The Sorted Effects Method: Discovering Heterogeneous Effects Beyond Their Averages
排序效应法：发现平均值之外的异质效应AI 解读 ↓
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排序效应法：发现平均值之外的异质效应
- 研究问题
- 当偏效应随协变量显著变化时，如何超越平均效应展示其完整分布，并描述受影响最多和最少群体的特征？
- 方法与思路
- 作者将估计偏效应按大小排序并以百分位索引，构造分类分析，并借助排序及分类算子的可微性发展推断。
- 材料陈述的贡献
- 摘要称提供排序效应的标准误和置信带、分类分析的不确定性量化及极端受影响群体的置信集合，并应用于性别工资差距。
- 阅读关注点
- 应核对偏效应的定义与识别、排序所用总体分布、算子可微性条件，以及群体选择与分类推断如何处理估计误差。
- 阅读边界
- 所给版本为 arXiv 预印本，同行评审及期刊接收未核实；摘要未说明应用的因果识别，排序偏效应不能自动解释为因果效应。
原文摘要
The partial (ceteris paribus) effects of interest in nonlinear and interactive linear models are heterogeneous as they can vary dramatically with the underlying observed or unobserved covariates. Despite the apparent importance of heterogeneity, a common practice in modern empirical work is to largely ignore it by reporting average partial effects (or, at best, average effects for some groups). While average effects provide very convenient scalar summaries of typical effects, by definition they fail to reflect the entire variety of the heterogeneous effects. In order to discover these effects much more fully, we propose to estimate and report sorted effects -- a collection of estimated partial effects sorted in increasing order and indexed by percentiles. By construction the sorted effect curves completely represent and help visualize the range of the heterogeneous effects in one plot. They are as convenient and easy to report in practice as the conventional average partial effects. They also serve as a basis for classification analysis, where we divide the observational units into most or least affected groups and summarize their characteristics. We provide a quantification of uncertainty (standard errors and confidence bands) for the estimated sorted effects and related classification analysis, and provide confidence sets for the most and least affected groups. The derived statistical results rely on establishing key, new mathematical results on Hadamard differentiability of a multivariate sorting operator and a related classification operator, which are of independent interest. We apply the sorted effects method and classification analysis to demonstrate several striking patterns in the gender wage gap.