Testing for programme effects in a regression discontinuity design with imperfect compliance

The administrators of an office automation training programme in Italy enrolled applicants on the basis of their score in an attitudinal test, with low scoring subjects mandated out of the programme. Some of the applicants who were mandated out resorted to an alternative programme. To identify the effect of the programme by comparing participants with non-participants we need to account properly for both the selection by the score and the contamination of the comparison group by a number of non-complying subjects. The estimand resulting from using the mandated status as an instrumental variable for the actual status identifies the effect of the programme on complying subjects exhibiting a score in the attitudinal test in the neighbourhood of the threshold for selection. Simple nonparametric instrumental variable estimators based on the work of Robinson and Hahn and co-workers reveal that the programme had no effect on the probability of being in work several months after its completion. Simulation results show that in spite of the small sample size the test for the no-impact hypothesis has non-negligible power even at small departures from the null hypothesis. As a side-result Robinson's test turns out to be appreciably more powerful than the other test.