Difference-inDifference model with Discontinued Treatment

Question

I have a situation where I observe two groups A and B for three years. Group A never received any treatment. Whereas group B received treatment in year 2 only. I can estimate the impact of the treatment by using only years 1 and 2 data with standard difference-in-difference approach. I am also interested in estimating the impact of discontinuation of treatment.

If I use year 2 and 3 data only, the treatment happens in period 2 and the treatment and control groups are not comparable. Would it be okay to use all three years of data and treat the "discontinuation of treatment" as second treatment?

Answer 1

You presumably should be using all 3 years for the data. Given that you had the appropriate conditions for diff-in-diff (parallel trends), and you're looking at a standard case of the treatment only being relevant in treated periods (no lagged effects), then the additional data should not hurt your estimates. Additional years of untreated data will help you more appropriately measure the de-facto difference between the two groups, and therefore more precisely measure the effect treatment.

Take a look at panel data and difference-in-differences application - you add fixed effects for all $t$ and all $i$, and create a DiD variable for the the interaction of the treatment and control variable. It doesn't, under ideal conditions, matter what the timing of treatment is. If you do have a reason to believe there are lagged effects you should, of course, account for that with lags/leads of treatment, which I believe the other answer is concerned about.

Answer 2

While I am but a novice when it comes to impact evaluation, I would say whether your comparison makes sense depends on whether it satisfies the parallel trend assumption.

The whole point of dif-in-dif strategy builds on this underlying assumption of similar trajectory of evolution in the absence of any exogenous shock. Ideally, in your case that would be all three period altogether since you want to observe the pre-treatment, treatment, and post-treatment period, each of which reveals different information with respect to the behaviors of the two groups. As long as this assumption holds, and there is no other time-varying factors that affect both groups differently, especially during the treatment period, the difference between period 1 & 2 reveals the impact of the treatment. The difference between period 2 & 3 is nonsensical, however as the treatment and control groups are already different in the 2nd period. If you want to compare the immediate effect and the long-run effect of the treatment then I think you should compare the difference between period 1 & 2 and the difference between period 1 & 3. Be mindful, however, of other time-varying factors that could affect the results other than the treatment in the long-run.