  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.
