Jackknife instrumental variable estimation with heteroskedasticity

Abstract

We present a new jackknife estimator for instrumental variable inference with unknown heteroskedasticity. It weighs observations such that many-instruments consistency is guaranteed while the signal component in the data is maintained. We show that this results in a smaller signal component in the many instruments asymptotic variance when compared to estimators that neglect a part of the signal to achieve consistency. Both many strong instruments and many weak instruments asymptotic distributions are derived using high-level assumptions that allow for instruments with identifying power that varies between explanatory variables. Standard errors are formulated compactly. We review briefly known estimators and show in particular that our symmetric jackknife estimator performs well when compared to the HLIM and HFUL estimators of Hausman et al. in Monte Carlo experiments.