  Instrumental variables have been widely used to estimate the causal effect of
a treatment on an outcome. Existing confidence intervals for causal effects
based on instrumental variables assume that all of the putative instrumental
variables are valid; a valid instrumental variable is a variable that affects
the outcome only by affecting the treatment and is not related to unmeasured
confounders. However, in practice, some of the putative instrumental variables
are likely to be invalid. This paper presents a simple and general approach to
construct a confidence interval that is robust to possibly invalid instruments.
The robust confidence interval has theoretical guarantees on having the correct
coverage and can also be used to assess the sensitivity of inference when
instrumental variables assumptions are violated. The paper also shows that the
robust confidence interval outperforms traditional confidence intervals popular
in instrumental variables literature when invalid instruments are present. The
new approach is applied to a developmental economics study of the causal effect
of income on food expenditures.
