具有辅助矩限制的部分识别
Partial Identification with Auxiliary Moment Restrictions
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中文总结 AI 辅助
研究指出部分识别因区域宽而常被搁置，利用多数区间值数据集中已有信息，开发框架限制数据补全集，刻画最佳线性预测器识别区域，不同限制效果不同，能恢复粗化结果丢失的部分识别能力。
中文摘要 AI 辅助
在实践中，部分识别往往被搁置，因为其给出的识别区域过宽而无用，这促使研究人员采用以可信度为代价换取点识别的强假设。我们表明，大多数区间值数据集中已有的信息源可以解决这个问题，而无需添加任何假设。当结果仅报告为一个区间时，数据保管人通常会继续发布该结果的准确总体汇总。我们开发了一个利用此信息的框架：将数据的可允许补全集限制为与已知汇总一致的那些，而不是限制区间本身，并刻画最佳线性预测器的精确识别区域。我们研究的限制行为方式截然不同，有些使区域缩小一整个维度，有些则在保持形状不变的情况下使其变窄。我们刻画了每个限制的几何效应，并推导了均值和条件均值情况下识别值的封闭形式方向度量。使用当前人口调查的区间值工资进行的说明表明，这种效应远非微不足道：适度的辅助信息可以恢复一旦结果被粗化通常认为会丢失的大部分识别能力。
英文摘要
Partial identification is often set aside in practice because the identification regions it delivers are too wide to be useful, pushing researchers toward strong assumptions that buy point identification at the cost of credibility. We show that a source of information already sitting in most interval-valued datasets can fix this without adding any assumption at all. When an outcome is reported only as an interval---because a data custodian bracketed, top-coded, or formally privatized it to protect respondents---the same custodian typically continues to publish accurate population aggregates of that outcome, precisely because doing so does not compromise any individual record. We develop a framework for exploiting exactly this information: restricting the set of admissible completions of the data to those consistent with a known aggregate, rather than restricting the interval itself, and characterizing the sharp identification region that results for the best linear predictor. The restrictions we study behave in strikingly different ways---some collapse the region by a full dimension, others narrow it while leaving its shape intact. We characterize the geometric effect of each restriction and derive closed-form directional measures of identifying value for the mean and conditional-mean cases. An illustration using interval-valued wages from the Current Population Survey shows that the effect is far from marginal: modest auxiliary information recovers a substantial share of the identifying power usually thought to be lost once an outcome is coarsened.
