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摘要翻译：
非线性和交互式线性模型中感兴趣的部分（ceteris paribus）效应是不均匀的，因为它们可以随着潜在的观察到或未观察到的协变量而急剧变化。尽管异质性显然很重要，但在现代经验研究中，一种常见的做法是通过报告平均部分效应（或者，充其量是某些群体的平均效应）来忽略它。虽然平均效应提供了典型效应的非常方便的标量总结，但根据定义，它们不能反映异质效应的全部变化。为了更充分地发现这些效应，我们建议估计和报告排序效应--按递增顺序排序并按百分位数索引的估计部分效应的集合。通过构造排序的效应曲线，完整地表示并帮助可视化异质效应在一个图中的范围。在实际应用中，它们与传统的平均部分效应一样方便和容易报告。它们也作为分类分析的基础，在分类分析中，我们将观察单元划分为受影响最大或最小的组，并总结它们的特征。我们为估计的排序效果和相关的分类分析提供了不确定度（标准误差和置信带）的量化，并为受影响最大和最小的组提供了置信集。所导出的统计结果依赖于建立关键，关于一个多元排序算子和一个相关分类算子的Hadamard可微性的新数学结果，这些结果是独立感兴趣的。本文运用排序效应法和分类分析方法，论证了性别工资差距的几种显著模式。
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英文标题：
《The Sorted Effects Method: Discovering Heterogeneous Effects Beyond
Their Averages》
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作者：
Victor Chernozhukov, Ivan Fernandez-Val, and Ye Luo
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最新提交年份：
2018
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分类信息：
一级分类：Statistics 统计学
二级分类：Methodology 方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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一级分类：Economics 经济学
二级分类：Econometrics 计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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英文摘要：
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.
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PDF链接：
https://arxiv.org/pdf/1512.05635
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