CFDP 1984R5

Isaiah Andrews and Timothy B. Armstrong, “Unbiased Instrumental Variables Estimation under Known First-Stage Sign” (February 2015, Revised November 2016) [37pp, abstract] [Supplemental Appendix, 31pp]

Publication Date: December, 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.

Keywords: Weak instruments, Unbiased estimation, Sign restrictions

JEL Classifications: C26, C36