We estimate the effects of active labour market policies (ALMP) on subsequent employment by nonparametric instrumental variables and matching estimators. Very informativeadministrative Swiss data with detailed regional information are combined with exogenousregional variation in programme participation probabilities, which generate an instrumentwithin well-defined local labour markets. This allows pursuing instrumental variable as well asmatching estimation strategies. A specific combination of those methods identifies a new typeof effect heterogeneity. We find that ALMP increases individual employment probabilities byabout 15% in the short term for unemployed that may be called ‘marginal’ participants. Theeffects seem to be considerably smaller for those unemployed not marginal to theparticipation decision.