Is the parallel trends assumption required for dynamic difference in differences model?

[Chul-Kyoo Jung]

Hello, I know parallel trends assumption (PTA) is essential to a simple difference in difference model. Is it also true for the case of dynamic difference in difference model? For example, in the following figure, I don't see any evidence of PTA, but can I still consider this plot useful and meaningful or should I just ignore the result? If the plot like this is still meaningful, then how should I interpret the plot in terms of the effect of a certain policy?

In the following figure, 1999 is the reference year when the policy was implemented. I think the reason why we have a big drop in year 1998 (just one year before the policy implementation year) is that there was another negative event like a natural disaster or financial crisis. In fact, the policy enacted in 1999 was a response to the previous disaster.

In sum, my question is: is this figure still meaningful despite the lack of PTA support? If it is still meaningful, how should I interpret the figure between the following two options: 1. the effect is due to the dominant disaster and the policy was not effective at all. 2. although the disaster is dominant, still we can find some significant negative or worsening effect from the bad policy because there was a huge drop in 2000 which was right after the year of implementation 1999?

I would really appreciate it if you could give me a piece of advice.

[Jared Greathouse]

PTA is required for any DD you do.

Edit: if I were you, do an in time placebo of one year (i.e., in 1998).

[Chul-Kyoo Jung]

Jared Greathouse Thanks, so if the placebo test does not support PTA, then should I simply give up this model or still there's a way to overcome this issue?

[Jared Greathouse]

Without getting technical, there are a few ways you might proceed. Firstly though, how many units were affected by this earthquake? Also, how many units are treated and untreated?

[Chul-Kyoo Jung]

every unit of firms was harmed by disaster and only large firms were treated. I just want to make sure PTA holds here to run dynamic DD model. Could you give me some more details even technical advice regarding the next step? At this point, I still don't see how your suggestion would make a difference about this issue. thank you so much!

[Jared Greathouse]

So wait, how many firms were treated though?

One thing you might do... is calculate the distance of the firms from the quake's epicenter, and exclude firms that were "too affected" by it (10 miles from it, say". That way, you can see if the degree of the earthquakes effect matters, and it'll also likely make the trends more parallel due to the absence of this confounder

[Chul-Kyoo Jung]

In fact, it is financial crisis which affected all the firms both big and small firms. So distance in this case will probably not work. Treated group is big firms who received the government's favour. I assume that the crisis impact would be the same for both firms. However, the figure shows the impact might affect differently for each group. This makes the whole DD worthless, I guess.

[Jared Greathouse]

I still wanna know how many firms were treated. If there's a sensible number of firms, then synthetic controls might be the answer here

[Chul-Kyoo Jung]

Sure, the treated firms were 1296 out of 7335. I am just curious that we still need to employ synthetic control even in the case when we can obviously identify control group? I understand it is because of PTA but is it only reason that we have to rely on synthetic control? I guess my more concern is how to separate the effect of policy from the effect of crisis in case the policy is due to the crisis. How do we know the decrease in firms' wage share is due to the crisis or due to the policy using synthetic control or dynamic DD?