I am following this answer from Thomas about the DDD for staggered event dates. In this post, he wrote
The more general representation of the DDD equation is as follows:
$$ Y_{iast} = \gamma_{st} + \lambda_{at} + \eta_{as} + \delta L_{ast} + u_{iast}, $$
where $Y_{iast}$, which denotes the earnings of individuals in age group $a$ in state $s$ and year $t$, is regressed on a full set of state $\times$ year effects (i.e., $\gamma_{st}$), age $\times$ year effects (i.e., $\lambda_{at}$), age $\times$ state effects (i.e., $\eta_{as}$), and a law dummy (i.e., $L_{ast}$).
I am wondering we have three terms of fixed effects as in this answer just because we multiple each element of state, year and age to each other. So, I imagine that if the laws are implemented in the same day, it seems that we only have one fixed effect term called age x state x year. Is it a correct thought?
To me it seems to be correct but Thomas also stressed that
I should stress that you must include all of the second level interaction terms or your model may be misspecified.
So it is better that I ask clearly.