thank you so much for your reply.
I tried your code but it gives me the following error message:
"invalid matrix stripe;
error in expression: _b[c.treatment_village##c.period]"
So I tried to generate the treatment variable:
ritest treatment_village _b[treatment], cluster(village): xtreg y i.treatment i.period, fe cluster(village)
Resulting however in a p-value = 1 which seems not right at all.