.ISSN (e) 1759-7331
(print) 1759-7323
Quantitative Economics
An open-access journal in quantitative economics
Journal of the
Econometric Society
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Quantitative Economics, Volume 8, Issue 2 (July 2017)

Unbiased instrumental variables estimation under known first‐stage sign

Isaiah Andrews, Timothy B. Armstrong


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 nonrandomized 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 two‐stage least squares 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.

Unbiased estimation weak instruments C13 C26

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