Sharp Bounds on Causal Effects under Sample Selection

In many empirical problems, the evaluation of treatment effects is complicated by sample selection so that the outcome is only observed for a non-random subpopulation. In the absence of instruments and/or tight parametric assumptions, treatment effects are not point identified, but can be bounded under mild restrictions. Previous work on partial identification has primarily focused on the ‘always observed’ (irrespective of the treatment). This article complements those studies by considering further populations, namely the ‘compliers’ (observed only if treated) and the observed population. We derive sharp bounds under various assumptions and provide an empirical application to a school voucher experiment.