## 12.28金融系Seminar：THE SORTED EFFECTS METHOD: DISCOVERING HETEROGENEOUS EFFECTS BEYOND THEIR AVERAGES发布日期： 2016-12-19  浏览次数：

罗晔，MIT经济系2015年博士，2005年第45届国际奥林匹克数学竞赛满分金牌得主，其导师是天才经济学家HAUSMAN和CHERNOZHUKOV教授，现为佛罗里达大学经济系助理教授，研究领域是计量经济学、金融经济学和国际经济学。有2篇论文即将在Econometrica上发表，另5篇投在国际顶尖和一流期刊的论文正在修改之中。担任Econometrica, Journal of Econometrics等6家国际一流学术期刊的匿名评审人。

【Abstract】
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, see e.g., Angrist and Pischke (2008)). While average effects provide very convenient scalar summaries of typical effects, by definition they fail to reflect the entire variety of the heterogenous 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 all of the heterogeneous effects in one plot. They are as convenient and easy to report in practice as the conventional average partial effects. We also provide a quantification of uncertainty (standard errors and confidence bands) for the estimated sorted effects. We apply the sorted effects method to demonstrate several striking patterns of gender-based discrimination in wages, and of race-based discrimination in mortgage lending.

Using differential geometry and functional delta methods, we establish that the estimated sorted effects are consistent for the true sorted effects, and derive symptotic normality and bootstrap approximation results, enabling construction of pointwise confidence bands (point-wise with respect to percentile indices). We also derive functional central limit theorems and bootstrap approximation results, enabling construction of simultaneous confidence bands (simultaneous with respect to percentile indices). The derived statistical results in turn rely on establishing Hadamard differentiability of a multivariate sorting operator, a result of independent mathematical interest.

Keywords: Sorting, Partial Effect, Marginal Effect, Sorted Percentiles, Nonlinear Model, Functional Analysis, Differential Geometry.