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I am working on a quasi-experimental study with a large unbalanced panel dataset. There are N=300,000 and T=20, where roughly 50,000 individuals receive treatment since several different periods.

I use a DiD estimator to estimate the ATT:

$y_{i,t} = \beta \times D_{i,t} + \alpha_{i} + \delta_{t} + \epsilon_{i,t},$

where $D_{i,t}=1$ iff individual $i$ has received treatment at period $t$. Besides, $\alpha_i$ and $\delta_t$ are individual FEs and time FEs, respectively.

Here comes my concern. When $t=1$, I have only 80,000 individuals in sample, and the number gradually increases to N=300,000 over time. The periods with treatment events are $t=6, 8, 10, 12$. That is to say, many individuals only have observations in later periods of the sample.

Is there an issue if I use all observations to estimate the equation? Is it legitimate to keep only individuals that exist from the beginning?

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