# Interpreting Triple Difference coefficient with dummy variable

In my paper, I have estimated a triple difference-in-difference model where the outcome variable is a dummy variable indicating if the given individual is employed or not. Let's say that policy that I am evaluating happened in the capital of country $$S$$, in year 2000. As treated group I choose the capital of country $$S$$, as control I choose all the other cities in country $$S$$. The model I am estimating is

$$y = \alpha + \beta\text{State} + \gamma\text{Post} + \omega\text{Capital} +\theta(\text{Post}\times\text{Capital})+ \rho(\text{Capital}\times\text{State})+ \\ \psi(\text{Post}\times\text{State}) + \delta(\text{State}\times\text{Capital}\times\text{Post}) + \epsilon$$

Assume that the outcome variable is a dummy that indicates if the individual $$i$$ is employed or not. If I estimate the regression model, and I get a coefficient of 0.06 on the triple interaction variable $$\delta$$, is it correct to say that the probability to be employed of an individual living in the capital of country $$S$$ in the post-treatment period (treated group) increases by 6 percentages points with respect to a same individual living in the control group (any of the other urban areas of country S) ?

• Welcome to CV paulo morales. A few suggestions to improve your question: (1) "get a[n estimated] coefficient of 0.06" for which coefficient?? ($\beta$? $\gamma$? etc.), and (2) "the probability to be employed of an individual living in the country S in the post-treatment period increases by 6 percentages points?" Please clarify "increases" relative to which group? You can edit your question to make such improvements by clicking the "edit" link in the lower left. – Alexis Jan 24 '19 at 20:53
• Please register your account (you can find information on how to do this in the My Account section of our help center), then you will be able to edit & comment on your own question. – gung - Reinstate Monica Jan 24 '19 at 21:11

I think it is easiest to think of $$\delta$$ as the time change in employment rate for the capital city residents, minus the change in employment for residents in the control cities (all non-capital), and also minus the change in employment for the non-capital city residents in target state S.