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

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.