If the coefficient on the self-employment dummy increases along the eamings distribution, this solely reflects that the dispersion that is due to the unobserved determinant is higher among self-employed since the impact of education is picked up by the education dummy. In the CQR example, the size of the two sectors was hardly affected as only one person was assumed to change employment status. Similarly, cross-country differences in earnings inequality can be decomposed into: i) differences in the composition of the population (for example, inequality should be higher in countries with a more unequal distribution of education endowment) and ii) differences in rates of return (for example, inequality should be higher in countries with a larger wage gap between highly- and low-educated workers).