性别工资差距中的分位数选择

Quantile selection in the gender paygap Egshiglen Batbayar, Christoph Breunig,Peter Haan, Boryana Ilieva 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 semiparametricidentification of the quantile parameters without imposing parametric restrictions on theselection probability, derive the asymptotic distribution of the proposed estimator basedon constrained selection probability weighting, and demonstrate how the approach appliesto the Roy model of labor supply.Using German administrative data, we analyze thedistribution of the gender gap in full-time earnings. We find pronounced positive selectionamong women at the lower end, especially those with less education, which widens thegender gap in this segment, and strong positive selection among highly educated men atthe top, which narrows the gender wage gap at upper quantiles. JEL codes:C14, C21, J16, J21, J31Keywords:Endogenous sample attrition, instrumental variables, inverse probability weighting,semi-parametric inference, wage inequality Nontechnical Summary This paper studies how selection into full-time employment affects estimates of the genderwage gap across the wage distribution.While many studies compare wages only amongthose who are observed working full-time, employment itself is not random:individualswith higher earning potential are more likely to work full-time. If this selection is ignored,measured wage gaps can be misleading, and the bias may differ across low, middle, andhigh earners. The paper develops a new method to estimate wage differences at different points ofthe wage distribution while accounting for non-random selection into employment.Theapproach uses an instrumental variable that affects potential wages but, once potentialwages and observed characteristics are held fixed, does not directly influence the employmentdecision.Under this condition, the method identifies wage quantiles without imposing aspecific functional form on how selection depends on unobserved factors.Estimation isbased on inverse probability weighting combined with quantile regression, with selectionprobabilities estimated flexibly rather than through a parametric selection model. The method is applied to German administrative data that track detailed employmentand earnings histories. Early-career wages are used as the instrument, capturing persistentindividual characteristics that shape long-run earning potential. The results show positiveselection into full-time employment for both women and men, meaning that observed full-time workers tend to have higher potential wages than those not working full-time. Selectionis particularly strong for women at the lower end of the wage distribution and for highlyeducated men at the top. After correcting for selection, estimated wages are lower than observed wages, especiallyfor lower-paid women.As a result, the gender wage gap increases at lower quantiles butis slightly smaller at higher quantiles, particularly among highly educated workers. Thesefindings highlight that selection into employment varies across groups and across the wagedistribution, and that accounting for this heterogeneity is essential for understanding howgender wage differences are distributed. 1Introduction In all countries, men continue to earn higher wages than women. Crucially, the gender wagegap spans the entire wage distribution and affects all educational groups (e.g., Goldin [2014],Blau and Kahn [2017], Olivetti et al. [2024]). To meaningfully quantify and analyze this gap,it is essential to account not only for gender differences in observable characteristics such aseducation and labor market experience, but also differences in selection into employment.The impact of selection on the gender wage gap is ambiguous and depends on the signand magnitude of gender-specific selection patterns (see, e.g., Mulligan and Rubinstein[2008], Arellano and Bonhomme [2017], or Blau et al. [2024]).Understanding why menconsistently out-earn women and designing policies to address this disparity requires tacklingthe challenging task of identifying and quantifying the role of employment selection inshaping the wage distribution, and of deriving a selection-corrected measure of the genderwage gap distribution. In this paper, we propose a new strategy to derive the selection-corrected wage distri-bution and to quantify the full distribution of the gender wage gap. Identification relies onexogenous variation that affects latent wages but, conditional on the latent wages and otherobserved variables, provides no additional information on the selection mechanism. In thecontext of a Roy model [Roy, 1951], as applied to labor supply decisions by Gronau [1974]and Heckman [1974], where individuals choose to work if their potential wage exceed