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.