Inference After Ranking with Applications to Economic Mobility
排序后的统计推断及其在经济流动性研究中的应用AI 解读 ↓
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排序后的统计推断及其在经济流动性研究中的应用
- 研究问题
- 当研究对象因估计效应、增加值或净收益的排名落入预设区间而被选中时，如何校正选择带来的偏差并构造有效统计推断？
- 方法与思路
- 作者提出两步推断方法，先在正态位置模型下证明有限样本有效性，再在弱一致可积条件下建立允许极限协方差退化的统一渐近结果。
- 材料陈述的贡献
- 摘要称框架将单一赢家推断扩展到排名区间选择；经济流动性应用显示，校正选择后较难区分高流动性与低流动性的普查区。
- 阅读关注点
- 应核对排名规则、并列排名处理、两步方法的校准及推断对象，并检查统一有效性的分布范围和协方差退化时的具体实现。
- 阅读边界
- 这是 arXiv 预印本，同行评审及期刊接收未核实。摘要未给出区间宽度或比较数值，应用中的难以区分不能解释为流动性完全相同。
原文摘要
This paper considers the problem of inference after ranking. In our setting, we are interested in any population whose rank according to some random quantity, such as an estimated treatment effect, a measure of value-added, or benefit (net of cost), falls in a pre-specified range of values. As such, this framework generalizes the inference on winners setting previously considered in Andrews et al. (2023), in which a winner is understood to be the single population whose rank according to some random quantity is highest. We show that this richer setting accommodates a broad variety of empirically-relevant applications. We develop a two-step method for inference, which we compare to existing methods or their natural generalizations to this setting. We first show the finite-sample validity of this method in a normal location model and then develop asymptotic counterparts to these results by proving uniform validity over a large class of distributions satisfying a weak uniform integrability condition. Importantly, our results permit degeneracy in the covariance matrix of the limiting distribution, which arises naturally in many applications. In an application to the literature on economic mobility, we find that it is difficult to distinguish between high and low-mobility census tracts when correcting for selection. Finally, we demonstrate the practical relevance of our theoretical results through an extensive set of simulations.