Measurement errors in the binary instrumental variable model. (21st November 2019)

• Record Type: Journal Article
• Authors: Jiang, Zhichao; Ding, Peng
• Is Part Of: Biometrika. Volume 107:Number 1(2020:Mar.)
• Page Start: 238
• Page End: 245
• Publication Date: 2019-11-21
• Subjects: Complier average causal effect -- Misclassification -- Noncompliance -- Sensitivity analysis -- Sharp bound; Biometry -- Periodicals; 570.1519505
• DOI: 10.1093/biomet/asz060
• Languages: English
• ISSNs: 0006-3444

Abstract

Summary: Instrumental variable methods can identify causal effects even when the treatment and outcome are confounded. We study the problem of imperfect measurements of the binary instrumental variable, treatment and outcome. We first consider nondifferential measurement errors, that is, the mismeasured variable does not depend on other variables given its true value. We show that the measurement error of the instrumental variable does not bias the estimate, that the measurement error of the treatment biases the estimate away from zero, and that the measurement error of the outcome biases the estimate toward zero. Moreover, we derive sharp bounds on the causal effects without additional assumptions. These bounds are informative because they exclude zero. We then consider differential measurement errors, and focus on sensitivity analyses in those settings.