I have a question regarding a difference-in-difference regression I want to run. I assume that it is rater trivial, however, I have not yet been able to confidently solve my problem.
In my research I am investigating the impact of a policy, which came into effect in 2005. The diff-in-diff regression I developed for the overall assessment his the following:
(1) Pit = alpha ETSi + beta post + gamma ETSi * post + deltai + epsilont + zeta,
where Pit is the patent output for a firm i in year t; ETSi is a dummy equal to one for a firm that becomes regulated in 2005; post is dummy equal to one for the post-treatment period; and ETSi * post is the interaction effect; deltai measures any firm fixed effects; epsilont measures common shock to firms; and zeta is the error term. The main coefficient of interest is gamma, which measures the policy effect onto the patent output of firms.
Now I want to extend this formula to assess a policy refinement which came into action in 2008 and am wondering how to extend the model. I am interested in particular in assessing:
- The impact of phase 1 of the policy (2005-2007)
- The impact of phase 2 of the policy (2008-2012)
- The phase difference, i.e. is there a significant difference in the impact of phase 1 versus phase 2
My question is now: How do I extend this model? Can I just add a dummy and another interaction term (e.g. phase1 and phase2 for the first and second period as depicted below)?
(2) Pit = alpha ETSi + beta phase1 + etaphase 2 + gamma ETSi * phase1 +theta ETSi * phase2 + iota ETSi * phase1 * phase2+ deltai + epsilont + zeta
I assume that this is not possible but also do not know how to further continue. Any help would be appreciated!
Thank you
Lennart
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