Publication Date: February 2015
Revision Date: November 2016
We derive mean-unbiased estimators for the structural parameter in instrumental variables models with a single endogenous regressor where the sign of one or more ﬁrst stage coeﬀicients is known. In the case with a single instrument, there is a unique non-randomized unbiased estimator based on the reduced-form and ﬁrst-stage regression estimates. For cases with multiple instruments we propose a class of unbiased estimators and show that an estimator within this class is eﬀicient when the instruments are strong. We show numerically that unbiasedness does not come at a cost of increased dispersion in models with a single instrument: in this case the unbiased estimator is less dispersed than the 2SLS estimator. Our ﬁnite-sample results apply to normal models with known variance for the reduced-form errors, and imply analogous results under weak instrument asymptotics with an unknown error distribution.
Supplemental Material: Supplemental material
Supplement pages: 31
Weak instruments, Unbiased estimation, Sign restrictions
JEL Classification Codes: C26, C36