Unbiased Instrumental Variables Estimation under Known First-Stage Sign
62 Pages Posted: 26 Mar 2015
There are 6 versions of this paper
Unbiased Instrumental Variables Estimation Under Known First-Stage Sign
Unbiased Instrumental Variables Estimation under Known First-Stage Sign
Unbiased Instrumental Variables Estimation Under Known First-Stage Sign
Unbiased Instrumental Variables Estimation Under Known First-Stage Sign
Unbiased Instrumental Variables Estimation Under Known First-Stage Sign
Unbiased Instrumental Variables Estimation Under Known First-Stage Sign
Date Written: March 24, 2015
Abstract
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, the unbiased estimator is unique. 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.
Keywords: Weak instruments, Unbiased estimation, Sign restrictions
JEL Classification: C26, C36
Suggested Citation: Suggested Citation