Sharp bounds on preferences in extended Roy models under stochastic monotonicity constraints

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 underrepresentation in mathematics intensive fields, and the impact of role models on choices and outcomes.