Victor Chernozhukov, Ivan Fernandez-Val, Ye Luo
arXiv 17 Dec 2015 · Statistics — Methodology · publishedEconometrica (2018) · 81 citations (OpenAlex)
arXiv:1512.05635 · PDF · DOI · OpenAlex · Extracted main text
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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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | van der Vaart and Wellner (1996) Weak Convergence and Empirical Processes | 0.794 | 10 | 6 | 50% |
| 2 | Chernozhukov, Fernández-Val, and Galichon (2009) Improving point and interval estimators of monotone functions by rearrangement | 0.644 | 3 | 2 | 67% |
| 3 | List, Shaikh, and Xu (2016) Multiple hypothesis testing in experimental economics | 0.644 | 2 | 2 | 100% |
| 4 | Spivak (1965) Calculus on manifolds. A modern approach to classical theorems of advanced calculus | 0.585 | 4 | 3 | 25% |
| 5 | van der Vaart (1998) Asymptotic Statistics | 0.585 | 3 | 3 | 33% |
| 6 | Chernozhukov, Kocatulum, and Menzel (2015) Inference on sets in finance | 0.585 | 3 | 1 | 100% |
| 7 | Chernozhukov, Fernández-Val, and Galichon (2010) Quantile and probability curves without crossing | 0.511 | 2 | 2 | 50% |
| 8 | Blau and Kahn (2017) The Gender Wage Gap: Extent, Trends, and Explanations | 0.511 | 2 | 1 | 100% |
| 9 | Chernozhukov, Hong, and Tamer (2007) Estimation and Inference on Identified Parameter Sets in Econometric Models | 0.511 | 2 | 1 | 100% |
| 10 | Oaxaca (1973) Male-Female Wage Differentials in Urban Labor Markets | 0.511 | 2 | 1 | 100% |
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