  There is an increasing interest in estimating heterogeneity in causal effects
in randomized and observational studies. However, little research has been
conducted to understand heterogeneity in an instrumental variables study. In
this work, we present a method to estimate heterogeneous causal effects using
an instrumental variable approach. The method has two parts. The first part
uses subject-matter knowledge and interpretable machine learning techniques,
such as classification and regression trees, to discover potential effect
modifiers. The second part uses closed testing to test for the statistical
significance of the effect modifiers while strongly controlling familywise
error rate. We conducted this method on the Oregon Health Insurance Experiment,
estimating the effect of Medicaid on the number of days an individual's health
does not impede their usual activities, and found evidence of heterogeneity in
older men who prefer English and don't self-identify as Asian and younger
individuals who have at most a high school diploma or GED and prefer English.
