DID with Treatment at Multiple Time Periods

[Ahmed Arif]

I am performing DID with a panel data. I don't have a specific time period for the treatment but some of the units receive treatment in one period but not in other and may receive the treatment again in some other time period. Moreover, there are 3 types of treatments, so three treatment groups and one control group. I am using the following model to estimate DID.



Where gamma is for the time fixed effects, C_it shows the choice (treatment) and G_it shows the treatment group.

I have two questions here. Is this model correctly specified given the above explained situation?

Secondly, I have the data for 269 banks form seven countries. Do I need to incorporate the country dummies as well?

[Clyde Schechter]

The data you describe does not have a DID design. In a classic DID design, all treated units (regardless how many treatments there are) begin treatment at the same time. The untreated units never do, so it is possible to compare the treated and untreated units both before and after the onset of treatment. The DID analysis then estimates the change in the treated units after treatment begins minus the change that the control units experienced after that same date. This difference is an estimator of the effect of treatment with secular trend removed, which is what you want.

If your data have different starting times for treatment, then you cannot get this estimator this way. To move in that direction, you would need to identify some way to match treated units with control units so that you could impute to the control unit the same treatment start date that the matched control unit has. That is, you impute to each control unit a date at which they would have started treatment if they were in a treated group. But, of course, this imputation process will rely on assumptions about what the determinants of the treatment start date in your treated units are. If that model is incorrect, your end results may not be valid. It's pretty dicey, and unless you can come up with a very credible way of doing this matching, I would advise you to forget about DID and just do an analysis of treatments vs controls, perhaps with a time variable added to account for secular trends.

As for your other question, if you have -xtset- your panel data specifying country as the panel, and if you use one of the -xt- estimators, then you do not need to explicitly incorporate indicators ("dummies") for the countries--Stata will handle that for you automatically.