[Maxence Morlet]

This will replicate the coefficients provided you have:

xtset firmID Quarter

[Maarten Loomans]

This will replicate the coefficients provided you have:

xtset firmID Quarter

Maxence:
Thank you! I have one more question. When I ran the regression, it gave a window which showed the absorbed degrees of freedom. It said: n_id : categories(2383) - redundant(2383) = 0*
* = FE nested within cluster, treated as redundant for DoF computation. How do I interpret this. I did indeed get the exact same coefficients, but with smaller SEs, hinting to a more efficient model.
I would like to add a question to this. How should I interpret the coefficients that I got from this model?

[Maxence Morlet]

Yep, because

reghdfe

will not apply a double penalty so to speak, and if fixed effects are nested within cluster (here, you have firm fixed effects and you are clustering by an equal or coarser entity, i.e. firms) then reghdfe will not count firms twice in the computation of absorbed degrees of freedom (hence the redundant).

The interpretation of the coefficients is the standard within coefficients interpretation; ceteris paribus, within one same unit over time, if x rises by one unit, y will rise by Beta units, where Beta is the coefficient on x.