Dear All,

I am working on a quasi-experimental study with a large unbalanced panel dataset. This is the specification that I use.

Y_it= β_1 Post_it + δi + γt+ u_it where Post_it is the value of treatment for individual i at week t, and δi and γt are individual and time fixed effect parameters that are estimated.

Here comes my concern. When t =1, I have only 10.000 individuals in sample, and the number gradually increases to 50.000 over time. 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? The value of dependent variable is decaying over time and therefore using calendar time fixed effects might not be enough. Do you have any suggestions?