Instrumental variables are widely used for estimating causal effects in thepresence of unmeasured confounding. The discrete instrumental variable modelhas testable implications on the law of the observed data. However, currentassessments of instrumental validity are typically based solely onsubject-matter arguments rather than these testable implications, partly due toa lack of formal statistical tests with known properties. In this paper, wedevelop simple procedures for testing the binary instrumental variable model.Our methods are based on existing approaches for comparing two treatments, suchas the t-test and the Gail--Simon test. We illustrate the importance of testingthe instrumental variable model by evaluating the exogeneity of collegeproximity using the National Longitudinal Survey of Young Men.
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