Matching methods for treatment evaluation based on a conditional independence assumption do not balance selective unobserved differences between treated and nontreated. We derive a simple correction term if there is an instrument that shifts the treatment probability to zero in specific cases. Policies with eligibility restrictions, where treatment is impossible if some variable exceeds a certain value, provide a natural application. In an empirical analysis, we exploit the age eligibility restriction in the Swedish Youth Practice subsidized work program for young unemployed, where compliance is imperfect among the young. Adjusting the matching estimator for selectivity changes the results toward making subsidized work detrimental in moving individuals into employment. © 2013 American Statistical Association.