We propose a job assignment model with individual heterogeneity and derive a measure of gender differences in the propensity to get job positions along the wage distribution. This measure is used to quantify gender disparities in the public and private sectors with a French exhaustive administrative dataset. We then show how the model can motivate decomposition and counterfactual exercises consistent with economic theory. Our approach constitutes an alternative to more descriptive methods such as Oaxaca decompositions and quantile counterfactual approaches. Gender differences in the propensity to get jobs along the wage distribution are found to be rather similar in the public and private sectors, although the gap is slightly larger in the public sector in the 0:5 – 0:85 rank interval (and slightly smaller at ranks above 0:85). The overall contribution of observables to explaining gender differences is small in the two sectors except for ranks below 0:5 in the public sector. Long part-time experience is the only factor with a sizable explanatory power. The gender wage gap in the public sector increases by only 0:7 points when workers are assigned to jobs according to the rules of the private sector, but the gender quantile gap at the last decile is significantly larger by 4:6 points.