Quantile regression estimands and models: revisiting the motherhood wage penalty debate

Abstract

This paper discusses the crucial but sometimes neglected differences between unconditional quantile regression (UQR) models and quantile treatment effects (QTE) models. We argue that there is a frequent mismatch between the aim of the quantile regression analysis and the quantitative toolkit used in much of the applied literature, including the motherhood wage penalty literature. This mismatch may result in wrong conclusions being drawn from the data, and in the end, misguided theories. In this paper, we clarify the crucial conceptual distinction between influences on quantiles of the overall distributions, which we term population-level influences, and individual-level QTEs. Further, we use data simulations to illustrate that various classes of quantile regression models may, in some instances, give entirely different conclusions (to different questions). Finally, we compare quantile regression estimates using real data examples, showing that UQR and QTE models differ sometimes but not always. Still, the conceptual and empirical distinctions between quantile regression models underline the need to match the correct model to the specific research questions. We conclude the paper with a few practical guidelines for researchers.

The association between cognitive ability and body mass index: A sibling-comparison analysis in four longitudinal studies

“…Next, we examined the association between cognitive ability and BMI across the distribution of BMI using RQR [ 49 ]. Unlike standard conditional quantile regression [ 56 ], RQR allows for the inclusion of (family) fixed effects in quantile regression models while retaining clear interpretability [ 57 ], a necessity here given we have more than one observation per family. RQR involves two steps.…”

Who Profits from Occupational Licensing?

“…Thus, in this case, UQR estimates how the overall wage distribution would change if all employees received the licensing wage premium (Rios-Avila and Maroto 2022). This influence is not only a function of the licensing premium but also of the share of unlicensed employees at different parts of the distribution and the shape of the unconditional wage distribution (Borgen, Haupt, and Wiborg 2023). The estimand for this article is the outcome difference between employees, which we expect to observe at the same point of the wage distribution in absence of a licensing premium.…”

The Association between Education and Cognitive Performance Varies at Different Levels of Cognitive Performance: A Quantile Regression Approach

“…We used conditional quantile regression (CQR) to estimate the association between education and cognitive performance at different percentiles of the cognitive performance distribution. This method is appropriate for exploring whether the effect of interest is uniform or varies across the conditional outcome distribution [ 29 , 30 ]. The statistical models were estimated using the quantreg package version 5.95 for R. In all regression models, the continuous education variable described above was used.…”