Unbiased Instrumental Variables Estimation under Known First-Stage Sign
We derive mean-unbiased estimators for the structural parameter in instrumental variables models 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 while retaining unbiasedness in ﬁnite samples. We show numerically that unbiasedness does not come at a cost of increased dispersion: in the single instrument 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.
Andrews, Isaiah and Armstrong, Timothy B., "Unbiased Instrumental Variables Estimation under Known First-Stage Sign" (2015). Cowles Foundation Discussion Papers. 2405.