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'' (whose outcomes are observed irrespective of the treatment). This paper complements those studies by considering further populations, namely the "compliers'' (whose outcomes are observed if they are treated) and the observed population. We derive sharp bounds under various assumptions (monotonicity and stochastic dominance) and provide an empirical application to a school voucher experiment.