  Data clustering reduces the effective sample size from the number of
observations towards the number of clusters. For instrumental variable models I
show that this reduced effective sample size makes the instruments more likely
to be weak, in the sense that they contain little information about the
endogenous regressor, and many, in the sense that their number is large
compared to the sample size. Clustered data therefore increases the need for
many and weak instrument robust tests. However, none of the previously
developed many and weak instrument robust tests can be applied to this type of
data as they all require independent observations. I therefore adapt two types
of such tests to clustered data. First, I derive cluster jackknife
Anderson-Rubin and score tests by removing clusters rather than individual
observations from the statistics. Second, I propose a cluster many instrument
Anderson-Rubin test which improves on the first type of tests by using a more
optimal, but more complex, weighting matrix. I show that if the clusters
satisfy an invariance assumption the higher complexity poses no problems. By
revisiting a study on the effect of queenly reign on war I show the empirical
relevance of the new tests.
