Uniformly Consistent Estimation of Linear Regression Models with Strictly Exogenous Instruments

This paper investigates estimation of linear regression models with strictly exogenous instruments under minimal identifying assumptions. It is known that under this setting the commonly used Instrumental Variables (IV) estimators are not uniformly consistent (uniformity is in the underlying data generating process). This negative result is due to the lack of "continuity" in the identification of IV caused by weak instruments. This paper introduces a uniformly consistent estimator in this setting. The proposed estimator, called here the Integrated Instrumental Variables (IIV) estimator, is a weighted least squares estimator with trivial implementation. Monte Carlo evidence supports the theoretical claims and suggests that the IIV estimator is a robust and reliable alternative to IV and optimal IV in finite samples under weak identification and strictly exogenous instruments. An application to estimating the elasticity of intertemporal substitution highlights the merits of the proposed approach over classical IV methods.