Partial Identification with Auxiliary Moment Restrictions
辅助矩约束下的部分识别AI 解读 ↓
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辅助矩约束下的部分识别
- 研究问题
- 当结果变量仅以区间报告时，如何利用同一数据管理方发布的准确总体汇总信息，收紧最佳线性预测参数的部分识别区域？
- 方法与思路
- 作者保留原有结果区间，改为限制与已知总体汇总一致的数据补全集合，刻画锐识别区域及不同辅助矩约束的几何作用。
- 材料陈述的贡献
- 摘要称部分约束可使识别区域降维，其他约束仅缩小区域，并给出均值和条件均值信息的方向性识别价值及工资数据示例。
- 阅读关注点
- 应核对辅助总体矩是否准确且与样本口径一致、补全集合与锐界的构造，以及约束几何变化和识别价值度量的适用条件。
- 阅读边界
- 这是 arXiv 预印本，同行评审或期刊接收未经核实；利用准确汇总是新增信息，摘要未说明汇总有误差或口径不一致时如何处理。
原文摘要
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.