We show how instrumental variable and matching estimators can be combined in order to identify a broader array of treatment effects. Instrumental variable (IV) estimators are known to estimate effects only for the compliers, representing a subset of the entire population. By combining IV with matching, we can estimate the treatment effects for the always- and never-takers as well. Since in many cases these groups are the (endogenous) outcome of some assignment process, such estimates also help in judging the implications of such a selection process. In our application to the effects of participation in active labour market programmes in Switzerland, we find large and lasting positive employment effects for the compliers, whereas the effects for the always- and never-participants are small. In addition, the compliers have worse employment outcomes without treatment than those who participate in the programme with or without the intervention under investigation. This suggests that the earlier assignment policy of the caseworkers was inefficient in that the always-participants were neither those unemployed who would experience the highest expected treatment effects nor those unemployed who had the largest need for assistance.