Measurement errors in the binary instrumental variable model

2019/06/05 by Zhichao Jiang, Peng Ding, Jiang, Zhichao +1 · 1 citation
Mathematics · #Advanced Causal Inference Techniques #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Methods and Bayesian Inference #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.1906.02030

openalex publication_date 2019/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 or outcome. We first consider non-differential measurement errors, that is, the mis-measured 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, the measurement error of the treatment biases the estimate away from zero, and 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.

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