Robust, accurate confidence intervals with a weak instrument: quarter of birth and education
Robust, accurate confidence intervals with a weak instrument: quarter of birth and education
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DOI：
10.1111/j.1467-985x.2004.00339.x
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发表时间：
2005-01-01
影响因子：
2
通讯作者：
Rosenbaum, PR
中科院分区：
文献类型：
--
作者：
Imbens, GW;Rosenbaum, PR
工具或工具变量操纵治疗，仅通过其对治疗的操纵间接影响结果。例如，鼓励锻炼可能会增加心血管健康，但只是间接地增加锻炼。如果仪器水平被随机分配给个体，那么仪器可能允许对治疗引起的效应进行一致的估计，即使治疗分配本身远非随机。例如，我们可以进行一项随机实验，将一些受试者分配给“鼓励锻炼”，另一些受试者分配给“不鼓励”，但是由于习惯或口味的原因，一些受试者在受到鼓励时不会锻炼，而另一些受试者在没有鼓励的情况下会锻炼;尽管如此，这种工具有助于估计锻炼的效果。弱的工具，即对治疗只有轻微影响的工具，存在推理问题。我们以四种方式评估最近提出的使用工具变量进行置换推理的建议：使用Angrist和Krueger关于教育对收入影响的数据，使用出生季度作为工具，遵循Bound，Jaeger和Baker使用模拟独立观察代替Angrist和Krueger数据中的工具，使用完全模拟的数据，其中正确的答案是已知的，最后使用统计理论来表明，只有置换推理保持正确的覆盖率。置换推理在简单和困难的情况下，弱工具，以及与长尾响应表现良好。
An instrument or instrumental variable manipulates a treatment and affects the outcome only indirectly through its manipulation of the treatment. For instance, encouragement to exercise might increase cardiovascular fitness, but only indirectly to the extent that it increases exercise. If instrument levels are randomly assigned to individuals, then the instrument may permit consistent estimation of the effects caused by the treatment, even though the treatment assignment itself is far from random. For instance, one can conduct a randomized experiment assigning some subjects to 'encouragement to exercise' and others to 'no encouragement' but, for reasons of habit or taste, some subjects will not exercise when encouraged and others will exercise without encouragement; none-the-less, such an instrument aids in estimating the effect of exercise. Instruments that are weak, i.e. instruments that have only a slight effect on the treatment, present inferential problems. We evaluate a recent proposal for permutation inference with an instrumental variable in four ways: using Angrist and Krueger's data on the effects of education on earnings using quarter of birth as an instrument, following Bound, Jaeger and Baker in using simulated independent observations in place of the instrument in Angrist and Krueger's data, using entirely simulated data in which correct answers are known and finally using statistical theory to show that only permutation inferences maintain correct coverage rates. The permutation inferences perform well in both easy and hard cases, with weak instruments, as well as with long-tailed responses.