In this paper, I consider identification of treatment effects when
the treatment is endogenous. The use of instrumental variables is a popular
solution to deal with endogeneity, but this may give misleading answers when
the instrument is invalid. I show that when the instrument is invalid due to
correlation with the first stage unobserved heterogeneity, a second (also
possibly invalid) instrument allows to partially identify not only the local
average treatment effect but also the entire potential outcomes distributions
for compliers. I exploit the fact that the distribution of the observed
outcome in each group defined by the treatment and the instrument is a
mixture of the distributions of interest. I write the identified set in the
form of conditional moment inequalities, and provide an easily implementable
inference procedure. Under some (testable) tail restrictions, the potential
outcomes distributions are point-identified for compliers. Finally, I
illustrate my methodology on data from the National Longitudinal Survey of
Young Men to estimate returns to college using college proximity as
(potential) instrument. I find that a college degree increases the average
hourly wage of the compliers by 38-79%.