This paper examines changes in the distribution of wages using bounds to allow for the impact of nonrandom selection into work. We show that worst case bounds can be informative. However, because employment rates in the United Kingdom are often low, they are not informative about changes in educational or gender wage differentials. Thus we explore ways to tighten these bounds using restrictions motivated from economic theory. With these assumptions, we find convincing evidence of an increase in inequality within education groups, changes in educational differentials, and increases in the relative wages of women.