We study the external validity of instrumental variable estimation. The key assumption we impose for external validity is conditional external unconfoundedness among compliers, which means that the treatment effect and target selection are independent among compliers conditional on covariates. We study this assumption with a case study about the impact of solid-fuel usage on women's average cooking time. Among the six countries examined, we find no statistical evidence that the assumptions required for external validity are violated for four countries (Ethiopia, Honduras, Kenya, and Zambia), but in Cambodia and Nepal, we find low external validity. These results provide suggestive evidence that the assumptions required for external validity are violated for these two countries.