Why the confusion in Difference-in-Differences with pre-intervention/post-intervention periods and treated/control units?

Question

In Difference-in-Differences, it typically has a pre-intervention and a post-intervention periods. This is coupled with treated and control units. From what I understand, since the comparison for the treatment effect occurs in the post-intervention, this will be the ATT.

My confusion is how the post-intervention is associated with treatment, yet the literature also mentions treated units. It seems that there are two types of treatment paradigms going on. Is there a way to neatly think about this? thanks.

Answer 1

There is only one paradigm here, and the name "difference-in-differences" itself reflects how you should think about it.

You have two different kinds of units: some get the treatment and some are in the control group. You measure all of the units (at least) twice: once before any of them have gotten the treatment and another time after the treatment group has gotten the treatment. To calculate the ATT you do the following:

1. Figure out how much the treatment group changed ("differed") between the pre- and post-treatment periods. Basically, how much did they change after getting the treatment.
2. Figure out how much the control group changed ("differed") during this same time period (that is, between the pre and post treatment periods). This, you assume, tells you how the treatment group would have changed if they had not gotten the treatment.
3. Figure out the "difference between these two differences." In other words, how much more did the treatment group change, above and beyond the change experienced by the control group.