Improving the robustness and efficiency of covariate-adjusted linear instrumental variable estimators

Proposition Two-stage least squares estimators and variants thereof are widely used to infer the effect of an exposure on an outcome using instrumental variables (IVs). Two-stage least squares estimators enjoy greater robustness to model misspecification than other two-stage estimators but can be inefficient when the exposure is non-linearly related to the IV (or covariates). Locally efficient double-robust estimators overcome this concern. These make use of a possibly non-linear model for the exposure to increase efficiency but remain consistent when that model is misspecified, so long as either a model for the IV or for the outcome model is correctly specified. However, their finite sample performance can be poor when the models for the IV, exposure, and/or outcome are misspecified. We therefore develop double-robust procedures with improved efficiency and robustness properties under misspecification of some or even all working models. Simulation studies and a data analysis demonstrate remarkable improvements.