessing the effect of a natural disaster on net GDP growth in Northeastern Asia. A few months before the event, a nearby seismograph station detects an earthquake of magnitude 8.0 in the region. A tsunami watch is in effect for approximately 100 of the 6,852 islands that make up the Japanese archipelago. A civil defense agency issues an evacuation warning to affected islands, and residents start to prepare for the possibility of a tsunami. Should you suspect anticipation? I would say so. Will residential mobility be high? Do you suspect flights be canceled? Note how this requires a deep understanding of what is happening in the days/weeks/months leading up to the event.

Anticipatory concerns also depends on your outcome of interest. Obviously, we should suspect a natural disaster will suppress economic activity. But say you're investigating the geographic distribution of residential dampness or mold in the post-shock era. Is anticipation a concern here? Perhaps not. How might the impending disaster affect reports of excess humidity or mold prevalence? It seems less of a concern in this setting.

As a final word, the absence of anticipation doesn't imply parallel trends in the pre-treatment epoch. Anticipatory behavior is usually something we suspect in the periods close to the event. We should still demonstrate in some way a parallel trajectory of the treatment/control group trends even before the anticipation period(s).

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  • $\begingroup$ A great answer, @Thomas, I found a way to test for anticipation effect here, could you please have a look on that but I do not know how to interpret it, much appreciated [stats.stackexchange.com/questions/548832/… $\endgroup$
    – Nguyen Lis
    Oct 19 '21 at 19:07
  • $\begingroup$ "We should still demonstrate in some way a parallel trajectory of the treatment/control group trends even before the anticipation period(s)." I understand that it mean we need to test for parallle before then anticipation event date, is it correct then? And, is there any paper supports that if the outcome variable is irrelevant and unexpected, we do not need to test for anticipation effect then? $\endgroup$
    – Nguyen Lis
    Oct 19 '21 at 19:11

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