Detecting Heterogeneous Treatment Effect with Instrumental Variables

Abstract: 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.