Jackknife estimation of a cluster-sample IV regression model with many weak instruments

This paper proposes new jackknife IV estimators that are robust to the effects of many weak instruments and error heteroskedasticity in a cluster sample setting with cluster-specific effects and possibly many included exogenous regressors. The estimators that we propose are designed to properly partial out the cluster-specific effects and included exogenous regressors while preserving the re-centering property of the jackknife methodology. To the best of our knowledge, our proposed procedures provide the first consistent estimators under many weak instrument asymptotics in the setting considered. We also present results on the asymptotic normality of our estimators and show that t-statistics based on said estimators are asymptotically normal under the null and consistent under fixed alternatives. Monte Carlo results show that our t-statistics perform better in controlling size in finite samples than those based on alternative jackknife IV procedures previously introduced in the literature.