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.

中文翻译：

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二元工具变量模型中的测量误差

即使在治疗和结果混杂的情况下，工具变量方法也可以识别因果效应。我们研究二元工具变量、治疗或结果的不完美测量问题。我们首先考虑非微分测量误差，即误测变量不依赖于其他变量给出其真实值。我们表明，工具变量的测量误差不会使估计产生偏差，处理的测量误差使估计偏离零，结果的测量误差使估计偏向于零。此外，我们在没有额外假设的情况下得出因果效应的明确界限。这些界限是有用的，因为它们不包括零。然后我们考虑差分测量误差，并专注于这些设置中的灵敏度分析。