Efficient Estimation Using Regularized Jackknife IV Estimator

We consider instrumental variables (IV) regression in a setting with many (possibly weak) instruments. In finite samples, the inclusion of an excessive number of moments may increase the bias of IV estimators. We propose a Jackknife instrumental variables estimator (RJIVE) combined with regularization techniques based on Tikhonov (T), Principal Components (PC) and Landweber Fridman (LF) methods to stabilize the projection matrix. We prove that the RJIVE is consistent and asymptotically normally distributed. Moreover, it reaches the semiparametric efficiency bound under certain conditions. We derive the rate of the approximate mean square error and propose a data-driven method for selecting the tuning parameter. Simulation results show that our proposed estimators provide more reliable confidence intervals than other regularized estimators.