Finding the strength in a weak instrument in a study of cognitive outcomes produced by Catholic high schools
Finding the strength in a weak instrument in a study of cognitive outcomes produced by Catholic high schools
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在天主教高中认知结果的研究中寻找薄弱工具的优势
DOI：
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发表时间：
2020
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影响因子：
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通讯作者：
P. Rosenbaum
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作者：
Siyu Heng;Dylan S. Small;P. Rosenbaum
我们表明，一个工具的强度是不完全的特点是由编译器的比例，我们提出和评估新的方法，从某些设置中提取更多的信息，相对较少的编译器。具体来说，我们证明，对于一个固定的小比例的顺从者，存在相同数量的总是接受者和从不接受者会削弱一个工具，而没有总是接受者，或者等价地，没有从不接受者会加强一个工具。在这个陈述中，工具的强度是指它识别和拒绝关于结构参数的错误假设的能力。同样，工具的强度是指其从置信区间中排除结构参数假值的能力。这种能力是通过假设仪器是无缺陷的测试的巴哈杜尔效率或假设仪器可能有点偏差的灵敏度分析的巴哈杜尔效率来衡量的。当遵从者很少时，大多数人的结果不受仪器波动的影响，因此关于治疗效果的大部分信息包含在结果分布的尾部。利用这一事实，我们提出了新的方法，强调结果分布的受影响的部分，从而从研究中提取更多的信息与少数服从者。天主教高中对学术测试成绩的影响的研究使用“天主教”作为“参加天主教高中”的工具，应用程序涉及使用美国国家教育纵向研究的比较。大多数天主教徒没有参加天主教学校，所以很少有编译器，但它是罕见的非天主教徒参加天主教学校，所以有很少总是takers。
We show that the strength of an instrument is incompletely characterized by the proportion of compliers, and we propose and evaluate new methods that extract more information from certain settings with comparatively few compliers. Specifically, we demonstrate that, for a fixed small proportion of compliers, the presence of an equal number of always‐takers and never‐takers weakens an instrument, whereas the absence of always‐takers or, equivalently, the absence of never‐takers strengthens an instrument. In this statement, the strength of an instrument refers to its ability to recognize and reject a false hypothesis about a structural parameter. Equivalently, the strength of an instrument refers to its ability to exclude from a confidence interval a false value of a structural parameter. This ability is measured by the Bahadur efficiency of a test that assumes that the instrument is flawless, or the Bahadur efficiency of a sensitivity analysis that assumes that the instrument may be somewhat biased. When there are few compliers, the outcomes for most people are unaffected by fluctuations in the instrument, so most of the information about the treatment effect is contained in the tail of the distribution of the outcomes. Exploiting this fact, we propose new methods that emphasize the affected portion of the distribution of outcomes, thereby extracting more information from studies with few compliers. Studies of the effects of Catholic high schools on academic test performance have used ‘being Catholic’ as an instrument for ‘attending a Catholic high school’, and the application concerns such a comparison using the US National Educational Longitudinal Study. Most Catholics did not attend Catholic school, so there are few compliers, but it was rare for non‐Catholics to attend Catholic school, so there are very few always‐takers.