The Sorted Effects Method: Discovering Heterogeneous Effects Beyond Their Averages

Victor Chernozhukov, Iván Fernández‐Val and Ye Luo
Authors registered in the RePEc Author Service: Ivan Fernandez-Val ()

Econometrica, 2018, vol. 86, issue 6, 1911-1938

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). 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. We find that this gap is particularly strong for married women, ranging from −60% to 0% between the 2% and 98% percentiles, as a function of observed and unobserved characteristics; while the gap for never married women ranges from −40% to +20%. The most adversely affected women tend to be married, do not have college degrees, work in sales, and have high levels of potential experience.

Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (47)

Downloads: (external link)
https://doi.org/10.3982/ECTA14415

Related works:
Working Paper: The Sorted Effects Method: Discovering Heterogeneous Effects Beyond Their Averages (2018)
Working Paper: The sorted effects method: discovering heterogeneous effects beyond their averages (2015)
Working Paper: The sorted effects method: discovering heterogeneous effects beyond their averages (2015)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wly:emetrp:v:86:y:2018:i:6:p:1911-1938

Ordering information: This journal article can be ordered from
https://www.economet ... ordering-back-issues

Access Statistics for this article

Econometrica is currently edited by Guido W. Imbens

More articles in Econometrica from Econometric Society Contact information at EDIRC.
Bibliographic data for series maintained by Wiley Content Delivery ().