Hello everyone!

I'm currently running a multi-way fixed effect regression using the command reghdfe. As I have data which is clustered on two dimensions I went through the classical paper by Cameron, Gelbach and Miller on the topic. To the best of my understanding, the two-way clustering estimator they describe in the article can be implemented on Stata using (this is just one of the possible solutions of course) as

reghdfe depvar indepvars, a(fe1 fe2) vce(cluster c1#c2)

However, I've noticed that there exists the possibility of running the following command

reghdfe depvar indepvars, a(fe1 fe2) vce(cluster c1 c2)

Here is my doubt: what kind of clusterisation does vce(cluster c1 c2) imply and in which sense does it differ from vce(cluster c1#c2)?

Thanks for your help,

Filippo