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