  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.
