Journal article: We propose an assignment model in which positions along a hierarchy are attributed to individuals depending on their characteristics. Our theoretical framework can be used to study differences in assignment and pay-offs across groups and we show how it can motivate decomposition and counterfactual exercises. In an application, we study gender disparities in the public and private sectors with a French exhaustive administrative dataset. The gender wage gap in the public sector is 13.3% and it increases by only 0.7 percentage points when workers are assigned to job positions according to the rules of the private sector.