We show that the Roy model has more precise predictions about the self-selection of migrants than previously realized. The same conditions that have been shown to result in positive or negative selection in terms of expected earnings also imply a stochastic dominance relationship between the earnings distributions of migrants and non-migrants. We use the Danish full population administrative data to test the predictions. We find strong evidence of positive self-selection of emigrants in terms of pre-emigration earnings: the income distribution for the migrants almost stochastically dominates the distribution for the non-migrants. This result is not driven by immigration policies in destination countries. Decomposing the self-selection in total earnings into self-selection in observable characteristics and self-selection in unobservable characteristics reveals that unobserved abilities play the dominant role.