Unbiased instrumental variables estimation under known first-stage sign
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Andrews_et_al-2017-Quantitative_Economics.pdf
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381.72 KB
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Author(s)
Armstrong, Timothy B.
Andrews, Isaiah Smith
Date Issued
July 2017
Journal
Quantitative Economics
Publisher
The Econometric Society
Citation
Andrews, Isaiah, and Armstrong, Timothy B. “Unbiased Instrumental Variables Estimation Under Known First-Stage Sign.” Quantitative Economics 8, 2 (July 2017): 479–503 © 2017 The Authors
Version
Final published version
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, 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. Keyword: unbiased estimation; weak instruments
MIT Department
Massachusetts Institute of Technology. Department of Economics
Terms of Use
Creative Commons Attribution-NonCommercial 4.0 International
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DOI of Published Version
https://doi.org/10.3982/QE700
