Inference in clustered IV models with many and weak instruments

Abstract

Data clustering reduces the effective sample size from the number of observations towards the number of clusters. For instrumental variable models 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. Consequently, weak and many instrument problems for estimators and tests in instrumental variable models are also more likely. None of the previously developed many and weak instrument robust tests, however, can be applied to clustered data as they all require independent observations. Therefore, I adapt the many and weak instrument robust jackknife Anderson--Rubin and jackknife score tests to clustered data by removing clusters rather than individual observations from the statistics. Simulations and a revisitation of a study on the effect of queenly reign on war show the empirical relevance of the new tests.