# Why do not we include post and treatment variables separarately in generalized DID?

In a generalized Difference-in-Difference, Dasgupta, 2019 using this equation

$$Y_{it}$$ = $$\alpha$$ + $$\beta$$ $$(Leniency Law)_{kt}$$ + $$\deltaX_{ikt}$$ + $$\theta_t$$ + $$\gamma_i$$ +$$\epsilon_{it}$$ (1)

The variable of interest here is $$(Leniency Law)_{kt}$$. This variable equals 0 before the passage of the leniency law in country $$k$$, and 1 afterward. Simplistically speaking, it is postxtreatment in DID setting. I am wondering why he did not add the variable post and treatment separately into equation (1) as the basic DID setting.

I read a clue here from a discussion but it is not totally clear to me.

The referenced post assumes you're estimating a generalized difference-in-differences equation. The model includes unit fixed effects, time fixed effects, and a binary treatment treatment. It is useful in settings with irregular exposure periods.

"irregular exposure periods" typically means any setting where the treatment starts at different times for different entities. It may start early for some and later for others. It may even switch 'on' and 'off' over time. Thus, this estimator may handle irregular treatment patterns.

What I want to focus on is how it is useful or how "this estimator may handle irregular treatment patterns"in this case.

• I go into some detail here. The fixed effects will absorb "treat" and "post" in this setting. For example, a simple dummy variable indexing the "group" of treated/untreated firms is already captured by the firm fixed effects. Remember that the firm fixed effects adjust for all time-constant factors specific to your firms, which includes a firms's membership to the group. Try estimating a dummy which only tells you whether a firm is in a treated group or not. Software will usually drop it for you. Jun 2 at 6:33
• @ThomasBilach Thank you so much for your further clarification Jun 2 at 6:37
• @ThomasBilach after a couple of days of asking and accumulate knowledge, now I understand clearly your statement as above. Just come back and say thank you very much! Jun 8 at 5:37

Basically it is because of difference in treatment timing. There is no single time $$t^\star$$ such that for any group who is at some time treated, it will be treated at any time after $$t^\star$$. When there is no single time of treatment initiation it is impossible to define a single post treatment variable.
Nevertreated ... $$(0,0,0,0,0,0,0,0)$$ Early treated $$(0,0,1,1,1,1,1,1)$$ Late treated $$(0,0,0,0,0,1,1,1)$$