We derive sharp bounds on the non consumption utility component in an extended Roy model of sector selection. We interpret this non consumption utility component as a compensating wage differential. The bounds are derived under the assumption that potential utilities in each sector are (jointly) stochastically monotone with respect to an observed selection shifter. The research is motivated by the analysis of women's choice of university major, their under representation in mathematics intensive fields, and the impact of role models on choices and outcomes. To illustrate our methodology, we investigate the cost of STEM fields with data from a German graduate survey, and using the mother's education level and the proportion of women on the STEM faculty at the time of major choice as selection shifters.