I have an experiment which has 2 treatment groups (effects) and a control group. Up until this point in my analysis, I've been carrying out a DID using a regression equation of the form:
$$Y= γD_t + β_1(TREAT_1) + β_2(TREAT_2)+ τ_1(TREAT_1D) + τ_2(TREAT_2D) + ε$$
Basically I've been including both treatment effects in the same regression equation which I've been running on STATA.
My question is, should I be including both interaction terms in one equation, or should I be splitting my data and analysis so that I'm estimating the ATE for both groups separately?
Best Answer
If you include both treatment effects, you'll have just as much information to estimate $\beta_i$ and $\tau_i$, and if the splitting is done correctly (and the groups are disjoint) it should give you the same result. If the groups are not disjoint, you should also try the interaction of the two treatments. You certainly should not use either of the treated groups as control for the other when you split your data. Including both treatments in a single regression also makes it extremely easy to test whether the two treatments significantly differ.