Causal Inference for Nonlinear Outcome Models with Possibly Invalid Instrumental Variables

Abstract: Instrumental variable methods are widely used for inferring the causal effect in the presence of unmeasured confounders. Existing instrumental variable methods for nonlinear outcome models require stringent identifiability conditions. This paper considers a flexible semi-parametric potential outcome model that allows for possibly invalid instruments. We propose new identifiability conditions to identify the causal parameters when the majority of the instrumental variables are valid. We devise a novel inference procedure for a new average structural function and the conditional average treatment effect. We establish the asymptotic normality of the proposed estimators and construct confidence intervals for the causal estimands by bootstrap. The proposed method is demonstrated in large-scale simulation studies and is applied to infer the effect of income on house ownership.