Inference in IV models with clustered dependence, many instruments and weak identification
Data clustering reduces the effective sample size down from the number of observations towards the number of clusters. For instrumental variable models this implies more restrictive requirements on the strength of the instruments and makes the number of instruments more quickly non-negligible compared to the effective 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 of such tests to clustered data. First, I derive a cluster jackknife Anderson-Rubin test by removing clusters rather than individual observations from the Anderson-Rubin statistic. Second, I propose a cluster many instrument Anderson-Rubin test which improves on the first test 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.