I have a staggered DID model as follows:
Here I is an indicator of whether the distance of the calendar year from the event year equals to q ( where q takes -3 to +3 and is my time window ). \delta is the DID estimate over time, T is the treatment time dummy that equals 1 if this year the firm is being treated, Treat is a treatment dummy that equals 1 if this firm belongs to the treatment group, and FE represent some fixed effect.
Now I also want to see if there is any difference in the effect between a large firm and a small firm, and I have a dummy(Size) that equals 1 if the firm is large, and 0 otherwise. I want to add it into the model through interaction, but I'm not sure if I can just interact it with the indicator and treat dummy, or should I also add some other terms? (like not just triple interaction, but also single variable and double interaction)
Do you have any ideas and can you write a formula for me?
Thank you so much