On falsification of the binary instrumental variable model

TL;DR

This paper develops formal statistical tests for the validity of binary instrumental variable models, addressing a gap where current assessments rely mainly on subject-matter arguments.

Contribution

It introduces simple procedures based on existing treatment comparison tests to evaluate instrumental variable validity with known statistical properties.

Findings

Proposed tests can effectively falsify invalid instruments.

Application to college proximity data demonstrates practical utility.

Highlights importance of formal testing over subjective assessments.

Abstract

Instrumental variables are widely used for estimating causal effects in the presence of unmeasured confounding. The discrete instrumental variable model has testable implications on the law of the observed data. However, current assessments of instrumental validity are typically based solely on subject-matter arguments rather than these testable implications, partly due to a lack of formal statistical tests with known properties. In this paper, we develop simple procedures for testing the binary instrumental variable model. Our methods are based on existing approaches for comparing two treatments, such as the t-test and the Gail--Simon test. We illustrate the importance of testing the instrumental variable model by evaluating the exogeneity of college proximity using the National Longitudinal Survey of Young Men.