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 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.