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I have Difference-in-Differences models with 3 periods: pre-treatment, treatment and post-treatment periods.

Normally, we could do DID in the following way: run DID between pre-treatment and treatment (DID_1 shown in the pic); or run the DID between treatment and post-treatment period (DID_2).

I think both of the methods could test the treated effects. DID_2 could be considered as a robustness check.

Is there any way to run this DID with these 3 periods together? (like run one regression, but not two separate regressions?) If these two methods have different conclusions, which one should be correct? Thanks.

enter image description here

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  • $\begingroup$ The information is incomplete. It seems mixed model can be used. $\endgroup$ – user158565 Jan 4 at 2:14
  • $\begingroup$ That depends on what the treatment is and what effect(s) are being measured. Some treatments are definitive, others are not. Some effects of treatment are temporary even if the treatment is curative. Some side effects of treatment are permanent, even if the treatment has no salutary effects. Not enough information given to answer question. $\endgroup$ – Carl Jan 4 at 6:50
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You want to run a panel fixed effects regression of the outcome on:

  1. treatment and post-treatment period dummies (dropping the pre-treatment one)
  2. the interactions of treatment group dummy with the two included period dummies.

Since the treatment group dummy is time-invariant, it will be absorbed by the fixed effect term and will be dropped from the model.

The coefficient(s) on the interactions are the DID effect(s).

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  • $\begingroup$ Many thanks for the response, Dimitriy. Actually not, I updated my questions to be more clearly and added a graph to help the understanding. Could you please look at it? $\endgroup$ – Lernst Jan 4 at 3:51
  • $\begingroup$ @Lernst I think my answer covers the exact scenario you have outlined. Here's another question where this comes up. $\endgroup$ – Dimitriy V. Masterov Jan 4 at 4:02
  • $\begingroup$ Thanks. 1- In this case, should I test both parallel trend assumption for pre- and post periods? 2- How to understand the DID effect? (e.g., for the second interaction, it compares pre-period and post-period?) If possible, could you please suggest any papers or textbooks that talk about this? $\endgroup$ – Lernst Jan 4 at 4:14
  • $\begingroup$ @Lernst You can't test the parallel trends assumption after treatment starts. You can test it in the pre-treatment regime if you have multiple periods there, which might make you more willing to believe it holds after treatment starts. The answer I linked deals with the interpretation question. The short answer is that the interaction coefficients give you the DID effects relative to the pre-treatment period. Jeff Wooldridge's Econometric Analysis of Cross Section and Panel Data is the best source on this. He also has good lecture notes from NBER that you can find floating around on the web. $\endgroup$ – Dimitriy V. Masterov Jan 4 at 4:21
  • $\begingroup$ Thanks Dimitriy. My last questions: 1- if I remove the treatment period, then I set original post-treatment as my new treatment period. If I run my did on this, should I get similar coefficient with the second interaction's coefficient? 2- For this case, do you think run two separate regressions right? the second one as a robustness check on DID effect. $\endgroup$ – Lernst Jan 4 at 4:30

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