Dear all

I am estimating IV model. I would like to cluster at the village level
We have only two villages.
Both x and z are dummy variables and we have x=1 and z=1 in both villages.

When I estimate
xi: ivreg2 y (x=z) i.village , cluster (village)
I got the following error message.

"Warning: estimated covariance matrix of moment conditions not of full rank.
overidentification statistic not reported, and standard errors and
model tests should be interpreted with caution.
Possible causes:
number of clusters insufficient to calculate robust covariance matrix
singleton dummy variable (dummy with one 1 and N-1 0s or vice versa)
partial option may address problem."


This sounds that clustering by only two village is not feasible.
However, if I estimate OLS
xi: y x i.village, cluster (village)
It works.

"partial option" did not help.

Can somebody give me advice on why this happen?

Thank you very much!