First-Stage F-test with xtivreg2 - within and between variation?

[Bobby Wood]

Hi,

I have a paper with panel data where I use an IV (xtivreg2 by Schaffer) with FE.
The First Stage F-test is sufficiently high (around 80).
However, one of the referees said that the variation comes from between variation.
This is not true and I show this in my reply using xtsum.

But I still wonder: is it possible to get a sufficiently high First Stage F-test if there is only between variation and only very little within?

Many Thanks,
Bobby