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. Commonly used Instrumental Variables (IV) estimators are not uniformly consistent in this setting (uniformity is in the underlying data generating process). This negative result is just one way to formalize the well-documented fact of high sensitivity of IV to the presence of weak instruments. This paper introduces a uniformly consistent estimator under nearly the minimal identifying assumption. The proposed estimator, called 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 alternative to IV and optimal IV in finite samples under weak identification and strictly exogenous instruments. In an application with quarterly UK data IIV estimates a positive and significant elasticity of intertemporal substitution and an equally sensible estimate for its reciprocal, in contrast to IV methods that fail to identify these parameters