Quantile regression (QR) provides an alternative to linear regression (LR) that allows for the estimation of relationships across the distribution of an outcome. However, as highlighted in recent research on the motherhood penalty across the wage distribution, different procedures for conditional and unconditional quantile regression (CQR, UQR) often result in divergent findings that are not always well understood. In light of such discrepancies, this paper reviews how to implement and interpret a range of LR, CQR, and UQR models with fixed effects. It also discusses the use of Quantile Treatment Effect (QTE) models as an alternative to overcome some of the limitations of CQR and UQR models. We then review how to interpret results in the presence of fixed effects based on a replication of Budig and Hodges’s work on the motherhood penalty using NLSY79 data.

分位数回归 (QR) 提供了线性回归 (LR) 的替代方案，允许估计跨结果分布的关系。然而，正如最近关于工资分布中孕产惩罚的研究中所强调的那样，有条件和无条件分位数回归（CQR、UQR）的不同程序通常会导致不同的结果，这些结果并不总是很好理解。鉴于这些差异，本文回顾了如何实现和解释一系列具有固定效应的 LR、CQR 和 UQR 模型。它还讨论了使用分位数处理效应 (QTE) 模型作为克服 CQR 和 UQR 模型的一些限制的替代方案。