Evaluating a policy *expansion* using Difference in Difference

[Long Hong]

Dear All:

I am writing to ask for a Difference-in-Difference question.

Usually in a standard DiD setting (as in Jeff Wooldridge's online lecture notes), there is a control group (in period 1 and period 2) and treatment group (becomes treated in period 2). The assumption one needs to check is the parallel "pre-trend" in the outcome variables.

However, in the setting of policy expansion, there is a treated group and control group in period 1, and the treated group remain treated in period 2 while the control group becomes treated in period 2. My idea of evaluating a policy expansion is to use a "reversed DiD". That means, we will need to check the parallel "post-trend" assumption instead. In addition, we will have to assume that the policy does not have a "time-accumulative" effect on the outcome variables.

Does my idea sound reasonable? Is this the way how people use DiD in evaluating policy expansion or is it just my own imagination?

I look forward to hearing from you! Thank you!

Best,
Long

[Clyde Schechter]

Yes, this is reasonable. In effect, you are reversing the roles of pre and post, and reversing the roles of treatment and control groups in the modeling. The main objection that could be raised is one that you have already mentioned your awareness of: if the policy has accumulating effects, then you would not expect the trends to be parallel between the long-treated group and the newly-treated group. There are other issues as well such as whether the group that was added in the expansion was perhaps aware ahead of time that the policy was coming and might have, based on the experience of the already treated groups, made some adaptations that modified the policy effect. But any approach you take will be subject to these inherent limitations.

I don't personally have much experience with this particular situation. Where I have evaluated policy expansions, it has usually been expansion in multiple phases and I have had data starting from a totally untreated period to a period where 1 group came under the policy, and then another period where a second group was added, and perhaps other periods where a third or subsequent group came under the policy, etc. The presence of that earliest period with nobody being treated does make things simpler.

Perhaps others who have more experience with this kind of situation will also respond, please.