Quantile Selection in the Gender Pay Gap

TL;DR

This paper tackles the distributional gender wage gap under nonignorable selection into employment. It introduces a semiparametric IV-based selection-correction method that identifies quantile effects by weighting outcomes with inverse selection probabilities, where the instrument shifts latent wages $Y^*$ but does not affect selection given $(Y^*,X)$. The approach bridges inverse probability weighting with a Roy framework via rank invariance, and provides nonparametric or semi-parametric identification and inference, including Monte Carlo validation. Empirically, using German SIAB data and an initial wage instrument, the authors find strong positive selection into full-time work among women, especially at the lower quantiles, and significant selection among highly educated men at the top, implying distributional shifts in the gender wage gap once selection is accounted for. These results underscore the importance of accounting for nonignorable selection in distributional wage analyses and offer a robust tool for policy evaluation of gender inequality across the wage distribution.

Abstract

We propose a new approach to estimate selection-corrected quantiles of the gender wage gap. Our method employs instrumental variables that explain variation in the latent variable but, conditional on the latent process, do not directly affect selection. We provide semiparametric identification of the quantile parameters without imposing parametric restrictions on the selection probability, derive the asymptotic distribution of the proposed estimator based on constrained selection probability weighting, and demonstrate how the approach applies to the Roy model of labor supply. Using German administrative data, we analyze the distribution of the gender gap in full-time earnings. We find pronounced positive selection among women at the lower end, especially those with less education, which widens the gender gap in this segment, and strong positive selection among highly educated men at the top, which narrows the gender wage gap at upper quantiles.

Figures (8)

• Figure 1: Years of initial wages
• Figure 2: Quantile Selection Effects (Unconditional)
• Figure 3: Conditional wage quantiles by education groups
• Figure C.1: Empirical and selection-corrected distributions by gender
• Figure E.1: Quantile Selection Effects (Unconditional) -- only IV up to 2011

Theorems & Definitions (8)

• Proposition 2.1
• Theorem 2.2
• Corollary 2.3
• Theorem 3.1
• proof : Proof of Proposition \ref{['lem:identification']}
• proof : Proof of Theorem \ref{['prop:1']}
• proof : Proof of Corollary \ref{['coro:roy_model']}
• proof : Proof of Theorem \ref{['thm:asymptotic_normality']}