Efficient estimation using regularized Jackknife IV estimator
Annals of Economics and Statistics No. 128 (December 2017), pp. 109-149.
47 Pages Posted: 18 Nov 2021
Date Written: June 01, 2017
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.
Keywords: Many instruments, mean square error, Jackknife, regularization methods.
JEL Classification: C13, C26, C52
Suggested Citation: Suggested Citation