  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.
