In this paper, we propose a job assignment model allowing for a gender difference in access to jobs. Males and females compete for the same job positions. They are primarily interested in the best-paid jobs. A structural relationship of the model can be used to empirically recover the probability ratio of females and males getting a given job position. As this ratio is allowed to vary with the rank of jobs in the wage distribution of positions, barriers in females' access to high-paid jobs can be detected and quantiffed. We estimate the gender relative probability of getting any given job position for full-time executives aged 40-45 in the private sector. This is done using an exhaustive French administrative dataset on wage bills. Our resu...