Parallel trends before the treatment

[Mahtab Karimi]

Hi all,

I am looking at trends of a control and treatment group. I can see the parallel trends before the treatment, but after the treatment, trends change for both of my control and treatment groups. Does that mean I can't use a diff in diff any more?

Thank you,
Mahtab

For example, is the attached picture violation of diff in diff? Blue is control and Red is treatment. right side of the black line is after treatment.

[Jared Greathouse]

Parallel trends is untestable in principle because it is a statement about the counterfactual, or how the difference between the counterfactual and treated group would have evolved absent treatment. The best we econometricians can hope for is parallel trends holding in the pre-treatment period, as close as it can hold anyways.

[Clyde Schechter]

While Jared is right that you cannot expect, nor even test, parallel trends post-intervention, the idea behind DID is that the treatment and control group were on similar trajectories before the intervention, and after that you see whether they diverge. The graphs you show suggest that this is precisely what happened. The assumption is not that the control group would continue along the same path that it was on pre-intervention. The assumption is that the treatment and control groups were on similar paths pre-intervention. And then you look to see if they evolve differently post-intervention.

[Mahtab Karimi]

Thanks so much.

[Jared Greathouse]

Yep! For more on this point, see my notes on this for my policy data analysis course. As Clyde says, the idea is that the trajectories are similar. Similar in the sense that the average difference between the treated and control group would be constant absent treatment. We can't see this globally, so we test this idea (or validate or, rather, argue for it) in the pre period.

That is, the groups do not need to be similar in levels, all DID asks is that we assume similarity in trends, such that any temporal variation (aside from the treatment) is common across all units. I do it with one example here, but this idea very easily generalizes to many treated units