Symmetric Jackknife Instrumental Variable Estimation

This paper gives a new jackknife estimator for instrumental variable inference with unknown heteroskedasticity. The estimator is derived by using a method of moments approach similar to the one that produces LIML in case of homoskedasticity. The estimator is symmetric in the endogenous variables including the dependent variable. Many instruments and many weak instruments asymptotic distributions are derived using high-level assumptions that allow for the simultaneous presence of weak and strong instruments for different explanatory variables. Standard errors are formulated compactly. We review briefly known estimators and show in particular that the symmetric jackknife estimator performs well when compared to the HLIM and HFUL estimators of Hausman et al. (2011) in Monte Carlo experiments.