An important concern in an observational study is whether or not there is unmeasured confounding, that is, unmeasured ways in which the treatment and control groups differ before treatment, which affect the outcome. We develop a test of whether there is unmeasured confounding when an instrumental variable (IV) is available. An IV is a variable that is independent of the unmeasured confounding and encourages a subject to take one treatment level versus another, while having no effect on the outcome beyond its encouragement of a certain treatment level. We show what types of unmeasured confounding can be tested for with an IV and develop a test for this type of unmeasured confounding that has correct type I error rate. We show that the widely used Durbin–Wu–Hausman test can have inflated type I error rates when there is treatment effect heterogeneity. Additionally, we show that our test provides more insight into the nature of the unmeasured confounding than the Durbin–Wu–Hausman test. We apply our test to an observational study of the effect of a premature infant being delivered in a high-level neonatal intensive care unit (one with mechanical assisted ventilation and high volume) versus a lower level unit, using the excess travel time a mother lives from the nearest high-level unit to the nearest lower-level unit as an IV.