  I analyze treatment effects in situations when agents endogenously select
into the treatment group and into the observed sample. As a theoretical
contribution, I propose pointwise sharp bounds for the marginal treatment
effect (MTE) of interest within the always-observed subpopulation under
monotonicity assumptions. Moreover, I impose an extra mean dominance assumption
to tighten the previous bounds. I further discuss how to identify those bounds
when the support of the propensity score is either continuous or discrete.
Using these results, I estimate bounds for the MTE of the Job Corps Training
Program on hourly wages for the always-employed subpopulation and find that it
is decreasing in the likelihood of attending the program within the
Non-Hispanic group. For example, the Average Treatment Effect on the Treated is
between \$.33 and \$.99 while the Average Treatment Effect on the Untreated is
between \$.71 and \$3.00.
