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