Unbiased instrumental variables estimation under known first-stage sign

• 成果类型: Article
• 署名作者: Andrews, Isaiah; Armstrong, Timothy B.
• 署名单位: Massachusetts Institute of Technology (MIT); Yale University
• 刊物名称: QUANTITATIVE ECONOMICS
• ISSN/ISSBN: 1759-7323
• DOI: 10.3982/QE700
• 发表日期: 2017
• 页码: 479-503
• 关键词: Unbiased estimation; weak instruments

摘要

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.