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 wages in each sector are (jointly) stochastically monotone with respect to an observed selection shifter. The lower bound can also be interpreted as the minimum cost subsidy necessary to change sector choices and make them observationally indistinguishable from choices made under the classical Roy model of sorting on potential wages only. The research is motivated by the analysis of women's choice of university major and their underrepresentation in mathematics intensive fields. With data from a German graduate survey, and using the proportion of women on the STEM faculty at the time of major choice as our selection shifter, we find high costs of choosing the STEM sector for women from the former West Germany, especially for low realized incomes and low proportion of women on the STEM faculty, interpreted as a scarce presence of role models.