Inference in IV models with clustered dependence, many instruments and weak identification

Abstract: 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.