Unbiased Instrumental Variables Estimation under Known First-Stage Sign

62 Pages Posted: 26 Mar 2015

See all articles by Isaiah Andrews

Isaiah Andrews

Harvard Society of Fellows

Timothy Armstrong

Yale University - Cowles Foundation

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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

Andrews, Isaiah and Armstrong, Timothy, Unbiased Instrumental Variables Estimation under Known First-Stage Sign (March 24, 2015). Cowles Foundation Discussion Paper No. 1984R, Available at SSRN: https://ssrn.com/abstract=2584594 or http://dx.doi.org/10.2139/ssrn.2584594

Isaiah Andrews

Harvard Society of Fellows ( email )

1875 Cambridge Street
Cambridge, MA 02138
United States

Timothy Armstrong (Contact Author)

Yale University - Cowles Foundation ( email )

Box 208281
New Haven, CT 06520-8281
United States

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