# Difference-in-differences with unbalanced panel data

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?